Major Challenges
* Keeping in touch with each person responsible for major activities
* Managing 100000 fans entering the venue
* The bottleneck in tasks with a longer duration
* Overshooting of costs
* Resignations of any of the key managers
Major Challenges
* Keeping in touch with each person responsible for major activities
* Managing 100000 fans entering the venue
* The bottleneck in tasks with a longer duration
* Overshooting of costs
* Resignations of any of the key managers
A solution for the HBR case study, We Googled You. The hiring firm Hathaway Jones, seems to face a problem as they seem to have found a perfect candidate for solving their problems, but land in a fix when some unpleasant news is digged up by the HR regarding her past. WHat should they do?
In August 2000, P&G introduced one of its kind product Crest Whitestrips, readily available online and through dentist offices
P&G claims that the new products are 10 times more effective than the Colgate Tartar Control Whitening Within two years P&G captured more than 80% of the share market. Colgate made a come back in August 2002 with Simply White. Colgate’s USP was that it focused on convenience and lower price. One month after introduction Simply White captures half the market with Crest Whitestrips losing 50% of its market share.
ASW Publishing, Inc. a small publisher of college textbooks, must make a decision regarding which books to
publish next year. The books under consideration are listed in the following table, along with the projected threeyear
sales
expected from
each book
Investment Strategy Case Analysis (MGT 3050)Afifah Nabilah
A case study of the J.D Williams Investment Strategy Problem. This is an assignment for IIUM students who took Decision Science (MGT 3050) in Semester 2, 2014/2015.
A solution for the HBR case study, We Googled You. The hiring firm Hathaway Jones, seems to face a problem as they seem to have found a perfect candidate for solving their problems, but land in a fix when some unpleasant news is digged up by the HR regarding her past. WHat should they do?
In August 2000, P&G introduced one of its kind product Crest Whitestrips, readily available online and through dentist offices
P&G claims that the new products are 10 times more effective than the Colgate Tartar Control Whitening Within two years P&G captured more than 80% of the share market. Colgate made a come back in August 2002 with Simply White. Colgate’s USP was that it focused on convenience and lower price. One month after introduction Simply White captures half the market with Crest Whitestrips losing 50% of its market share.
ASW Publishing, Inc. a small publisher of college textbooks, must make a decision regarding which books to
publish next year. The books under consideration are listed in the following table, along with the projected threeyear
sales
expected from
each book
Investment Strategy Case Analysis (MGT 3050)Afifah Nabilah
A case study of the J.D Williams Investment Strategy Problem. This is an assignment for IIUM students who took Decision Science (MGT 3050) in Semester 2, 2014/2015.
Steel building Graded Unit Civil Engineering Project HND Project Glasgow Kel...Tehmas Saeed
This was my second Graded unit Project, it involved construction of Steel framed Office building, based on HND modules we were advised to devise solution of Steel building which two areas of specialisation in which I chose Sustainability and Frame Structure. This assignment does not have drawings and calculations unfortunately i have lost them, however their is a copy at Former Stow College now Glasgow Kelvin college so students can access from there. For any structural help, I would strongly advise to meet Mr Murdo a very competent lecturer in Kelvin college.
Although its rough guide, we were not heavily using journals at that stage, as we relied mostly on our course material. However some of the Green material which i used was taken from companies publications.
Crude-Oil Blend Scheduling Optimization: An Application with Multi-Million D...Alkis Vazacopoulos
The economic and operability benefits associated with better crude-oil blend scheduling are numerous and significant. The crude-oils that arrive at the oil-refinery to be processed into the various refined-oils must be carefully handled and mixed before they are charged to the atmospheric and vacuum distillation unit or pipestill. The intent of this article is to highlight the importance and details of optimizing the scheduling of an oil-refinery’s crude-oil feedstocks from the receipt to the charging of the pipestills.
