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Health Care Supply Chain Analytics
An analysis of Plexxus hospital consumption data to identify
opportunities for supply chain efficiencies and savings
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Peter (Yinan) Zhang
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Table of Content
Executive Summary 4
Introduction 5
Background 6
1.1 Challenges & Solutions 6
1.2 Access to Data 7
1.3 Supply Side Data 7
1.4 Demand Side Data 8
1.5 Data-mining & Forecasting 8
Literature Review: Group Purchasing Organization 9
2.1 Supply Chain Cost Reduction 9
2.2 Key Issue in Healthcare Supply Chain — Standardization 9
2.3 Virtual Centralization of the Healthcare Supply Chain 10
2.4 Supply Chain Management Integration and Implementation 12
2.5 Supply Chain Management Integration 12
2.6 Supply Chain Management Implementation 14
2.7 IT in the Management of Healthcare Supply Chain — RFID 14
2.8 Making Business Sense 15
Literature Review: Ontario Healthcare Funding Reform 16
3.1 Healthcare Funding Reform and its Impact on UHN 16
3.2 Health System Funding Reform (HSFR) 16
3.3 Health Based Allocation Model (HBAM) 17
3.4 Service Component 18
3.5 Unit Cost Component 19
3.6 Getting to Hospital Expected Expenses 22
3.7 Quality Based Procedures (QBP) 23
Statistical Methods & Data Analysis 24
4.1 Data Collection 24
4.2 Data Cleaning 24
4.3 Data Subsection 26

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4.4 Top 10 Purchased Items 26
4.5 Individual Item Purchasing Pattern 27
4.6 Daily Number of Transactions 29
4.7 Linear Regression between Daily Number of Transactions and Daily Net Value 31
4.8 Testing Assumptions of Linear Regression Model 35
4.9 Forecasting and Prediction 37
Application & Implication 39
5.1 Benchmarking 39
5.2 Forecasting Demand 39
5.4 Implication for UHN 40
Conclusion & Further Research 41
Reference 42
Appendix A 44

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Executive Summary
The Ontario Health System Funding Reform (HSFR) ushered in a completely new system in
which to allocate funds to Ontario hospitals. Unlike before, hospitals have to analyze and justify
the cost associated with health service provided. Plexxus is a group purchasing organization for
Ontario hospitals, and the organization wants to find a way to identify tangible and realizable
hospitals savings for the hospitals it serves.
!The Health Based Allocation Model (HBAM) under HSFR is most relevant to the goal of
Plexxus. HBAM represent 40% of total hospital funding, and it does not tie in with clinical
outcomes. Expected service multiplied by expected unit cost per service determines expected
funding for a hospital. Since Expected service level is determined by the Ministry of Health,
hospitals can only control the expected unit cost component. Moreover, two major components
of unit cost per service are overhead cost and medical supply cost, but overhead cost is difficult
to negotiate, therefore focusing on medical supply cost is most appropriate for finding savings
opportunity.
!For this research paper, data collected from Plexxus are sub-sectioned into only gloves category
due to its ease of calculation and the commodity nature. This research is focused on one of the
Plexxus hospital organizations, University Health Network (UHN) which is one of the largest
and most complex hospital organizations in Ontario and perhaps all of Canada. Cyclicality is
observed in both the daily number of transactions processed by Plexxus, and the daily net value
($ CAD). There is close similarity between the movement of daily net value and the number of
transactions. A linear regression model containing daily net value as the dependent variable, and
daily number of transactions is created. R2 is 0.92, indicating a high statistical relationship. The
linear equation: Expected Daily Number of Transaction = e-1.5012 + 0.65826±0.02256 * log (Daily Net Value)
can be used to estimate the output variable.
!This equation can be used as a benchmarking tool for Plexxus to determine transaction
processing efficiency of Plexxus, and facilitate forecast of the number of transactions. The latter
application can aid UHN in controlling transaction cost associated with commodity products
such as gloves.

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Introduction
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This report is the continuation of the 2013 research supported by Plexxus regarding healthcare
supply chain analytic. In addition, University Health Network (UHN) representatives are
involved with this study, and requested a contextual study on the healthcare supply chain
efficiency within their hospitals.
The purpose of this study is to “identify tangible and realizable hospital savings for a sample of
items used by UHN”, and “successfully test and document a repeatable process that Plexxus can
provide as a part of its value proposition” (Edmison, Mouradov, Popescu & Sulatycki, 2014).
Several recommendations issued from the 2013 research indicated that data quality, data sources,
data consistency, and data attributes are major challenges for Plexxus. In addition, analytic
technologies are limited to Excel Pivot Tables and tools from the Plexxus SAP system (Edmison,
Mouradov, Popescu & Sulatycki, 2014). However, these challenges are ameliorated as of today,
and further statistical and quantitative approach could be applied on the issue of healthcare
supply chain efficiency.
Building on the proof-of-concept effort in the original research, this report focuses on the
financial implication of supply chain efficiency on hospital finance (i.e. the Health System
Funding Reform), various statistical and quantitative methods (e.g. linear regression, time series
forecasting) suitable for the task at hand, and final recommendations and statistical models built.
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Background
1.1 Challenges & Solutions
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On January 2012, Ontario Ministry of Health and Long-Term Care introduced the Health System
Fund- ing Reform (HSFR), which replaced the current global funding system that is based on
historic costs of hospitals. The HSFR intends to replace 70% of the global funding with Quality-
Based Procedures (QBP), and Health Based Allocation Model (HBAM), which represent 30%,
40% of the total funding respectively (MOHLTC, 2014).
These unforeseen changes in the way hospitals in Ontario are being funded had placed enormous
pressure on the management team to adapt their current financial and operating plans. These
changes in funding will also likely to have a lasting impact on how budget control and
organizational process will be planned in the future.
The key for hospitals to accommodate this significant funding change is the ability to analyze
and forecast supply and demand of healthcare services, and be able to have a quantitative way of
managing cost associated with satisfying the demand, given limited resources.
Given appropriate data, we can model the relationship between demand and supply using
regression analysis and decision tree analysis; in the sense that given existing services UHN
provide (demand), and the existing resources (supply), the management team can anticipate the
resources needed. This provides tangible savings for UHN since over-staffing and/or excess
inventories could be avoided.
As for Plexxus, UHN's resource-need estimate would inform product purchasing and negotiation,
resulting in more informed and methodical purchasing procedures. Moreover, provided that
Plexxus had to manage the purchases for multiple hospitals, optimal product mix could prove
challenging, since product standardization process maybe arduous, and the amount of products
and hospital needs are different. This could be solved by adapting linear optimization algorithm,
which minimizes total cost of purchase given the constrains and requirement of different hospital
budgets and needs.

