IFSM 300 – Class 22
                             April 17, 2002
Preliminaries
      • Assignment 22: homework 5 in this as...
•   Undertaking OR to improve aspects of the supply chain (e.g., transportation,
    manufacturing, distribution, inventor...
•   Better sales and matching of customer needs from greater product
                  variety.
              • Higher war...
In an EPQ model, the replenishment level of inventory R* is not the DL of an
       EOQ model, but rather is (P - D)(T - L...
c – cost per unit produced ($ per unit)
        c0 – cost to set up for one replenishment order ($ per order)
        ch –...
(annual manufacturing cost) = (cost per unit produced)(no. of units produced annually)
                           = c D.

...
minus leadtime) = T – L. The inventory level at that point, which is the reorder point we
seek, is the amount of inventory...
Summary. In summary, the total related cost is

       TC = c D + c0 (D / Q) + ch [1 – (D/P)] (Q / 2).


                 ...
To minimize this cost function, and to reorder at the correct time, we have

       Q* = √ (2 c0 D) / {ch [1 – (D/P)]}

  ...
IBM BREAKTHROUGH IN SUPPLY CHAIN IS KEY TO OR PRIZE

        Fewer Unsold Computers; Over $750 Million Savings

LINTHICUM,...
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Lecture 22

  1. 1. IFSM 300 – Class 22 April 17, 2002 Preliminaries • Assignment 22: homework 5 in this assignment – due Monday, April 22. • Class website reminder: http://www.gl.umbc.edu/~rrobinso/ Economic Production Quantity • Complete notes below. Summary here. • In this refinement, we extend the EOQ idea to address producing to meet demand. • Refer to Producing Office Supplies, situation 14.4, page 699. • Derive the (R*, Q*) policy. • Inventory versus time graph. • Find Q* and R*. • Numerical example. Supply Chain Management • The field called supply chain management is extremely active these days. • When you encounter inventory control in practice, it may well be part of a supply chain management project. We’ll take a quick look therefore at what’s entailed. • What is supply chain management (abbreviated SCM)? • It focuses on the sequence from procurement of raw materials to manufacturing to the delivery of products to customers. It’s a synthesis of purchasing, transportation, manufacturing, warehousing, distribution, and stocking at customer sites, so as to better control total system cost and customer service (for example). • In some applications, total costs were reduced yet responsiveness to customers was increased. • Another name, also popular now, is integrated supply chain management. • OR analysis is one kind of support among several that matter. Others include up-to-date data collection and storage, fast communication between participants, and computerization to speed up information-accessing and decision-making. • What are the analytical methods? • Any of the OR methods might be used, including optimization models, simulation models, and pattern recognition models (for forecasting and data mining, for instance). 1
  2. 2. • Undertaking OR to improve aspects of the supply chain (e.g., transportation, manufacturing, distribution, inventory management) is well established. The crucial new ingredient is the focus on considering the entire system to seek improvement. • The scope may be quite large, therefore. That often leads to application of multiple models, often of different types, in combination. • Decision support systems in supply chain management: • Support three aspects of management – • Strategic management. For example, • Design of the supply chain network (vendors, plants, warehouses). • Tactical management. For example, • Assignment of products to warehouses and manufacturing plants. • Operational management. For example, • Production scheduling, selection of delivery mode, vehicle routing. • Support various types of planning and scheduling, such as -- • Demand planning. For example, • Make better forecasts. • Understand customer buying patterns. • Supply planning and scheduling. For example, • Overall supply chain planning. • Inventory planning. • Distribution planning. • Transportation planning and scheduling. • Manufacturing planning and scheduling. For example, • Production planning and scheduling. • Scheduling and control of purchased and manufactured parts. • Quoting leadtimes to customers. • Some tradeoffs in supply chain management: • Production lot size versus inventory. • Manufacturing economy from large production lot sizes. • Lower inventory investment from smaller inventories. • Inventory versus transportation. • Lower inventory investment from shipping small quantities. • More efficient transportation from shipping large quantities. • Leadtime versus transportation. • Reduced leadtime from more frequent shipment. • Lower transportation cost from less frequent shipment. • Product variety versus inventory and manufacturing. 2