Distillation Blending and Cutpoint Temperature Optimization in Scheduling Ope...Brenno Menezes
In oil refinery manufacturing, final products such as fuels, lubricants and petrochemicals are produced from crude-oil in process units considering their operations in coordination with tanks, pipelines, blenders, etc. In this process, the full range of hydrocarbon components (crude-oil) is transformed (separated, reacted, blended) into smaller boiling-point temperature ranges resulting in intermediate and final products, in which planning, scheduling and real-time optimization using distillation curves of the streams can be used to effectively model the unit-operations and predict yields and properties of their outlet streams.1 The hydrocarbon streams’ characterization or assays of both the crude-oil and its derivatives are decomposed, partitioned or characterized into several temperature cuts based on what are known as True Boiling Point (TBP) temperature distribution or distillation curves.2,3 These are one-dimensional representations of how quantity (yields) and quality (properties) data of hydrocarbon streams are distributed or profiled over its TBP temperatures where each cut is also referred to as a component, pseudocomponent or hypothetical in process simulation and optimization technology.4
To improve efficiency, effectiveness and economy of mixing/blending, reacting/converting and separating/fractionating inside the oil-refinery, we proposed a new technique to optimize the blending of several streams’ distillation curves with also shifting or adjusting cutpoint temperatures of distilled streams, i.e, their initial boiling point (IBP) and final boiling point (FBP), in order to manipulate their TBP curves in either off-line or on-line environment. By shifting or adjusting the front-end and back-end of the TBP curve for one or more distillate blending streams, it allows for improved control and optimization of the final product demand quantity and quality, affording better maneuvering closer and around downstream bottlenecks such as tight property specifications and volatile demand flow and timing constrictions. This shifting or adjusting of the TBP curve’s IBP and FBP (front- and back-end respectively) ultimately requires that the unit-operation has sufficient handles or controls to allow this type of cutpoint variation where the solution from this higher-level optimization would provide set points or targets to a lower-level advanced process control systems, which are now commonplace in oil refineries.
By optimizing both the recipes of the blended material and its blending component distillation curves, very significant benefits can be achieved especially given the global push towards ultralow sulfur fuels (ULSF) due to the increase in natural gas plays reducing the demand for other oil distillates. One example is provided to highlight and demonstrate the technique.
Crude-Oil Scheduling Technology: moving from simulation to optimizationBrenno Menezes
Scheduling technology either commercial or homegrown in today’s crude-oil refining industries relies on a complex simulation of scenarios where the user is solely responsible for making many different decisions manually in the search for feasible solutions over some limited time-horizon i.e., trial-and-error heuristics. As a normal outcome, schedulers abandon these solutions and then return to their simpler spreadsheet simulators due to: (i) time-consuming efforts to configure and manage numerous scheduling scenarios, and (ii) requirements of updating premises and situations that are constantly changing. Moving to solutions based in optimization rather than simulation, the lecture describes the future steps in the refactoring of the scheduling technology in PETROBRAS considering in separate the graphic user interface (GUI) and data communication developments (non-modeling related), and the modeling and process engineering related in an automated decision-making with built-in problem representation facilities and integrated data handling features among other techniques in a smart scheduling frontline.
CRUDE-OIL BLEND SCHEDULING OPTIMIZATION OF AN INDUSTRIAL-SIZED REFINERY: A DI...Brenno Menezes
We propose a discrete-time formulation for optimization of scheduling in crude-oil refineries considering both the logistics details practiced in industry and the process feed diet and quality calculations. The quantity-logic-quality phenomena (QLQP) involving a non-convex mixed-integer nonlinear (MINLP) problem is decomposed considering first the logistics model containing quantity and logic variables and constraints in a mixed-integer linear (MILP) formulation and, secondly, the quality problem with quantity and quality variables and constraints in a nonlinear programming (NLP) model by fixing the logic results from the logistics problem. Then, stream yields of crude distillation units (CDU), for the feed tank composition found in the quality calculation, are updated iteratively in the following logistics problem until their convergence is achieved. Both local and global MILP results of the logistics model are solved in the NLP programs of the quality and an ad-hoc criteria selects to continue those among a score of the MILP+NLP pairs of solutions. A pre-scheduling reduction to cluster similar quality crude-oils decreases the discrete search space in the possible superstructure of the industrial-sized example that demonstrates our tailor-made decomposition scheme of around 3% gap between the MILP and NLP solutions.
Distillation Blending and Cutpoint Temperature Optimization (DBCTO) in Schedu...Brenno Menezes
To improve efficiency, effectiveness and economy of mixing/blending, reacting/converting and separating/fractionating inside the oil-refinery.