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Before delving into the details of our literature review and methodology, we have to evaluate the
feasibility of obtaining appropriate data from UNH and Plexxus.
1.2 Access to Data
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We categorized our data needs into supply-side and demand-side. The analogy being drawn here
is that, one can view the healthcare sector as a vibrant economic system, with its own supplies
and demands. The demand side represents the multifarious health needs of our citizens, and the
supply side represents the ability and capacity of hospitals to meet those needs.
By using the supply and demand analogy, we can align this research to the HSFR guideline,
which aims to bring supply and demand into equilibrium (MOHLTC, 2014). Moreover, our
search for data can be streamlined, and our findings could be placed within the context of
hospital funding system.
1.3 Supply Side Data
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Supply side data refer to any data involved in providing healthcare services (e.g. gloves, nurses),
and clinical metrics. These data pertain any quantitative information from the ERP system of
Plexxus (i.e.SAP), reporting database of UHN (e.g. Discharge Abstract Database, National
Ambulatory Care Reporting System), and any relevant data from UHN's electronic health
records.
For example, Plexxus has the purchasing data of hospital commodity products such as gloves, IV
solutions; UHN maintains records of overhead costs, and patient discharge data. In addition,
certain internal hospital performance metrics such as patient turn-over rate, hospital-related
infection rate, and average waiting time, also prove to be reliable source of data.
Supply side data are linked to HSFR, and the individual investigation in the supply side will
prove invaluable to the Health Based Allocation Model (HBAM) section of HSFR, which
requires hospitals to provide “utilization estimates and multi-year forecasts by program, detailed
analysis of resource use, including profile of highest use population providers’ costs and

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expenses, including detailed information on hospitals’ unit cost variance for each of its care
types.” (MOHLTC, 2014)
1.4 Demand Side Data
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Demand side data comes from UHN, Statistics Canada, and Ontario Ministry of Health and
Long-Term Care. These data include metadata of patient diagnosis groups, population growth,
and census information.
Under HBAM, a number of publicly available inputs (e.g. expected population growth, health
care access pattern, etc.) are used to predict how many services each hospitals are expected to
provide in a given year, and what should be the cost benchmark for each service rendered (Born
& Dhalla, 2012).
1.5 Data-mining & Forecasting
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Having identified reliable source of data, there are two objectives to be achieved. For UHN,
forecasting and modelling will be conducted using decision-tree model, and regression analysis.
For Plexxus, product mix optimization will be calculated using linear optimization algorithm.
An example of forecasting and modelling for UHN is as follows. It can hypothesized that there is
a causal relationship between glove and alcohol swab utilization rate and hospital-related
infection rate, controlling for patient diagnosis and condition. Statistical test will tell us whether
this relationship holds true or not. If there is indeed a causal relationship, adjustment of input
variables (e.g. the type of gloves used, or the frequency of alcohol swabs used) will change the
output variable (i.e. the rate of hospital-related infection rate).
Using Plexxus' data, linear optimization allow us to find the product mix that minimizes total
cost. For instance, given the constant costs of gloves, and different purchase portfolio and
budgets for these gloves by different hospitals, we can satisfy both conditions by solving for the
amount of gloves that should be purchased for each category of gloves.
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Literature Review: Group Purchasing Organization
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2.1 Supply Chain Cost Reduction
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Many models exist within the healthcare supply chain, such as simple supplier to contractor
relationship, group purchasing organizations, and consolidated service centre (Vries & Huijsman,
2011). The cost saving opportunity for hospitals relies on the selection of appropriate model, and
an understanding of the processes of supply chain management. This literature review
encompasses: a) key issue in healthcare supply chain; b) virtual integration of the healthcare
supply chain; c) theories of supply chain management integration and implementation; d) IT
application example and potential in the healthcare supply chain; e) the business case for
healthcare supply chain integration.
2.2 Key Issue in Healthcare Supply Chain — Standardization
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Standardization of healthcare supplies reduces costs by increasing bargaining power of hospitals,
reducing time and efforts needed to negotiate and re-negotiate contracts, and improving health
outcome of patients. Many ills and inefficiencies in the supply chain can also be greatly
diminished ( McKone, Sweek, Hamilton & Willis, 2005).
Other than providing updated infrastructure and equipments, healthcare supply chain for
commodity products such as gloves and surgical sutures provides hospitals with an untapped
source of financial saving (Roark, 2005). In the primary and tertiary healthcare setting, the
typical supply budget represent 25% to 30% of the operating cost. This budget is largely
determined by physician preferences other than budgetary considerations, therefore, cost
reduction efforts and benchmarking prove difficult (Roark, 2005).
One of the cause for this conundrum is because regular frontline professionals are not normally
trained in business processes. They also believed that maximum availability of medical supplies
is crucial to the lives of their patients, therefore sacrificing patient safety due to cost
consideration is unacceptable (Rahimnia & Moghadasian, 2010). Group purchasing

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organizations (GPO) such as Plexxus are critical gatekeepers and have the bargaining power to
ensure supply chain efficiency.
GPOs negotiate contracts and manage supplier relationships, they are responsible for obtaining
optimal price for the hospitals (Vries & Huijsman, 2011). Hospitals, in turn, still have to
purchase in bulk in order to maintain the con- tract price obtained by GPOs (Brennan, 1998).
However, such contract arrangement may lock hospitals into position as commodity prices drop,
and such purchasing flexibility may reduce the adoption of new innovations (Roark, 2005).
Moreover, anti-trust and price manipulation allegations had been concerns regarding GPOs, and
both the U.S. and Canadian government have regulations concerning the quantity and total
purchase from GPOs (Roark, 2005).
Shipping and delivery represent a large portion of the overall spending, since hospitals use
thousands of types and brands of medical equipments. In addition, the projection of the demand
of equipments is difficult to measure, therefore leading to supply chain inefficiencies (Roark,
2005). In a way, it is the method of negotiating contract and managing logistics that determine
the saving opportunities, less so to do with the actual benchmarking. Standardization of
equipments, on the other hand, provide the area of greatest savings. Many industries have
realized reduction of cost by removing the “transactions costs” between switching between
standard (Brennan, 1998; Vries & Huijsman, 2011).
Other than cost saving, standardization can sometimes improve patient outcome. For instance, by
standardizing pressure ulcer dressings, there is noticeable reduction in the incidence of
nosocomial pressure-ulcers (Roark, 2005). In the case of healthcare related supplies, such
approach will be deemed appropriate first in the regional level, municipal level, and eventually
national level. The following section provides frameworks on how to create a GPO-like supply
chain structure to foster standardization, and circumvent the problems discussed above.
2.3 Virtual Centralization of the Healthcare Supply Chain
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While diagnostic and treatment breakthrough are constantly evolving, the delivery method of
healthcare through the three tiers (primary, secondary, tertiary) of healthcare has been relatively

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stable for decades (Parker & DeLay, 2008). Following similar trend, medical supplies also
enjoyed tremendous improvement regarding their safety, ease-of-use, and efficacy. Nevertheless,
the supply chain structure of medical supplies had remained the same (Parker & DeLay, 2008).
One way of improving the supply chain structure is through using virtually centralized supply
chain management. A prominent example of this is a consolidated service centre (CSC).
Differing from the group purchasing organizations (GPO) discussed in the previous section, CSC
is not only focused with contracting, procurement and customer services, but also distribution
(Parker & De- Lay, 2008). Other benefits of CSC include:
• Networking opportunities for participating hospitals, sharing best practices, and products
experiences.
• Exceptional pricing and order accuracy, and lowered operation expenses associated with
individual supply chain management.
• Encourage standardization and volume aggregation, thus reducing inventory, lower
distribution costs, and reduce transportation costs.
• Provide medium to small sized facilities with the benefit of bargaining power previously
enjoyed only by large hospitals.
• Freeing management attention towards clinical quality instead of budgeting by
outsourcing supply chain to CSC (Parker & DeLay, 2008).
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There are several steps to take in order to form a CSC from the ground: “partner with other
regional hospitals, standardize products, foster a spirit of cooperative competition, leverage
partnerships, centralize material management, share consulting resources, and elevate materials
management leadership.” (Parker & DeLay, 2008). The salient points are hospital partnerships,
standardization, and leveraged partnership.
Hospital Partnerships: hospitals from proximal geographical locations should form regional
CSCs (Parker & DeLay, 2008). The resulting aggregation of purchasing power will not only
secure optimal prices from suppliers, but also establish consistent relationship with those