  3. 3. • Better sales and matching of customer needs from greater product variety. • Higher warehousing and transportation costs from greater product variety. • Customer service versus total cost. • Higher cost from greater responsiveness and shorter leadtimes. • The rise of SCM is all around us. • Many organizations in business, government, and the military are establishing departments to concentrate on integrated SCM. • Seminars are being presented. • Recent example right in our own backyard: Workshop on Supply Chain Management co-sponsored by National Institute of Standards and Technology, U. of Maryland Smith School of Business, and the National Science Foundation, April 18-19, 2001. See their website: http://www.mel.nist.gov/msid/conferences/scmpconf.html • Ittoolbox Supply Chain Management website: http://www.supplychain.ittoolbox.com (linked from our class Web site). • Example: IBM Project. • Review press release (copied below). • Review presentation slides. Website at http://www.research.ibm.com/ees/, click on “Click here for details,” click on “Presentation Charts.” In class we will see slides 3, 4, 11, 12, 13, 14, 15, 16, 25, 33, 42, 48, 49. Millionaire Q1 The economic production quantity (EPQ) model in the book differs from the plain EOQ model primarily because an EPQ model contemplates: A. Producing so as to fill backorders. B.Purchasing from an external producer. C. Producing so as to replenish inventory exactly when inventory level reaches zero. D. Producing so as to replenish inventory gradually. (!!) Millionaire Q2 In the EPQ model, when production is active, the inventory level is: A. Decreasing at rate P – D. B. Decreasing at rate P + D. C. Increasing at rate P – D. (!!) D. Increasing at rate P + D. Millionaire Q3 3
  4. 4. In an EPQ model, the replenishment level of inventory R* is not the DL of an EOQ model, but rather is (P - D)(T - L), when the leadtime L extends back from the end of the cycle to: A. The inventory stage. B. The production stage. (!!) C. Either the inventory or production stage. D. None of the above. Millionaire Q4 The following is NOT a sufficient description of supply chain management: A. Managing all supplies throughout the organization. (!!) B. Managing the sequence from procurement to manufacturing to delivery of products. C. Management to plan, source, make, and deliver products. D. Synthesis of purchasing, transportation, manufacturing, distribution, and warehousing. Millionaire Q5 The different kinds of modern support for supply chain management do NOT ordinarily include: A. Up-to-date data collection and storage. B. Dynamic pricing. (!!) C. Fast communication between participants. D. OR analysis. Millionaire Q6 Modern supply chain management differs from what was done before primarily in that modern SCM: A. Uses the Internet. B. Includes faster communication. C. Tries to optimize over the entire system. (!!) D. Is mostly a new buzzword. Notes: Inventory Management Economic Production Quantity Concept. The economic production quantity (EPQ) model is another refinement of the original EOQ model. In this case we make two key assumptions: (1) an order Q goes to our own manufacturing facility, rather than to an outside supplier, and (2) items we produce are moved immediately into inventory, rather than arriving in inventory in one total replenishment delivery of size Q. Notation. For the EPQ model our notation is: 4
  5. 5. c – cost per unit produced ($ per unit) c0 – cost to set up for one replenishment order ($ per order) ch – annual cost of holding one item in inventory ($ per year) D – annual rate of demand for units (units per year) P – annual rate of production of units (units per year) Q – quantity of units produced in one production run (units) L – lead time to begin a production run (years) R – reorder point: inventory level at which we start setting up a new production run (units) t – cycle time when in production (years) T – total cycle time: the time between production start-ups (years) TC – total cost related to inventory decisions ($ per year). Inventory-Versus-Time Graph. Production starts just as inventory reaches zero. We produce at the rate P, greater than the rate D at which inventory is drawn down by demand. Because produced units move immediately into inventory, the inventory builds up during production at the rate P – D. Once production stops, the inventory declines at rate D. The maximum inventory level, reached when we stop production, is (P –D) t where t is the time of production. But P t = Q, so t = Q/P. Therefore the maximum inventory level is (P – D)(Q/P) = [(P – D)/P] Q = [1 – (D/P)] Q. Total Related Cost. The general method of minimizing total related cost TC applies here. The applicable costs are similar to those for the EOQ but different in that procurement cost is replaced by manufacturing cost and ordering cost is replaced by setup cost: TC = (manufacturing cost) + (setup cost) + (holding cost). As we did for EOQ, we assume that over the year we produce an amount that meets demand exactly: 5
  6. 6. (annual manufacturing cost) = (cost per unit produced)(no. of units produced annually) = c D. If we need D units in a year and we produce Q at a time, the number of production set- ups is D / Q. So: (annual setup cost) = (cost per setup)(number of setups annually) = c0 (D / Q). Again, as in the EOQ and shortage models, we calculate the annual holding cost to be the annual cost of holding one unit in inventory times the average number of units held. And again we assume no partial cycles, so the average number held in a cycle is the average number held in a year. With a sawtooth inventory pattern, as we encountered in the EOQ model, although a different sawtooth pattern in this case, the average inventory level in a cycle is half the maximum level: (annual holding cost) = (annual holding cost per unit)(average inventory level) = ch [1 – (D/P)] (Q / 2). Minimizing the Total Related Cost. For the EPQ model, therefore, we have total cost: TC = c D + c0 (D / Q) + ch [1 – (D/P)] (Q / 2). Compare this with the total cost in an EOQ model: TC = c D + c0 (D / Q) + ch (Q / 2). This comparison suggests that Q* of the EPQ differs from Q* of the EOQ only in that ch is replaced by ch [1 – (D/P)], which is the case: Q* = √ (2 c0 D) / {ch [1 – (D/P)]}. Reorder Point. The best reorder point R* differs depending upon whether allowing leadtime requires reordering action in the inventory stage or production stage. If the leadtime L is short, so that we can allow for it starting in the inventory stage, the situation is the same as in the EOQ model and thus R* is (demand over leadtime) = DL. If, on the other hand, leadtime L is long enough to require reordering action while still in the production stage, the concept of demand over leadtime stays the same but the expression for R* is different. The simplest way to derive R* now is to recognize that inventory is accumulating in this production stage. If leadtime L remains, then the time elapsed so far is: (total cycle time 6