To integrate blending of several streams’ distillation curves with also shifting or adjusting cutpoints of distilled streams (i.e., initial and/or final boiling-points, IBP and FBP) in order to manipulate their TBP curves in an either off- or on-line environment (Kelly et al, 2014).
Why linear programming is a very important topic?
• A lot of problems can be formulated as linear
programmes
• There exist efficient methods to solve them
• or at least give good approximations.
• Solve difficult problems: e.g. original example given
by the inventor of the theory, Dantzig. Best
assignment of 70 people to 70 tasks.
Overview on Transmission pipeline of gas over the world
and the transnational pipelines fro India
Includes many countries pipelines such as Russia , Europe , China , Pakistan , India , Gulf Nations , Iran , Iraq and issues and challenges faced foe these pipelines by diffrent nations, both origin nation , destination and the mediator nations
Good Overalling
total slides = 46
pressented in year 2015
Chatty Kathy - UNC Bootcamp Final Project Presentation - Final Version - 5.23...John Andrews
SlideShare Description for "Chatty Kathy - UNC Bootcamp Final Project Presentation"
Title: Chatty Kathy: Enhancing Physical Activity Among Older Adults
Description:
Discover how Chatty Kathy, an innovative project developed at the UNC Bootcamp, aims to tackle the challenge of low physical activity among older adults. Our AI-driven solution uses peer interaction to boost and sustain exercise levels, significantly improving health outcomes. This presentation covers our problem statement, the rationale behind Chatty Kathy, synthetic data and persona creation, model performance metrics, a visual demonstration of the project, and potential future developments. Join us for an insightful Q&A session to explore the potential of this groundbreaking project.
Project Team: Jay Requarth, Jana Avery, John Andrews, Dr. Dick Davis II, Nee Buntoum, Nam Yeongjin & Mat Nicholas
06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Data and AI
Round table discussion of vector databases, unstructured data, ai, big data, real-time, robots and Milvus.
A lively discussion with NJ Gen AI Meetup Lead, Prasad and Procure.FYI's Co-Found
Techniques to optimize the pagerank algorithm usually fall in two categories. One is to try reducing the work per iteration, and the other is to try reducing the number of iterations. These goals are often at odds with one another. Skipping computation on vertices which have already converged has the potential to save iteration time. Skipping in-identical vertices, with the same in-links, helps reduce duplicate computations and thus could help reduce iteration time. Road networks often have chains which can be short-circuited before pagerank computation to improve performance. Final ranks of chain nodes can be easily calculated. This could reduce both the iteration time, and the number of iterations. If a graph has no dangling nodes, pagerank of each strongly connected component can be computed in topological order. This could help reduce the iteration time, no. of iterations, and also enable multi-iteration concurrency in pagerank computation. The combination of all of the above methods is the STICD algorithm. [sticd] For dynamic graphs, unchanged components whose ranks are unaffected can be skipped altogether.
06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Data and AI
Discussion on Vector Databases, Unstructured Data and AI
https://www.meetup.com/unstructured-data-meetup-new-york/
This meetup is for people working in unstructured data. Speakers will come present about related topics such as vector databases, LLMs, and managing data at scale. The intended audience of this group includes roles like machine learning engineers, data scientists, data engineers, software engineers, and PMs.This meetup was formerly Milvus Meetup, and is sponsored by Zilliz maintainers of Milvus.
Enhanced Enterprise Intelligence with your personal AI Data Copilot.pdfGetInData
Recently we have observed the rise of open-source Large Language Models (LLMs) that are community-driven or developed by the AI market leaders, such as Meta (Llama3), Databricks (DBRX) and Snowflake (Arctic). On the other hand, there is a growth in interest in specialized, carefully fine-tuned yet relatively small models that can efficiently assist programmers in day-to-day tasks. Finally, Retrieval-Augmented Generation (RAG) architectures have gained a lot of traction as the preferred approach for LLMs context and prompt augmentation for building conversational SQL data copilots, code copilots and chatbots.
In this presentation, we will show how we built upon these three concepts a robust Data Copilot that can help to democratize access to company data assets and boost performance of everyone working with data platforms.
Why do we need yet another (open-source ) Copilot?
How can we build one?