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suppliers. In addition, as demands fluctuate, supplies can be swapped between partners for better
inventory control (Brennan, 1998). Such CSCs can also be sub-specialized according to
specialty, for instance, family physicians within the same city could form a CSC to request for
items commonly used in that setting.
Standardization: commodity products such as gloves, dressings, and sutures should be
standardized to secure maximized purchasing bulk. The identification and categorization of
commodity products should be done collaboratively, and the final decision of the selection of
products should be based on evidence (e.g. peer reviewed journals). Other specialized, high-price
physician items such as generic medications, imagining devices should be the second priority of
standardization (Vries & Huijsman, 2011). The end goal of standardization is to reduce the
number of suppliers thus increasing bargaining power and complexity of contracts. Even in the
case that standardization does not take place, the process of sharing evidence will stir the CSC
towards commonality of choice (Parker & DeLay, 2008).
Leveraged partnership: some hospitals may have dealings with other supply chain partners other
than GPOs, such as distributors, and progressive suppliers. Hospitals should leverage the
knowledge and experience of these partners (Parker & DeLay, 2008). However, there would be
difficulties in this endeavour due to conflict of interests, as CSC would exert greater pressure on
existing suppliers or terminate existing unfavourable contracts.
2.4 Supply Chain Management Integration and Implementation
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With the framework of CSC in mind, the next hurdle lies in how to integrate existing supply
chain divi- sions of hospitals into a CSC. A comprehensive literature review has been done by
Damien Power (2005) at the University of Melbourne to address this issue.
2.5 Supply Chain Management Integration
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The three elementary components of integrated supply chain are information systems, inventory
management, and supply chain relationships (Power, 2005). The basis of integration can be
defined by “co- operation, collaboration, information sharing, trust, partnerships, shared

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technology and a fundamental shift away from managing individual functional process, to
managing integrated chains of processes” (Power, 2005, p. 253).
Information System: Information flow between organizations are driven by both hardware and
software technology. Examples of hardware technology include telephone, fax machines, etc.,
and software technology are represented by tabulation software (Excel) and enterprise resource
planning (ERP) software (Lee, Lee & Schniederjans, 2011). These information technologies
reduce the complexity of communication and provide details and comparison between
organizations (Power, 2005). Miscommunication can break the basis of integration such as trust,
and collaboration. Other more practical impacts of asynchronous IT are: excessive inventories,
untimely planning, and increased logistical costs (Power, 2005).
Physical logistics: having an integrated supply chain means that organizations can have
accelerated response rate of market demand, and at the same time holding on to minimum level
of inventory. This reduced cycle in supply chain often translate business advantages (Power,
2005). IT again comes into the fore as the most important factor that determines the success of
improved logistics. Physical distribution centres depend on IT to optimize best in-bound, out-
bound routings. IT also provides a way of benchmarking suppliers, and allows CSC to decide
which suppliers to keep or drop.
Partnerships, alliances and cooperation: supply chain analysis and a clear identification of
common interests between parties are essential to align the objectives of organizational partners
(Power, 2005). Upper management attentions are needed to ensure full-cooperation. Before the
full fledging of CSC, trust can be developed directly through negotiations and stakeholder
meetings, and in directly through commitments in smaller purchases. One of the challenges of
partnerships is when “the benefits ‘pool’ with some members at the detriment of others” (Power,
2005, p. 257). However, in the case of CSC, hospitals’ interests converge towards cost-reduction,
and the “benefits pool” of the hospitals and of suppliers are mutually exclusive.
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2.6 Supply Chain Management Implementation
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Key criterion of supply chain management implementation are suitable selection of IT, and the
use of “third-party providers for both transportation and information management” (Power, 2005,
p. 258). A successful implementation example in a European company elucidate seven critical
success factors that are applicable for CSC (Power, 2005, p. 258):
1. a committed organization, from the board down;
2. effective programme management;
3. consistent, pre-emptive communications;
4. positive action to identify and manage key risks before they become issues;
5. a well-defined and managed programme baseline, changed as necessary;
6. a succession of manageable delivery millstones to maintain momentum and confidence;
7. an actionable, owned, manageable and measurable set of business benefits.
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CSC will rely heavily on the selection and deployment of appropriate IT, the next section discuss
the usage of radio frequency identification devices (RFID) in the healthcare supply chain.
2.7 IT in the Management of Healthcare Supply Chain — RFID
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Radio frequency identification devices (RFID) are electronic signal senders embedded into or in
close proximity of a product or shipment (Kumar, Swanson & Tran, 2008). They can track the
location of product which in turn can improve information passed onto supply chain managers,
thus benchmarking and optimizing supply chain efficiency (Smith & Flanegin, 2004). Three
ingredients are essential for CSC to provide the cost saving it purports: prices, logistic efficiency.
CSC already provides a platform to track pricing, RFID can control for logistic efficiency.
Kumar, Swanson & Tran (2008) studied the cost benefit analysis of applying RFID in the
healthcare supply chain setting. They found that the benefits of RFID are invaluable, such as
“reduced time, effort, and patient deaths” (p. 78). However, the cost of implementing RFID at
this stage surpasses the value it generates. Even so, outsourcing RFID management to a three-

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party, for example Amazon, could potentially solve the cost consideration. We can see that the
fruition of CSC relies on IT, physical logistics, and partnerships.
2.8 Making Business Sense
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What ties everything together is whether a business case exists in improving healthcare supply
chain efficiency (Brennan, 1998). Economic savings, economic investment, and noneconomic
factors should be included in the CSC proposal.
Economic savings: economic benefits are not necessarily related to cash flow, it could be savings
that are gained from reductions of inefficiencies. A financial assessment should be conducted,
and specific cost savings and assumptions should be clarified (Brennan, 1998). Scenario analysis
needs to be included to indicate the time-sensitivity of proposed plan. If operational changes are
proposed, the scenario analysis should reflect the impact of these changes on anticipated returns
(Brennan, 1998).
Economic Investment: the proposal should include forecasting of capital and personnel
investments required to fully or partially implement CSC. Transactions costs, such as relocation
fees, travelling, train- ing, and organizing costs should be fore-sought (Brennan, 1998).
Non-economic factors: CSC’s impacts on existing supplier relationship, management shortages,
change managements, should be evaluated. It is important to note that hospitals are non-for-profit
organizations, and non-economic benefits should be quantified and distributed among frontline
healthcare professionals (Brennan, 1998).
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Literature Review: Ontario Healthcare Funding Reform
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3.1 Healthcare Funding Reform and its Impact on UHN
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The Health System Funding Reform (HSFR) is the driving force behind the need for this report,
and the funding formula and rationale are essential to the replicability of this research finding to
other hospitals. HSFR will be discussed in detail in the following section.
3.2 Health System Funding Reform (HSFR)
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Ontario's healthcare system is shifting towards a patient-based funding system instead of a global
one, and the HSFR is implemented in 2012 by the Ontario Ministry of Health and Long-term
Care (MOHLTC) in order to fulfill the requirement set by the Excellent Care for All Act passed
in 2010. This entails that HSFR will eventually account for 70% of the total funding provided to
hospitals, and the remaining 30% will still be rationed out on a global basis (MOHLTC, 2014).
Traditionally, each hospital’s fund allocation is determined by historical spending patterns,
inflation, and one-off negotiations between hospital executives and civil servants (MOHLTC,
2014). Even though this global funding provides stable budget for hospitals, it does not provide
financial incentives for those hospitals to increase efficiency. In addition, some hospitals have
been more successful at negotiating with unions than others, and critics of global budgeting
argue that these negotiations lead to some hospitals receiving more than their fair share of
resources. (Born & Dhalla, 2012; Sutherland, 2011).
HSFR's patient-based funding takes measures to provide more equitable and evidence-based
fund allocation by taking into consideration population metrics, numbers of patients actually
served, evidence-based quality of service and population needs (MOHLTC, 2014).
HSFR contains two components: Health Based Allocation Model (HBAM), and Quality-Based
Procedures (QBP), each dealing with funding equality and evidence-based practice issues. The
current funding allocation has not reached the proposed proportion yet, as only certain items on
QBP had been implemented. Figure 1 illustrates the present breakdown of HSFR (MOHLTC,
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3.3 Health Based Allocation Model (HBAM)
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HBAM represents 40% of total funding sanctioned by HSFR, and its purpose is to provide an
evidence-based, and health based funding formula. HBAM estimates hospital's future expenses
based on a Service Component and a Unit Cost Component (MOHLTC, 2014).
The Service Component estimates the amount of market share a hospital has among the total
health service providers (HSP). The Unit Cost Component calculates expected unit cost for
hospitals based on regression equations specific to each hospital and modules. The total
Expected Expenses is derived from the product of the Service Component and the Unit Cost
Component. Then the total Expected Expenses for one hospital is divided by total Provincial
Expected Expenses to determine HBAM Expected Share represented as a percentage. This
percentage is then multiplied to the actual provincial healthcare funding to derive the finally
funds allocation to each hospitals (MOHLTC, 2014). The relationship of the formula is shown
below:
Service Component * Unit Cost Component=HSP HBAM Expected Expense
HSP HBAM Expected Expense/ Total Provincial HBAM Expected Expenses= HBAM Expected
! Share HBAM Expected Share * MOHLTC funding = Actual funding to individual HSP
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Moreover, HBAM has five modules of clinical areas which only three are fully in effect
(discounting HBAM for Community Care Access Centres, which handles community health and
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Full Implementation
HBAM
Global
FundingQBP
CurrentR
g HBAM Global
Funding
QBP
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Figure 1. Current HBAM distribution (left), target HBAM distribution (right)