  7. 7. minus leadtime) = T – L. The inventory level at that point, which is the reorder point we seek, is the amount of inventory accumulated so far: R* = (rate of inventory accumulation)(time elapsed so far) = (P – D)(T – L). We can tell into which stage the leadtime L takes us by comparing the time elapsed so far (T – L) with the time interval of production (t). If leadtime L brings us all the way back into the production stage, T – L < t. But if leadtime L brings us only into the inventory stage, T – L > t. 7
  8. 8. Summary. In summary, the total related cost is TC = c D + c0 (D / Q) + ch [1 – (D/P)] (Q / 2). 8
  9. 9. To minimize this cost function, and to reorder at the correct time, we have Q* = √ (2 c0 D) / {ch [1 – (D/P)]} (P – D)(T – L) if (T – L) < t R* = where T = Q* / D and t = Q* / P. DL if (T – L) > t Numerical Example. The data for an example are: c – $0.40 per unit produced c0 – $5.40 per setup ch – $0.072 annually per unit in inventory D – 81,000 units demanded per year P – 202,500 units produced per year L – 3 days / 250 working days per year = 0.012 years. From these numbers, we compute: Q* = √ (2 c0 D) / {ch [1 – (D/P)]} = √ (2)(5.40)(81,000) / {(0.072) [1 – (81,000 / 202,500)]} = √ 874,800 / 0.0432 = √ 20,250,000 = 4,500 units in a production run. T = Q* / D = 4,500 / 81,000 = 0.05555… years. t = Q* / P = 4,500 / 202,500 = 0.02222… years. T – L = 0.05555 – 0.012 = 0.043555… years. Since T – L > t, the leadtime is in the inventory stage and therefore R* = D L = (81,000)(0.012) = 972 units remaining in inventory. TC = c D + c0 (D / Q) + ch [1 – (D/P)] (Q / 2) = (0.40)(81,000) + (5.40)(81,000 / 4,500) + (0.072)[1 – (81,000 / 202,500)](4,500 / 2) = 32,400 + 97.20 + 97.20 = $32,594.40 per year. Summary Table in the Book. Again, the formulas in table 14.7, page 711, differ somewhat from our notation. In the table: R is our R* Times T, L, and t are in days. 9
  10. 10. IBM BREAKTHROUGH IN SUPPLY CHAIN IS KEY TO OR PRIZE Fewer Unsold Computers; Over $750 Million Savings LINTHICUM, MID, May 17, 1999 - IBM's success at reengineering its supply chain was a key factor in its selection as winner of the 1999 Franz Edelman Award for Achievement in Operations Research and the Management Sciences in Cincinnati earlier this month. The company's reengineering efforts resulted in over $750 million in savings in 1998, the company reports. The Institute for Operations Research and the Management Sciences (INFORMS) presented the award for a study entitled "Extended Enterprise Supply Chain Management at IBM Personal Systems Group and Other Divisions." Keeping Up With Changing Market IBM developed the Asset Management Tool (AMT), an advanced supply chain optimization and simulation tool, as part of its reengineering effort. IBM made a commitment to reengineering in 1993 to keep up with rapid technology changes that Have seen PC prices drop and the average shelf life of PC's decline from 12-18 months in 1990 to 4-6 months in 1998. Shortened product life cycles for computers and components can result in as much as a 100% loss due to scrapping of unsold, obsolete inventory, the company says. Increased competition and a decline in the demand for mainframe computers motivated the reengineering drive. In making its commitment to reengineering, IBM faced the challenge of streamlining one of the most complex corporate supply chains in the world. Range of Uses AMT has been used in a number of IBM units as well as in other businesses, like the food industry, notably by Tesco, the largest food retailer in Great Britain. AMT addresses a wide range of logistics and business topics, including inventory and customer service level target, supply network configuration, supplier terms and conditions, lead time reduction, fulfillment policies, forecast accuracy, and supply-chain scenario analysis. The implementation of AMT resulted in substantial business benefits, most notably in IBM Personal Systems Group. AMT helped IBM Personal Systems Group reduce its channel inventory from over three months to just one month. As a direct consequence the division reduced its 1998 price protection expenses by over $100 million. The Personal Systems Group reduced its end-to-end inventory from 4 1/2 months to less than 2 months by the end of 1998. This helped IBM realize additional savings on product cost of an additional $650 million. AMT also contributed to IBM’s overall reengineering achievements of an over 50% turn improvement and a 55% cycle time reduction. AMT integrates simulation, animation, graphical process modeling, analytical performance optimization, and activity-based costing into an Internet-enabled system that allows quantitative analysis of extended supply chains. Presentation slides: Website at http://www.research.ibm.com/ees/, click on “click here for details,” click on “Presentation Slides.” In class we will see slides 3, 4, 11, 12, 13, 14, 15, 16, 25, 33, 42, 48, 49. 10

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