Architecture and evaluation
Adjusting primitives for graph : SHORT REPORT / NOTESSubhajit Sahu
Graph algorithms, like PageRank Compressed Sparse Row (CSR) is an adjacency-list based graph representation that is
Multiply with different modes (map)
1. Performance of sequential execution based vs OpenMP based vector multiply.
2. Comparing various launch configs for CUDA based vector multiply.
Sum with different storage types (reduce)
1. Performance of vector element sum using float vs bfloat16 as the storage type.
Sum with different modes (reduce)
1. Performance of sequential execution based vs OpenMP based vector element sum.
2. Performance of memcpy vs in-place based CUDA based vector element sum.
3. Comparing various launch configs for CUDA based vector element sum (memcpy).
4. Comparing various launch configs for CUDA based vector element sum (in-place).
Sum with in-place strategies of CUDA mode (reduce)
1. Comparing various launch configs for CUDA based vector element sum (in-place).
Adjusting OpenMP PageRank : SHORT REPORT / NOTESSubhajit Sahu
For massive graphs that fit in RAM, but not in GPU memory, it is possible to take
advantage of a shared memory system with multiple CPUs, each with multiple cores, to
accelerate pagerank computation. If the NUMA architecture of the system is properly taken
into account with good vertex partitioning, the speedup can be significant. To take steps in
this direction, experiments are conducted to implement pagerank in OpenMP using two
different approaches, uniform and hybrid. The uniform approach runs all primitives required
for pagerank in OpenMP mode (with multiple threads). On the other hand, the hybrid
approach runs certain primitives in sequential mode (i.e., sumAt, multiply).
1. Operational Research
GROUP-6
Rishabh Surana
Riddhima Kartik
RajveerSinh Chauhan
Shobhit Garg
Ronak Sani
CASE STUDY
1. Workload Balancing
2. Production Strategy
3. Hart Venture Capital
4. Product Mix
5. Investment Strategy
2. DIGITAL IMAGING (DI)
PHOTO PRINTERS
( A N I N T R O D U C T I O N T O M A N A G E M E N T S C I E N C E )
P G : 8 4 - 8 5
WORKLOAD BALANCING
3. DI Printers
Digital Imaging (DI) produces photo printers for both
professional and consumer markets. The company recently
introduced two new models of color photo printers namely
DI-910 model and DI-950 model.
Features DI- 910 DI – 950
Photo Size 4” * 6” Borderless 13” * 19” Borderless
Time Taken / Print 37 seconds Faster than DI-910
Profit / Unit $ 42 $ 87
4. Manufacturing
The company has two manufacturing lines to assemble, test and pack
the printers.
LINE 1 - Performs assembly operation
LINE 2 - Performs testing and packaging part
Line DI- 910 DI – 950 Time Available /
Shift
Line – 1 3 mins 6 mins $ 480
Line - 2 4 mins 2 mins $ 480
Profit / Unit $ 42 $ 87
5. Objective Functions
Decision Variables
Let, X - Number of units of DI-910 model produced in each shift.
Let, Y - Number of units of DI-950 model produced in each shift.
Objective
The company’s objective is to maximize its profit from overall
production.
Objective Function
Z (Max.) = 42(X) + 87(Y)
6. Constraints
Subject To :
For Line 1
3X + 6Y <= 480
For Line 2
4X + 2Y <= 480
Non-Negativity Constraints
X >= 0
Y >= 0
7. 1 (a).
Recommended number of units of each printer to be produced to maximize
the profit :
No. of DI-910 model printers to be produced i.e. X = 0
No. of DI-950 model printers to be produced i.e. Y = 80
Z(Max.) = 42 (0) * 87 (80) 6960
Now while producing 80 DI-950 printers :
Time used in Assembly Line = 6 X 80 = 480 minutes
Time used in Testing & Packaging = 2 X 80 = 160 minutes
Time i.e. not utilised in Testing & Packaging = 480 – 160 = 320
minutes
Line -2 i.e. Testing & Packaging is Idle for 320 minutes/shift
8. Area under ABCD
is the feasible region
Optimal solution i.e.
Z(max) is at A = 6960
9. (b).
Possible reasons for not implementing the recommendation :
Thus, management may not be manufacturing only DI-
950 model printers as :
Resources on Line 2 will not be utilized fully as there will be an
idle time of 320 minutes (more than half of the total time of the
shift).
Production/Supply of DI-950 model printers may be in excess of
market demand.