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home care). These modules are: acute inpatient & day surgery, complex continuing care,
emergency department, inpatient rehabilitation, and inpatient mental health (MOHLTC, 2014).
In the case that expected funding is insufficient or that HBAM cannot model HSP’s true expense,
mitigation strategy and special provisions for technical insufficiency will be in situ. The final
released funds are allocated from MOHLTC to the Local Health Integration Network (LHIN)
which subsequently get passed on to HSP (MOHLTC, 2014).
3.4 Service Component
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The Service Component includes four stages, and it estimates the approximate marketshare of
HSP based on population and census information. This is to ensure that HSP’s services and
capacity are adjusted to the demand of the population (MOHLTC, 2014). For instance, if the
prevalent condition in the Milton region is mostly cardiac related, extra X-ray machines and
technicians for the Milton General Hospital would be considered wastage.
HBAM collects data from HSP and databases such as Discharge Abstract Database, National
Ambulatory Care Reporting Systems, and Ontario Cost Distribution Methodology. This
information is used to inform the Person Profile, Expected Weighted cases, Growth Adjustment,
and HSP Market Share stages of the Service Component (MOHLTC, 2014).
Person Profile is consists of all hospital services received by a person that are covered by OHIP,
and that person’s socioeconomic status extrapolated from census data. An aggregate of Person
Profiles from a HSP is then categorized into Modelled Expected Weighted Cases and Non-
Modelled Actual Weighted Cases (MOHLTC, 2014).
Modelled Expected Weighted Cases are common ailments and expected services provided for
those ailments. The details of the models are not disclosed publicly but the variables used are
disclosed: age & gender, socio-economic census, and rurality (MOHLTC, 2014).
If a patient has indigestion and sought out treatment, his/her visit for this specific condition will
be compared to others’ with the same condition (thus called “modelled”), and the average time
and resource that are dedicated to this indigestion are assigned to this his/her “case” without
consideration of the actual time and resources spent. The assumption here is that the variation of

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costs eventually cancel each other out because these modelled cases are so numerous that
statistically, it makes sense to take the average without fixation on individual cases.
Non-Modelled Actual Weighed Cases are special services that may or may not be provided for a
unique population, and they do not represent typical Ontario cases. These cases can not be
modelled either due to low frequency or complexity. Organ transplant, Aboriginal health, and
neonatal patients are such examples (MOHLTC, 2014).
Non-Modelled cases and Modelled cases are combined for for a case mix, which in turn
undergoes Growth Adjustment. HBAM uses publicly available predictions of population
parameters such as demographical shifts, immigration, and emigration, to calibrate the forecast
for case mix (since HBAM is concerned with future budget). The lowest rank of such population
data is based on regional census data collected by Statistics Canada, and at this level, census
divisions match with corresponding LHIN operational boundaries, so that population projections
reflect concise health needs of census population (MOHLTC, 2014). On top of that, in order to
account for patients seeking health service outside of their census area, Growth Adjustment will
take the patients census data from their most recent residence and augment to the case mix
(MOHLTC, 2014).
The last stage in the Service Component of HBAM is calculating HSP Market Share. All Ontario
HSPs’ expected weighted cases (Non-modelled cases plus Modelled cases) will be calculated
using the previous three stages (with the exception of Inpatient Mental Health and Complex
Continuing Care), however, individual HSP’s expected weighted cases are subject to change
(MOHLTC, 2014).
3.5 Unit Cost Component
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The Service Component measures expected units of services delivered by HSP, and the Unit Cost
Component estimates the unit costs that correspond to the expected units of services.
Specifically, HBAM uses linear regression to find HSP’s expected unit costs, which measures the
relationship between multiple changing variables (MOHLTC, 2014). However, linear regression
does not differentiate between clinical setting and specific cost variables of HSPs. Therefore, cost

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modifiers are applied to different clinical settings (i.e. modules) in order to recognize HSP
characteristics.
Since the detailed linear regression formulae are not publicly released, several hypotheses will be
given here as plausible methodologies of the linear regression formulae used.
1) Total costs of all hospitals in Ontario are normalized by total services provided by HSPs.
2) Cost variables are separated by LHINs, and total costs of all hospitals are normalized by total
services provided by HSPs in one LHIN.
3) Individual HSP’s historical costs are analyzed, and the resulting formulae discounts cost
abnormalities.
Hypothesis 1 over-generalizes cost factors to a provincial level that are not useful in informing
distinctive cost structures of HSPs, population clinical needs, nor geographical differences.
Hypothesis 3 does not deviate too much from the previous global funding system, and it
discounts the fact that there are similarity between HSPs and possible benchmarking of
reasonable cost levels. Hypothesis 2 is the most likely scenario since it combines the benefits
from both hypothesis 1 and 3, while mitigating their deficiencies.
14 Local Health Integration Networks (LHINs) are created by MOHLTC in 2006, and their
purpose is to plan, integrate and fund HSPs (LHIN, 2014). LHINs work closely with local HSPs
and communities, and they ensure the correct coordination of HSPs to deliver optimal tax-dollar
values. They study the healthcare needs, trends and best practices. LHINs also negotiated with
HSPs regarding the services HSPs provide, and the terms and conditions are reinforced through
formal and legal agreements. By segmenting HSPs costs using LHINs, regional health needs are
well defined and controlled for, and HSPs are expected to justify their costs according to those
regional health needs (MOHLTC, 2014). A linear regression based on hypothesis 2 is shown
below:
!