Demand of DI-910 model printers will be left unfulfilled.
11. 2.
DI Company wants to produce as many DI-910
model printers as DI-950 model printers :
Now in this case, a new constraint will further be added to the original
problem :
X >= Y, or
X – Y >= 0
We will achieve our optimal point at :
X = 53.33
Y = 53.33
But since production of printers can not be done in this way,
the company would produce :
X = 54
Y = 53
Z(Max.) = 42 (54) * 87 (53) 6880
12. Feasible region is ABCD
Optimal point at A (x=54,y=53)
Max. profit i.e. Zmax = 6880
14. 3.
Analysis of resource utilization on Line 1 and Line 2 in reference to
solution developed in part (2) :
Time used in Assembly line = (3 X 54) + (6 X 53) = 480
minutes
Time used in Testing & Packaging = (4 X 54) + (2 X 53) = 322
minutes
Time i.e. not utilized in Testing & Packaging =
480 – 322 = 158 minutes
Now as there is a lot of time in Line 2 still unused, the main
concern for the company would be how to utilize this unused
time in a productive manner so that it add value to the
company as well as its profits.
15. 4.
Management wants to limit the time difference between both the lines
by 30 minutes or less :
In this case, a new constraint will be added to the original problem :
(3X + 6Y ) – (4X + 2Y) <= 30, or
- X + 4Y <= 30
Through Management Scientist Software, the new calculated values will
be :
X = 96.667
Y = 31.667
Z(Max.) = 42(96.667) + 87(31.667) 6815
Time consumed in Line 1 = (3 X 96.667) + (6 X 31.667) = 480 minutes
Time consumed in Line-2 = (4 X 96.667) + (2 X 31.667) = 450 minutes
Time Difference = 480 – 450 30 minutes
17. Feasible region is ABCD
Optimal solution is at A (x=96.667,y=31.667)
Max. profit i.e. Zmax= 6815
18. Now again since the production of printers can not be
done in this way, the company would produce :
X = 98
Y = 31
Z(Max.) = 42 (98) * 87 (31) 6813
Time consumed in Line 1 = (3 X 98) + (6 X 31) = 480 minutes
Time consumed in Line-2 = (4 X 98) + (2 X 31) = 454 minutes
Time Difference = 480 – 454 26 minutes
19. 5.
Objective is to maximize the number of printers
produced :
Since the objective of the company has changed from maximizing profits to maximizing
production, the objective function would also change :
New Objective Function :
Z(Max.) = X + Y
Through Management Scientist Software, the new calculated values will
be :
X = 106.227
Y = 26.667
For convenience in production, the company would produce :
X = 106
Y = 27
Z(Max.) = 42 (106) * 87 (26) 6801
Time consumed in line-1 = (3 X 106) + (6 X 27) = 480 minutes
Time consumed in line-2 = (4 X 106) + (2 X 27) = 478 minutes
21. BETTER FITNESS INC. (BFI)
EXERCISE EQUIPMENT MANUFACTURING
( A N I N T R O D U C T I O N T O M A N A G E M E N T S C I E N C E )
P G : 8 5 - 8 6
PRODUCTION STRATEGY
22. Components of Machines
Two machines are to be Manufactured :
Body Plus 100
1. Frame Unit
2. Press Station
3. Pec-Dec Station
Body Plus 200
1. Frame Unit
2. Press Station
3. Pec-Dec Station
4. Leg Press Station
23. Activities Involved in Manufacturing
There are various activities involved in per unit
manufacturing of ‘Body Plus 100’ and ‘Body Plus 200’ :
Machining and Welding
Painting and Finishing
Assembling, Packaging and Testing
Three of these activities take separate time for both the
machines
24. Body Plus 100
Machine &
Welding
Time
(Hrs)
Painting &
Finishing
Time
(Hrs)
Assembling,
Testing &
Packaging
(Hrs)
Raw
Material
Cost
($)
Packaging
Cost
($)
Frame Unit 4 2
2
450
50Press Station 2 1 300
Pec-Dec Station 2 2 250
Total 8 5 2 1000 50
25. Body Plus 200
Machine &
Welding
Time
(Hrs)
Painting &
Finishing
Time
(Hrs)
Assembling,
Testing &
Packaging
(Hrs)
Raw
Material
Cost
($)
Packaging
Cost
($)
Frame Unit 5 4
2
650
75
Press Station 3 2 400
Pec-Dec Station 2 2 250
Leg Press
Station
2 2 200
Total 12 10 2 1500 75
26. Process Time
Machine & Welding
Time
Painting & Finishing
Time
Assembling, Testing
& Packaging Time
Labor Cost / Hour $ 20 $ 15 $ 12
Total Time (Hrs) Cost / Hour
Machine & Welding Time 600 20
Painting & Finishing Time 450 15
Assembling, Testing and Packaging Time 140 12
For the Next Production Period Management Estimates the Hours and Labor Cost
27. Body Plus 100 Body Plus 200
Retail Price = $ 2400
Labor Cost = (20*8)+(15*5)+(12*2)
= $ 259
Raw Material Cost = $ 1000 + $ 50
= $ 1050
Dealer Price = 0.70*2400 = $1680
(Because Dealer can purchase at 70%)
.
Retail Price = $ 3500
Labor Cost = (20*12)+(15*10)+(12*2)
= $ 414
Raw Material Cost = $ 1500 + $ 75
= $ 1575
Dealer Price = 0.70*3500 = $ 2450
(Because Dealer can purchase at 70%)
.
Manufacturing Cost
28. Body Plus 100 Body Plus 200
Total Cost = RM cost + Labor Cost
Total = $ 1050 + $ 259
= $ 1309
Price Sold = $ 1680
Profit = $ 1680 - $ 1309
= $ 371
.
Total Cost = RM cost + Labor Cost
Total = $ 1575 + $ 414
= $ 1989
Price Sold = $ 2450
Profit = $ 2450 - $ 1989
= $ 461
.
Profit
29. LPP
A. Decision Variable
X = No. of Units of Body Plus 100 to be produced
Y = No. of Units of Body Plus 200 to be produced
B. LPP Equation (Profit Maximization)
Max Z = 371 X + 461 Y
C. Constraints
1. Machine & Welding Hours :
1. 8 X + 12 Y <= 600
2. Painting & Finishing Hours :
1. 5 X + 10 Y <= 450
3. Assembly & Packaging Hours :
1. 2 X + 2 Y <= 140
4. Y >= 0.25 (X + Y)
5. Non – Negative Constraints :
X >=0 ; Y >= 0
31. 1.
The Optimal Solution is from one among the Feasible region points
Hence, the recommended number of machines are :
Body Plus 100 = 50
Body Plus 200 = 16
Points Max Z Solution
A 0 , 45
Z = 371 X + 461 Y
20,745
B 30 , 30 24,960
C 50 , 16.667 26,233.48 Optimal Solution
32. 2.
If the constraint of “producing atleast 25% of Body Plus 200” is
removed.
Then the graph shall be plotted for the following constraints:
1. Machine & Welding Hours :
1. 8 X + 12 Y <= 600
2. Painting & Finishing Hours :
1. 5 X + 10 Y <= 450
3. Assembly & Packaging Hours :
1. 2 X + 2 Y <= 140
4. Non – Negative Constraints :
X >=0 ; Y >= 0
34. New Solution
The Optimal Solution is from one among the Feasible region points
Hence, the recommended number of machines are :
Body Plus 100 = 60
Body Plus 200 = 10
The Profit Margin Increases by
= $ 26,870 - $ 26,233.48
= $ 636.52
Points Max Z Solution
A 0 , 45
Z = 371 X + 461 Y
20,745
B 30 , 30 24,960
C 60 , 10 26,870
D 70 , 0 25,970
Optimal Solution
35. 3.
We can see that the “Upper Limit” in ‘X’ is not fixed, whereas in ‘Y’ it is
1113 units
When looking at the Objective function Coefficient ranges we see that
the objective function yields maximum profits (1113 units) by selling
only Body Plus 200.
Also, the reduced costs of manufacturing only Body Plus 200 is 652.
Therefore, the efforts should be expended, in Body Plus 200 to yield
maximum profit.
37. HART VENTURE CAPITAL (HVC)
VENTURE CAPITAL FOR SOFTWARE
DEVELOPMENT
( A N I N T R O D U C T I O N T O M A N A G E M E N T S C I E N C E )
P G : 8 6 - 8 7
HART VENTURE CAPITAL
38. Objective Function
Decision Variables
X1= Percentage of fund invested in Security systems.