21. Page !21
∑ Cost of HSPs from Toronto Central LHIN = ⍺ * services provided in Acute Inpatient & Day
Surgery + ß * services provided in Emergency Department + … + ei
⍺ = expected total cost of Acute Inpatient & Day Surgery
ß = expected total cost of Emergency Department
Expected Unit Cost of Acute Inpatient & Day Surgery = Total cost of Acute Inpatient & Day
Surgery / Total services provided in Inpatient & Day Surgery
Within the regression model, there will be other variables that are statistically significant in
explaining the total cost of HSPs, and these variables are the Cost Modifiers. For example, taking
into consideration the number of medical interns and the rurality of the HSP, the unit cost of the
emergency department of a small rural HSP will be higher compared to that of an inner city ER
department. There are five Cost Modifiers that are either activate or deactivated across five
modules of HBAM (MOHLTC, 2014) (Figure 2).
!
The formula that demonstrates the Cost Modifiers are as follows:
Module Teaching Rural
Geography
Economy of
Scale (size)
Specialized
Services
HSP type
Acute Inpatient
& Day Surgery
✓ ✓ ✓
ER ✓
Complex
Continuing
Care (CCC)
✓ ✓ ✓
Inpatient
Rehabilitation
✓ ✓ ✓
Mental Health ✓ ✓ ✓
Figure 2. Cost Modifiers for 5 HBAM modules

22. Page !22
∑ Cost of HSPs from Toronto Central LHIN = ⍺ * services provided in Acute Inpatient & Day
Surgery + ß * services provided in Emergency Department + ∂ * number of interns + µ *
number of employee + π * population density of the LHIN + … + ei
⍺ = expected total cost of Acute Inpatient & Day Surgery
ß = expected total cost of Emergency Department
∂ = Cost Modifier for teaching HSPs
µ = Cost Modifier for Economy of Scale
π = Cost Modifier for Rural Geography
In conclusion, there are five Expected Unit Costs for each HBAM module, and they are adjusted
by Cost Modifiers. For the year of 2012, Expected Unit Costs do not apply to small HSPs and
Mental Health module, and HBAM Expected Unit Cost equals to the actual unit cost (MOHLTC,
2014).
3.6 Getting to Hospital Expected Expenses
!
With the Expected Service and Expected Unit Cost estimated for five HBAM modules, a final
HBAM Expected Cost is calculated (MOHLTC, 2014).
For each of the five modules of HBAM, there are five HBAM Expected Costs. Actual service
provided and cost of the CCC and Inpatient Mental Health modules are used instead of the
Expected Service and Expected Unit Costs. This is due to HBAM’s inability to estimate the costs
correctly within a acceptable margin of error (MOHLTC, 2014). Non-HBAM Expenses are costs
associated with out patient clinic or expected growth in service capacity. Five HBAM Expected
Costs plus Non-HBAM Expenses equals HBAM Overall Hospital Expected Expenses. Each
individual HSP will have a HBAM Expected Share calculated based on HBAM Overall Hospital
Expected Expenses (MOHLTC, 2014).
HBAM Expected Share (%) = HSP HBAM Expected Expense / Total Provincial HBAM Expected
Expenses

23. Page !23
HBAM Expected Share is represented as a percentage point, and HSP’s Expected Share times
the actual funding allocated by MOHLTC equals to the final dollar amount individual HSP will
receive.
Final dollar amount = HBAM Expected Share * MOHLTC funding
This process is done to ensure that, were there any universal changes in the case models or
readjustment to the inputs of the Service Component or Unit Cost formulae, there will be no
need to recalculate HBAM Overall Hospital Expected Expenses (MOHLTC, 2014).
3.7 Quality Based Procedures (QBP)
!
QBP have similar funding structure as HBAM where the Expected Service for clinical
procedures, such as cataract surgery, times the Expected Unit Cost equals to the expected
funding HSP will receive. QBP concerns with clinical outcome and evidence based practice, and
not medical products, therefore detailed information will not be provided here.
!
!
!
!
!
!
!
!
!
!

24. Page !24
Statistical Methods & Data Analysis
4.1 Data Collection
!
Data from the Plexxus supply chain ERP (SAP) regarding purchasing orders were collected by
the researcher, and the data span from April 2013 to April 2014. The SAP data were converted
into spreadsheet format for Microsoft Excel program, and the final Excel file contains 20
variables, and 629692 observations. Figure 3 represents an example of one of these observations.
!
4.2 Data Cleaning
!
Certain variables are either not useful or distracting for the purpose of cost analysis. For
example, SAP Material refers back to the original location of the data extracted, and this piece of
information is not needed unless a double-checking of data-quality is required. Therefore the
researcher decided to only contain meaningful quantitative data such as PO Quantity, and
relevant categorical variables such as Recipient/Department Name.
Figure 3. One observation of purchase order from Plexxus
Purchasing
Document
Company Code Document Type Document Type
Description
Created On
1000000000 1000 XC Ad-hoc STO to DC 2013-04-01
Vendor Vender Name Purchasing Group Currency Line Item
1000000 Hospital Admin. PLX CAD 10000
Key Account
Assignment
SAP Material Material
Description
Plant
400000000000000 K 333333 TIP BULB Suction 1000
Material Group Material Group
Description
Vendor Material
Number
Manufacturer Part
Number
PO Quantity
24444444 Medsrug General D00000M D11111M 50
Order Unit Net Price Per Order Price Unit Net Value
EA 22.22 1 BX 13444
Currency Cost Centre Recipient Recipient/
Department Name
Reference: !
Contract
CAD 10000000 11BB4-Unit ICU DCCWXT2304
Vendor Vender Name Purchasing Group Currency Line Item
1000000 Hospital Admin. PLX CAD 10000
Reference: Contract line item Reference: Purchasing Info Record
34442 42235

25. Page !25
There are also redundant variables in the dataset, for example, Currency appears three times in
the data set. Interchangeable variables, such as Material Group and Material Group Descriptions,
also encumber data analysis. The redundant and interchangeable variables are also removed from
the original dataset, resulting in 10 variables shown in figure 4 .
Four currencies are used for purchasing purposes by Plexxus: Canadian Dollar, Euro, British
Pound, and U.S. Dollar. 98% of all transactions are done using the Canadian Dollar, and 2.2%
are done via U.S. Dollar. There are only three transactions through Euro and British Pound, and
the total net value of these transactions are only $ 2,254 CAD out of $700 million. Due to the
insignificant share of other currencies, the researcher converted USD, EUR and GBP in to CAD
using July, 2014 conversion rate.
Data inconsistencies exist around Net Price and Net Value in the dataset. The formula for
calculating Net Value is PO Quantity times Net Price. However, for certain observations, this
formula does not hold. On closer inspection, two main issues arise: Net Price conversion units
inconsistency, and Order Unit variations.
Most observations use dollar as a base unit, but a minority uses cents. This unit base error is
corrected by applying Original Price/10 formula to affected observations. Also, there are five
Order Units: BX, CA, EA, PK, PR, (i.e box, case, each, package, pair) and the Net Price/Order
Unit calculation is different for PR. This is corrected by applying Original Price*0.005 to the
affected observations. Finally, Net Value is checked by using the Adjusted Net Price times PO
Quantity, and IF formula in Excel.
!
Created On Currency Material
Description
PO Quantity Order Unit
2014-05-30 CAD Glove Procedure S 40 BX
Net Price Per Order Price Unit Net Value Recipient/
Department Name
30 1 BX 1200 Medicine
Figure 4. Cleaned observation of purchase order from Plexxus

26. Page !26
4.3 Data Subsection
!
The scope of this research is only concerned with commodity products, which are specifically
IV products, gloves, and sutures & staples. These products are consistent with the 2013
research. However, the only analysis that will be presented in this report focuses on the gloves
category.
4.4 Top 10 Purchased Items
!
There are 57 different types of gloves being purchased and the total net value is $455,307.76
(CAD). The top 10 types of gloves represent 60% of the total spending, one out of the ten is
surgical glove and the rest being examination gloves (Figure 5).
!
The average amount spent on individual glove type is $7,717, and the range starts from $68.2 for
GLOVE WORK COTTON, to $36,046 for GLOVE EXAM CURAD TEXTURED PF SMALL.
!$36,046.30!! !$36,005.90!!
!$32,063.19!!
!$30,072.55!!
!$28,338.13!!
!$24,989.35!!
!$23,237.82!!
!$22,482.60!!
!$20,557.56!!
!$19,017.67!!
!$/!!!!
!$5,000.00!!
!$10,000.00!!
!$15,000.00!!
!$20,000.00!!
!$25,000.00!!
!$30,000.00!!
!$35,000.00!!
!$40,000.00!!
GLOVE!EXAM!
CURAD!
TEXTURED!PF!
SMALL!!!!!!!
GLOVE!SURG!
DERMAPRENE!
PF!SZ!6!!!!!!!!!!!!
GLOVE!EXAM!
NIT!FGRTXT!
PF!SNSCRICE!
BLU!M!!
GLOVE!EXAM!
NITRL!TXT!PF!
LF!CURAD!BLU!!
M!!
GLOVE!EXAM!
CURAD!
TEXTURED!PF!
MEDIUM!!!!!!
GLOVE!EXAM!
NITRL!TXT!PF!
LF!CURAD!BLU!!
L!!
GLOVE!EXAM!
NITRL!TXT!PF!
LF!CURAD!BLU!!
S!!
GLOVE!
NITRILE!EXAM!
PURPLE!MED!
BX100!!!!!!
GLOVE!EXAM!
NIT!FGRTXT!
PF!SNSCRICE!
BLU!L!!
GLOVE!EXAM!
SYN!STRETCH!
PFREE!UNIV!
3G!M!!!
Figure 5. Top 10 items in terms of total net value