X2= Percentage of fund invested in Market analysis.
Objective Function
To maximize the net present value of the total investment in Security
systems and Market analysis.
Max Z= X1/100(1,800,000)+X2/100(1,600,000)
Constraints
X1/100(600,000)+X2/100(500,000)<=800,000
X1/100(600,000)+X2/100(300,000)<=700,000
X1/100(250,000)+X2/100(400,000)<=500,000
Non negativity condition X1,X2>=0
40. Graph
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Y=Percentageofinvestmentinmarketanalysis
X = Percentage of investment in security system
600000X+500000Y<800000
600000X+350000Y<700000
250000X+400000Y<500000
41.
42. 1.
HVC should invest 60.87% in Security systems and 86.95%
in Market analysis.
Net present value of total investment is $2,486,956.522
43. 2.
Capital Allocation Plan :
Year 1 Year 2 Year 3
Security Systems $ 3, 65, 220 $ 3, 65, 220 $ 1, 52, 175
Market Analysis $ 4, 34, 750 $ 3, 04, 325 $ 3, 47, 800
Slack Funds $ 30 $ 30, 455 $ 25
44. 3.
Assuming that the additional $100000 is made available to
HVC to be invested in any year.
HVC should choose to invest these funds in these
proportions in the two projects
The following effects will take place :
A. % invested funded for Security Systems will become 68%
B. % invested funded for Market Analysis will become 82%
C. Net Present Value will become $2536000.
46. 4.
Assuming the additional $100000 is committed for
the first year itself, the capital allocation plan is
For Security systems:
1. Year 1 = $413,112
2. Year 2 = $413,112
3. Year 2 = $172,130
For market analysis:
1. Year 1 = $409,835
2. Year 2 = $286,884
3. Year 2 = $327,868
47. 5.
As we saw, when an additional $100000 is invested,
the net present value goes up by $49140 with a slack
of $89000. These slack funds may be reinvested in
lucrative options available with HVC.
48. TJ’S INC.
NUT MIXES FOR SALE TO GROCERY
CHAINS
( A N I N T R O D U C T I O N T O M A N A G E M E N T S C I E N C E )
P G : 1 5 1 - 1 5 2
PRODUCT MIX
49. Problem
TJ’s Incorporated makes three nut mixes for sale to grocery chains located in
the southeast. The three mixes, referred to as the Regular Mix, the Deluxe Mix,
and the Holiday Mix, are made by mixing different percentages of types of nuts.
In preparation for the fall season, TJ’s has just purchased the following
shipments of nuts at the prices shown :
Type of Nut Shipment Amount Cost per Shipment
Almond 6000 7500
Brazil 7500 7125
Filbert 7500 6750
Pecan 6000 7200
Walnut 7500 7875
51. Managerial Report
Perform an analysis of TJ’s product mix problem, and prepare a report for
TJ’s president that summarizes your finding. Be sure to include
information and analysis on the following:
1. The cost per pound of the nuts included in the Regular, Deluxe, and
Holiday mixes.
2. The optimal product mix and the total profit contribution.
3. Recommendations regarding how the total profit contribution can be
increased if additional quantities of nuts can be purchased.
4. A recommendation as to whether TJ’s should purchase an additional
1,000 pounds of almonds for $1,000 from a supplier who overbought.
5. Recommendations on how profit contribution could be increased (if
at all) if TJ’s does not satisfy all existing orders.
52. L.P.P Formulation
Decision variables :
R = pounds of Regular Mix
D = pounds of Deluxe Mix
H = pounds of Holiday Mix
Objective function :
Z = 1.65R + 2.00D + 2.25H - 36450
56. Interpretation
The Objective Function Value : optimal solution - maximum profit -
$61375.
Subtract $36450 from the original Objective Function Value
Subtract the total cost per shipment of the different nuts,
Optimal Solution - maximum profits - $24935.
Optimal decision production = 17500 of regular mix,10625 of deluxe mix,
and 5000 of holiday mix.
Optimal solution exceeds the customer orders for regular Mix by 7500
pounds
Optimal solution exceeds the customer orders for deluxe Mix by 7625
pounds
Holiday mix binding constraint(zero surplus)
The negative dual price indicates that increasing the customer orders for
Holiday mix from 5000 to 5001 pounds will actually decrease the profit
contribution by $0.18.
57. Recommendations
Increase the quantity of almonds and walnuts purchased by Tj’s and
increase their profit contribution at rate of $8.5 per pound of almonds
and $1.5 per pound of walnuts.
No more buying of brazil nuts, filberts and pecans.
Almonds - For each additional pound purchased the profit would
increase @ $8.5 for 583 pounds.
Walnuts - For each additional pound purchased the profit would
increase @ $1.5 for 250 pounds.
Dual price of -.175 for the pounds of holiday mix indicate the desire to
reduce the production of this mix.
The range of feasibility indicates the need to reduce the customer
orders to zero and the value of reduction @ $.18 per pound.
58. J.D. WILLIAMS INC.
INVESTMENT ADVISORY FIRM
( A N I N T R O D U C T I O N T O M A N A G E M E N T S C I E N C E )
P G : 1 5 2 - 1 5 3
INVESTMENT STRATEGY
59. Objective Function
The Case talks about an Investment Advisory firm having more than $120
million of funds with numerous clients.
The problem at hand is about an $800,000 new investment which is to be
invested in three portfolios
Therefore
Decision Variables:
X1=Investment in growth fund
X2=Investment in income fund
X3=Investment in money market fund
Objective Function:
Maximize Z= 0.18X1+0.125X2+0.075X3
61. Solution
LINEAR PROGRAMMING PROBLEM
Max Z = 0.18 X1+0.125 X2+0.075 X3
OPTIMAL SOLUTION
Objective Function Value = 94133.333
Variable Value Reduced Costs
-------------- --------------- ------------------
X1 248888.889 0.000
X2 160000.000 0.000
X3 391111.111 0.000
63. OBJECTIVE COEFFICIENT RANGES
Variable Lower Limit Current Value Upper Limit
------------ --------------- --------------- ---------------
X1 0.150 0.180 No Upper Limit
X2 No Lower Limit 0.125 0.145
X3 0.015 0.075 0.180
RIGHT HAND SIDE RANGES
Constraint Lower Limit Current Value Upper Limit
------------ --------------- --------------- ---------------
1 -88888.889 0.000 No Upper Limit
2 No Lower Limit 0.000 71111.111
3 -133333.333 0.000 106666.667
4 No Lower Limit 0.000 240000.000
5 -151111.111 0.000 No Upper Limit
6 0.000 800000.000 No Upper Limit
7 -8000.000 0.000 6400.000
64. 1.
From the above solution out of 800,000 the
investment should be as follows:
Growth Fund: $248888.889
Income Fund: $160000.000
Money Market Fund: $391111.111
The annual growth anticipated from the investment
recommendation is $94133.333
65. 2.
If the clients risk index increased from 0.05 to 0.055
The new yield index would increase by $4666.67 to
$98800
66. 3 (a).
If the annual yield for growth fund is decreased to 16% for
Growth then the investment recommendation would be
as follows
Growth fund :$248890; Change: 1.111
Income Fund :$160000; Change: 0
Money Market Fund :$391110 ; Change: 0
The value of yield per year is $89155.650 from $94133.333
with a change of $4977.68
67. 3 (b).
If the annual yield for growth fund is decreased to 14% for
Growth then the investment recommendation would be as
follows
Growth fund :$160000; Change: $88888.889
Income Fund :$293335; Change: $133335
Money Market Fund :$346665 ;Change: $44446.11
The value of yield per year is $85066.750.650 from
$94133.333 with a change of $9066.583
68. 4.
According to the question there will be an additional constraint added
as:
X1<=X2
i.e., X1-X2<=0
With the following constraints added the investment recommendation
is as follows :
Growth fund :$213334; Change: $35554.889
Income Fund :$213334; Change: $53334
Money Market Fund :$373332; Change: $17779.11
The value of yield per year is $93066.770 from $94133.333 with a change
of $1066.563
69. 5.
Yes the asset allocation model can be used can be used for
any number of clients as long as the values of
Growth Fund is above 15%
Income Fund is below 14.5%
Money market Fund is in between 1.5% to 18%
70. Bibliography & Reference
An Introduction to Management Science :
Quantitative Approaches to Decision Making
The Management Scientist Version 6.0 Software