27. Page !27
The quartiles are: Q1 $483, Q2 $2,225, Q3 11,368 (Figure 6). The box-
plot shows that purchasing amount varies the least below median at
$2,252. This means that below the median, the Net Value differences
between each glove types are small. For instance, GLOVE EXAM
NITRILE PF MFLX XCEED BLU S with a annual net value of $978 only
has 1 dollar difference to the item next to it, while $2,500 more GLOVE
EXAM CURAD TEXTURED PF MEDIUM are purchased compared to
the item below it.
Glove types beyond the upper whisker represent really far-lying values that
are not expected from the rest of the data. However, in this case,
those data points are of interest, since outlier values often lead to
intriguing explanations. On top of that, these data represent high
value purchases, therefore any potential findings for cost reduction will lead to greater total
dollar saved compared to that for lesser net value items. The top 10 items in terms of total net
value will be analyzed in the next sections.
4.5 Individual Item Purchasing Pattern
!
The daily net values of each item are plotted against time, and two types of purchasing patterns
are observed. The first type of pattern is cyclical. Figure 7 is a typical time series graph for the
!
!
!
0
10000
20000
30000
NetValue($CAD)
!$#!!!!
!$200.00!!
!$400.00!!
!$600.00!!
!$800.00!!
!$1,000.00!!
!$1,200.00!!
!$1,400.00!!
2013#04#01!
2013#04#08!
2013#04#15!
2013#04#23!
2013#05#01!
2013#05#10!
2013#05#17!
2013#05#27!
2013#06#03!
2013#06#11!
2013#06#19!
2013#06#26!
2013#07#04!
2013#07#11!
2013#07#19!
2013#07#30!
2013#08#08!
2013#08#16!
2013#08#26!
2013#09#04!
2013#09#11!
2013#09#18!
2013#09#26!
2013#10#07!
2013#10#15!
2013#10#24!
2013#11#01!
2013#11#08!
2013#11#15!
2013#11#22!
2013#12#02!
2013#12#11!
2013#12#19!
2013#12#30!
2014#01#09!
2014#01#17!
2014#01#24!
2014#01#31!
2014#02#07!
2014#02#18!
2014#02#27!
2014#03#06!
2014#03#14!
2014#03#24!
GLOVE&EXAM&CURAD&TEXTURED&PF&SMALL&(Total&Net&Value&$36,046.30)&
&
Figure 6. Box-plot of Net Value
Figure 7.
Purchasing
pattern for one
of the top
purchased items
in terms of net
value

28. Page !28
top 10 purchased items, and there are regular intervals where the daily net value rises an falls.
This can be explained by the fact that as gloves are being depleted, automatic orders will be
make from the hospital to Plexxus.
The second type of purchase pattern is associated with average infrequent purchases combined
with the few large purchases (figure 8). This is likely associated with stockpiling practices
common in certain department (e.g. specimen procurement) or attributable to unpredictable
events (e.g. flu immunization).
!
!
!
!
!
!
!
!
!
!
!
!
!
!$#!!!!
!$2,000.00!!
!$4,000.00!!
!$6,000.00!!
!$8,000.00!!
!$10,000.00!!
!$12,000.00!!
2013#04#03!
2013#04#19!
2013#04#24!
2013#05#06!
2013#05#13!
2013#05#22!
2013#05#27!
2013#05#31!
2013#06#06!
2013#06#17!
2013#06#21!
2013#06#26!
2013#07#12!
2013#07#19!
2013#07#25!
2013#08#07!
2013#08#12!
2013#08#20!
2013#08#30!
2013#09#06!
2013#09#10!
2013#10#01!
2013#10#08!
2013#10#11!
2013#10#22!
2013#11#05!
2013#11#07!
2013#11#20!
2013#11#25!
2013#12#02!
2013#12#09!
2013#12#17!
2014#01#07!
2014#01#15!
2014#01#21!
2014#02#03!
2014#02#18!
2014#02#21!
2014#03#07!
2014#03#12!
2014#03#27!
GLOVE&EXAM&NIT&FGRTXT&PF&SNSCRICE&BLU&L&&(Total&Net&Value&$&
$20557.56)&
&
Figure 8. Purchasing pattern for one of the top purchased items in terms of net value

29. Page !29
4.6 Daily Number of Transactions
!
The daily number of transactions is defined as the number of items being purchased disregarding
ordering quantity and price. There are no extreme values, and the maximum number of orders
placed in a given day is 55 (Figure 9).
One thing to note is that there is a pattern of cyclicality presenting in frequency of purchases.
Figure 10 shows a three-weeks segment from the figure above.
!
!
!
!
!
0"
10"
20"
30"
40"
50"
60"
2013)04)01"
2013)04)08"
2013)04)15"
2013)04)22"
2013)04)29"
2013)05)06"
2013)05)13"
2013)05)21"
2013)05)28"
2013)06)04"
2013)06)11"
2013)06)17"
2013)06)24"
2013)07)03"
2013)07)10"
2013)07)17"
2013)07)24"
2013)07)31"
2013)08)07"
2013)08)14"
2013)08)21"
2013)08)28"
2013)09)05"
2013)09)12"
2013)09)19"
2013)09)26"
2013)10)03"
2013)10)10"
2013)10)18"
2013)10)24"
2013)10)31"
2013)11)08"
2013)11)15"
2013)11)21"
2013)11)29"
2013)12)06"
2013)12)13"
2013)12)20"
2013)12)30"
2014)01)07"
2014)01)14"
2014)01)21"
2014)01)28"
2014)02)04"
2014)02)11"
2014)02)19"
2014)02)26"
2014)03)05"
2014)03)13"
2014)03)20"
2014)03)28"
Number'of'transac/on'
0"
10"
20"
30"
40"
50"
60"
Mon" Tue" Wed" Thu" Fri" Sat" Mon" Tue" Wed" Thu" Fri" Sat" Mon" Tue" Wed" Thu" Fri" Sat" Mon" Tue" Wed"
Number'of'transac/on'
Figure 9. Daily number of transactions over time
Figure 10. Three-weeks segment of daily number of transactions

30. Page !30
The purchase amount is at minimum on Mondays, increases over the week and decreases close to
Saturday. Plexxus does not open for operation on Sundays.
Figure 11 is taken from the same three-weeks segment, however net value is being measured
here. The same cyclicality pattern is also observed. This figure also ensures that unit price
differences between items do not confound daily net value.
In fact, another insight is gained from comparing the two graphs: the daily net value can predict
the daily number of transaction, not knowing which item and how many are sold that day.
Despite the different measuring units, the direction, shape, and magnitude of the curves share
close resemblance. Also, there should be no relationship between the number of transactions and
net value, since there are multiple items/price being order per day and the exact quantity per item
is not given in the two graphs. Lastly, on an “eye-ball” inspection on the product mix and PO
quantity, there are no regularity of the types of products nor PO quantity to be found. In sum, all
these considerations point to the direction that two unrelated variables correlate somehow, and
the statistical tests of this relationship is given below.
!
!$#!!!!
!$500.00!!
!$1,000.00!!
!$1,500.00!!
!$2,000.00!!
!$2,500.00!!
!$3,000.00!!
!$3,500.00!!
!$4,000.00!!
Mon! Tue! Wed! Thu! Fri! Sat! Mon! Tue! Wed! Thu! Fri! Sat! Mon! Tue! Wed! Thu! Fri! Sat! Mon! Tue! Wed!
Net$Value$
Figure 11. Three-weeks segment of daily net value

31. Page !31
4.7 Linear Regression between Daily Number of Transactions and Daily Net Value
!
Two columns of data, one represents the number of transactions, the other total net value, are put
in the statistical software R! for further processing. Linear regression method is used, since there
seemed to be a simple linear relationship between number of transactions and net value.
Figure 12 is the box-plots for our two variables, and there are seven outliers in Net Value, and
one in Number of Transactions. Theses outliers may affect the outcome of linear model since the
goodness of fit R2 is heavily influenced by outliers.
!
!
!
!
!
!
!
!
Figure 13 shows the two scatterplots with or without these outliers. Two analyses are done in the
following sections with and without the removal of outliers.
In addition, the shape of the scatterplots is funnel like, indicating that data transformation using
logarithms is warranted. Logarithm will improve the linearity of data since it reduces the
variance of data due to the difference between unit of measurements. For example, when
comparing one variable that is measured in billions of dollar, and the other variable that is
0
10000
20000
30000
Net.Value
0
20
40
Number.of.Transaction
Figure 12. Box-plots for Daily Net Value (left), and Daily Number of Transactions

32. Page !32
measured in thousands of dollars, logarithm will with enable you to find the order of magnitudes
(e.g. the exponent of 102), which downplays the absolute differences in measurement.
0
1000
2000
3000
4000
0 20 40
Number of Transaction
NetValue
1
2
3
0.0 0.5 1.0 1.5
Log(Freqency of transtions)
log(Netvalue)
0
10000
20000
30000
0 20 40
Number of Transactions
NetValue
1
2
3
4
0.0 0.5 1.0 1.5
log(Number of Transactions)
log(NetValue)
Figure 13. Scatter-plots of Daily Net Value verses Daily Number of Transactions. Outliers removed
(left), outliers not removed (right)
Figure 14. Scatter-plots of log Daily Net Value verses log Daily Number of Transactions. Outliers
removed (left), outliers not removed (right)

33. Page !33
Figure 14 shows the scatterplots of two datasets, the one on the left with the removal of outliers,
and the one on the right without the removal of outliers, in logarithmic terms. Even though the
scatterplot on the right still shows outliers, however, the degree to which it affects the rest of the
data is diminished greatly.
There are two linear regression models processed in the statistical software R — one model
removed outliers, the other did not. The resulting two linear equations are:
1) log(Daily Number of Transactions)= -1.50120 + 0.65826*log(Daily Net Value)
p-value<2e-16; R2 = 0.92; modified R2= 0.927699422 (Outliers removed)
2) log(Number of Transactions)= -1.64738 + 0.64654*log(Net Value)
p-value<2e-16; R2 = 0.88; modified R2= 0.928497103 (Outliers included)
Both p-values are <2e-16, which are significant, meaning that our model results are not obtained
based on chance. However, it is the R2 value that tells us the the goodness of fit of our model, in
other words, how much of the change in net value is explained by change in number of
transactions. R2 values are 0.92 and 0.88, which means 92% (or 88%) of the change in net value
can be attributed to change in number of transactions to the respective models.
However, we are dealing with log-log models, and the resulting R2 values does not express the
true measurement of change in net value, since the the interpretation of log-log models result in
measurement in elasticity (i.e. the % change in one value verses the % change in the other). The
ultimate method of deriving a true R2 value in log-log model is to take the log(Net Value)
outcome and manually calculate R2 (Shazam,1995).
The equation for R2 is:
!
In practice, the Number of Transaction actual value is put in the equation 1) and 2), for example:

34. Page !34
log(Daily Number of Transactions)= -1.50120 + 0.65826*log(Daily Net Value)
Daily Net Value = 399
log(Daily Number of Transactions)= -1.50120 + 0.65826*log(399)
log(Daily Number of Transactions) = 2.4413
Daily Number of Transactions = e2.4413
Expected Daily Number of Transactions ≈ 11
After obtaining Expected Net Value for all the input variable of Number of Transactions, the
following calculations are carried out:
∑i (Expected Daily Number of Transactions - Mean of Actual Daily Number of Transactions)2 =
SSregression
∑i (Actual Daily Number of Transactions - Mean of Actual Daily Number of Transactions)2 =
SStotal
R2 = SSregression / SStotal
The modified R2 value for equation 1), the model with outliers removed, is 0.9276; the modified
R2 value for equation 2), the model without outliers removed, is 0.9254. Model 1 (with outliers
removed) is preferable, since the original R2 is identical with modified R2 value, hence more
reliable. Model 1 is also less computationally demanding, because the above transformation from
log to actual value can be discarded.
The final formula to derive Daily Number of Transaction, given Daily Net Value is:
!
Expected Daily Number of Transaction = e-1.5012 + 0.65826±0.02256 * log (Daily Net Value)
!

35. Page !35
4.8 Testing Assumptions of Linear Regression Model
!
Before accepting our model, four factors regarding the assumptions of linear regression model
have to be considered: linearity, independence of the errors (free from autoregression),
homoscedasticity, and normality of error distribution (Duke University, 2014).
In order to check linearity, the scatterplot from
previous section is used (figure 15).
After log transformation, it can be observed that
the observations fits symmetrically around the
diagonal regression line, indicating linearity
between the two variables.
Linear regression should also be free of
autoregression. Autoregression is a problem
frequently encountered when analyzing time-
series data, where today’s value is correlated
with yesterday’s value. Two additional tests
were completed to rule out this problem.
In the first test, a time sequence indicator (dummy variable) is introduced, which indicate the
order of the two variables (figure 16). Then Time is used as an additional independent variable
beside Number of Transactions in order to predict Net Value. If autoregression exists, then Time
would be a statistically significant variable. The p-value of Time is 0.613, indicating that Time is
not a related variable.
1
2
3
0.0 0.5 1.0 1.5
Log(Freqency of transtions)
log(Netvalue)
Time Net
Value
Number
of
Transac3ons
1 399.15 10
2 995.97 28
Figure 15. Scatter-plots of log Daily Net Value
verses log Daily Number of Transactions.
Figure 16. Example of creating a dummy variable
(Time) to test autoregression

36. Page !36
Another more established test is the Durbin-Watson (DW) test which measures the possible
correlation in predictor errors from a regression analysis. A DW test of 2 means that there is no
autoregression, while a DW > 2 indicates a negative correlation, and DW < 2 points to a positive
correlation(Jank, 2011). An associated p-value measures the validity of DW test. The results
shows that DW = 2.0432 and p-value = 0.6464. Even though there is a finding of slight negative
correlation in the predictor errors, but p-value is not statistically significant. In conclusion, after
running the two tests above we are sure that autocorrelation is not present in our model.
Homoscedasticity is the condition where
all random variables in the sequence or
vector have the same finite variance.
Series violation of this condition will
result in over-estimation of R2 value.
Homoscedasticity is tested by plotting the
residuals versus fitted values (predicted
values). The residuals in figure 17 did not
get larger (i.e., more spread-out) as a a
function of the predicted value. In other
words, the variables have similar variance
(distance from the circle in the figure to
the line).
The violation of normality of the error distribution assumption in linear regression means that the
estimation of coefficients and the calculation of confidence intervals are violated. Since the least
squared method for determining line of best fit is based on minimization of squared error, if there
are large outliers in the error distribution, those numbers will disproportionally influence the line
of best fit (Duke University, 2014).
1.5 2.0 2.5 3.0 3.5
0.0020.0100.0500.2001.0005.000
Spread-Level Plot for
RegModel.1
Fitted Values
AbsoluteStudentizedResiduals
Figure 17. Residuals from the linear regression
plotted against predicted value.

37. Page !37
Visually, a Q-Q plot will inform us of the normality of error distribution. Figure 18 shows that
our model error distribution is not perfectly randomly distributed (a randomly distributed error
will show up as a straight diagonal-line).
However, we should still assume normality of
error distribution, since the error distribution is
only skewed on the high value end, which
means there are high-value outliers affecting
the linear regression, but the existence of these
outliers are already acknowledged and justified
for in previous section.
The four assumptions of linear regression are
satisfied, therefore the validity of the our model
is assured.
4.9 Forecasting and Prediction
!
Regression analysis alone cannot guarantee the predictive ability of the linear equation, since
historical data cannot be used to forecast without a major assumption that future data will lie in
the same parameter as historical data (Williams, 2011). This means that although forecast can be
generated using historical data, but the utility and validity of the forecast can be cast in to doubt
if the conditions of the historical data are violated in the future. For instance, a cyclical pattern is
observed in the sales of gasoline, and a forecast was created based on this pattern. If the macro-
economical condition changes in the future, the forecast will not stand.
One method of circumventing this problem is to randomly segment historical data into three
partitions: training, validation, and testing (Williams, 2011). The training partition will generate
the linear equation, and validation and testing partitions are used as future data to affirm the
forecast ability of the linear equation. This method does not completely eliminate the uncertainty
-3 -2 -1 0 1 2 3
-2-101234
QQ Plot
t Quantiles
StudentizedResiduals(RegModel.3)
Figure 18. QQ plot of the error distribution.

38. Page !38
of future data parameter. However, it is the best method available to simulate a future-like
condition, compared to strictly using historical data (Williams, 2011).
The dataset for gloves is randomly
partitioned by the ratio 70:15:15 (for
training, validation, and testing
respectively) in the program Rattle.
Figure 19 displays the relationship
between predicted (y-axis) and observed
values (x-axis). Predicted values are
generated using linear equation derived
from the training partition, while
observed values are taken from the
testing partition. The dotted blue line is a
hypothetical equation if perfect
correlation exist between the observed
and predicted values (i.e. the linear
equation perfectly predicts future data). Another
linear equation is calculated based on the position of predicted and observed values using
ordinary least squares method, presented by the solid blue line.
Visually, the more resemblance there are between the two lines, the stronger the predictive power
of the linear equation have. Numerically, the predictive strength of the new linear equation is
described by pseudo-R2 . Pseudo-R2 is the value which measure the correlation between the
predicted and observed values, and the closer this value is to 1, the better the linear equation
predicts the data in testing partition (Williams, 2011). Pseudo-R2 equals to 0.9392 in this case,
and it is a sign that the linear equation derived from the training partition has close to perfect
accuracy in predicting the log of Daily Net Value/Daily Number of Transactions. The linear
equation derived from the training partition is virtually identical compared to the equation
derived in previous section.
1.0 1.5 2.0 2.5 3.0 3.5
1.52.02.53.03.5
Log.Net.Value
Predicted
Linear Fit to Points
Predicted=Observed
Pseudo R-square=0.9392
Predicted vs. Observed
Linear Model
Model data.xlsx [test]
Rattle 2014-Jul-25 05:51:03 peterzhang
Figure 19. Scatter-plot between predicted value and
observed values.

39. Page !39
Application & Implication
!
There are two major applications of the linear equation: benchmarking efficiency of Plexxus, and
facilitating forecast of demand. Furthermore, the latter application can aid UHN in controlling
transaction cost associated with commodity products such as gloves.
5.1 Benchmarking
!
The strong statistical relationship between daily net value and daily number of transactions can
act as a formula to benchmark Plexxus’ efficiency in dealing with daily transactions. Daily
number of transactions can be viewed as a performance metric for the ability of Plexxus to
handle hospital requests. In addition, the daily number of transactions does not specify the type
and quantity of gloves being processed, therefore Plexxus does not need to worry about the
variability of those two factors.
For instance, given a certain amount of daily net value, Plexxus can derive the expected daily
number of transactions. When the observed number of transactions for that day deviates
significantly from expected number of transactions, Plexxus gains the information that the
normal performance level is not being reached, and can investigate further of the cause of such
deviation.
5.2 Forecasting Demand
!
The available daily net value data shows cyclicality
on a weekly basis, and this pattern can be used for
forecasting by the Holt-Winters seasonal method
(Athanasopoulos & Hyndman, 2014). The blue line
in figure 20 shows the rough forecast of daily net
values for two weeks ahead, and the grey area
represent 95% confidence interval of the forecast.
Under the condition in which the relationship
Forecasts from HoltWinters
5 10 15
01000200030004000
Figure 20. Time series forecast using Holt Winters
method.

40. Page !40
between daily number of transactions and net value is unknown, a separate forecast has to be
conducted and fine-tuned. However, only one set of forecast need to be made, and the values can
be transformed between the two variables.
The forecasted daily number of transactions is a forecasted demand for Plexxus, and Plexxus can
plan and optimize its resources based on forecasted demand. For example, if the average quantity
(e.g. boxes) per transaction can be calculated, and the average cost per quantity (e.g.
transportation, handling, processing fees) can also be known, then the forecasted number of
transactions times the average quantity per transaction, times the average cost per quantity will
give Plexxus a forecast of the daily cost per day based on demand. To further illustrate, consider
the example:
Average quantity per transaction= 10 boxes
Average cost per box = $100
Forecasted number of transactions = 10
Forecasted daily transaction cost = 10 * $100 * 10 = $10,000
Similar forecasting of daily transaction cost can be applied with UHN data when more UHN
specific information becomes available.
5.4 Implication for UHN
!
Recalling from previous discussion of HBAM, Expected Unit Costs is the only variable UHN
can affect since Expected Services are determined by the government. Expected Unit Costs
includes overhead expenses and medical supply costs. Overhead expenses are difficult to
negotiate due to union presence (Born & Dhalla, 2012), therefore medical supply costs is one
area UHN could find savings opportunity.
The demand of specialty medical supplies, such as prosthetics, is hard to forecast due to its
irregularities, leaving the forecast of commodity products demand/associated costs in the

41. Page !41
forefront. Moreover, Plexxus already achieved significant purchasing power to ensure optimal
pricing for commodity products, as a result, only the forecast of associated costs of commodity
products would be useful. Therefore, when negotiating with LHIN on the topic of Expected Unit
Costs, being able to control transaction cost of commodity products will prove to be valuable.
Conclusion & Further Research
!
Descriptive statistics and analyses of glove purchasing data are given in this report based on
purchasing order data from Plexxus. A linear regression equation between the daily number of
transactions and daily net value of transactions is found and validated, which can be used for
benchmarking and forecasting purpose. However supply side data from UHN and the Ministry of
Health could not be obtained to this date. A more comprehensive analysis using these additional
data is warranted, and tangible cost savings and a repeatable process would be identified.
Only linear regression method is used in this report, and additional forecasting and data-mining
methods would bring us closer to the goal of this research of finding cost saving opportunity for
UHN. Decision-tree and neural network techniques can be used to evaluate commodity
consumption rate related to clinical outcome; time-series analysis such as autoregressive
integrated moving average model (ARIMA) and Hold-Winter seasonal method could be
conducted on both patient turn-over rate and expected admissions; multi-variate regression and
logit regression can be used on categorical variables.
Immense opportunities are available for applying data-mining techniques to hospital related data.
Discoveries of hidden relationships between variables and applying the relationship to the
finance of hospitals would be the future of healthcare analytics.
!
!
!
!

42. Page !42
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