OMIS 671: Management Science
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Some 2 past exam questions are added below for your look. Best
Lectures added below:
Lectures 1 & 2 (introduction, linear program, graphical approach)
Lectures 3 & 4 (LP, PC application & sensitivities)
Lecture 3b (simplex method)
Lecture 5 (Integer programing problems, applications, fixed charge)
Lecture 6&7 (Duality in LP, Transportation, Transshipment & Assignment)
Lecture 8 (Probability & Statistics)
Lecture 9 (Decision Analysis)
Lecture 10 (Queuing Models)
Latest Breaking News
URGENT: Please you are strongly reminded to come with your laptops to class. Ensure you have excel & " excel solver" add-in in it
Breaking News
Lectures 1 & 2 are attached below
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Module leader -
Information on Restrictions and Pre- and co-requisites, Teaching Format, Academic Aims, and Learning Objectives can be found in the module thumbprint.
Context -
3 credit hour course. This module is complemented with knowledge of intermediate maths - calculus, equations and inequalities etc. It is a prerequisite for the Decision and Risk Analysis course in 2nd semester. All students have A-level Mathematics or the equivalent. Teaching some topics will be coordinated with Excel modelling to implement some techniques.
Teaching Times & format-
13 lectures (1 per week in 1st semester), plus some tutorials. Teaching begins Monday, 07 Sept 2014
Assessment-
Assignments, Participation (10%),
IA or Group Paper in Oct (25%),
Three-hour exam (70%) in Nov 18 to Dec 9.
Academic aims-
To develop the learner's interest in, & knowledge and understanding of, a wide range of MS techniques to support decision making in organisations. Students will learn the theoretical underpinnings of the main MS techniques and the range of applications for which they are useful. They will gain practical experience in modelling and problem solving using excel solver and may be Lingo, Precision Tree & @risk software.
Learning outcomes-
By the end of the module the student should be able to...
Subject Knowledge and Understanding.Demonstrate knowledge of Management Science techniques and effective problem solving and decision making skills.
Key Skills.Demonstrate ability to create,evaluate and assess a range of options together the capacity to apply ideas and knowledge to a range of organisational problem situations.
Subject specific and Professional skills.Given a practical problem,a student should be able to :
Formulate a module;
Select the most efficient module to tackle the problem ;
Use appropriate software to solve the model;
Report findings using a range of media that are widely used in med.
Optimisation modeling
TOPICS
Linear Programming
Duality & Sensitivity
Transportation, Transshipment & Assignment Problems
Integer Programming
Network Models
Project Management
CPA, PERT. Use of LP to solve CPA problems.
Queuing Theory
Decision Analysis
Deterministic Inventory Control
Multi-criteria decision analysis
Probability & Statistics
Time Series Analysis.
Robust & Convex Optimisation
Stochastic, Nonlinear & Dynamic Programming
Simulation Modelling (Monte Carlo)
Game theory
Markov Chain
READINGS
1. TaylorIII, Bernard W. (2010):Introduction to Management Science, 10thedition, Prentice Hall
2. Anderson, D. R., Sweeney, D. J., and Williams, T. A. (2004): Quantitative methods for Business, 6th edition, West Publishing Company.
3. Swift Louise (2001): Quantitative Methods for Business, ManagementFinance, Palgrave
4. Anderson Sweeny & Williams 2012 An Introduction to Management Science
5. Winston, Albright 2009 Practical Management Science, Revised
6. Winston 2004 4e Operations Research Applications and Algorithms (world standard)
7. Ragsdale 2008 Spreadsheet Modeling and Decision Analysis Intro to ORMS
8. Taha H 2010 Operations Research, An Introduction 9e
9. Hillier and Lieberman 2001 Introduction to Operations Research 7e
10. Oakshott, L. Essential Quantitative Methods for Business, Management and Finance 3rd edition (2006). Palgrave Macmillan
Assignment 1 (submit on 22/09/2014)
Assignment 1 Metropolitan Police Patrol
CASE PROBLEM: Metropolitan Police Patrol, Bernard W. Taylor III to be handed in 1 week. Bernard W.
Taylor III 10th edition, page 79 question number 3; OR page 69 in soft copy version
Assignments 2 & 3 (submit on 13/10/2014)
Assignment 2 The Possibility Restaurant: Attempt the CASE PROBLEM: “The Possibility Restaurant”, on page 70 of the soft copy of the book, to be handed in 1 week. Now, using PC, continue solving the case: "THE POSSIBILITY" RESTAURANTCONTINUED" on page 108 of the same soft copy
Assignment 3 MOSSAIC TILES, LTD.: Attempt the CASE PROBLEM: “MOSSAIC TILES, LTD.”, on page 107 of the soft copy of the book, to be handed in 1 week. You will be using both hand computation and computer software to attempt the question.
Some problems on Integer programming problems
A textbook publishing company has developed two new sales regions and is planning to transfer some of its existing sales force into these two regions. The company has 10 salespeople available for the transfer. Because of the different geographic configurations and the location of schools in each region, the average annual expenses for a salesperson differ in the two regions; the average is $10,000 per salesperson in region 1 and $7,000 per salesperson in region 2. The total annual expense budget for the new regions is $72,000. It is estimated that a salesperson in region 1 will generate an average of $85,000 in sales each year and a salesperson in region 2 will generate $60,000 annually in sales. The company wants to know how many salespeople to transfer into each region to maximize increased sales. Formulate the Integer Programming Model
A tailor makes wool tweed sport coats and wool slacks. He is able to get a shipment of 150 square yards of wool cloth from Scotland each month to make coats and slacks, and he has 200 hours of his own labor to make them each month. A coat requires 3 square yards of wool and 10 hours to make, and a pair of slacks requires 5 square yards of wool and 4 hours to make. The tailor earns $50 in profit from each coat he makes and $40 from each pair of slacks. He wants to know how many coats and pairs of slacks to produce to maximize profit. Formulate an integer linear programming model for this problem. Find the integer solution to this problem by using pc. Compare this solution with the solution without integer restrictions and indicate whether the rounded-down solution would have been optimal.
The Otter Creek Winery produces three kinds of table winea blush, a white, and a red. The winery has 30,000 pounds of grapes available to produce wine this season. A cask of blush requires 360 pounds of grapes, a cask of white requires 375 pounds, and a cask of red requires 410 pounds. The winery has enough storage space in its aging room to store 67 casks of wine. The winery has 2,200 hours of production capacity, and it requires 14 hours to produce a cask of blush, 10 hours to produce a cask of white, and 18 hours to produce a cask of red. From records of previous years' sales, the winery knows it will sell at least twice as much blush as red and at least 1.5 times as much white as blush. The profit for a cask of blush is $12,100, the profit for a cask of white is $8,700, and the profit for a cask of red is $10,500. The winery wants to know the number of casks of each table wine to produce. Formulate and solve an integer programming model for this problem and solve it.
Rowntown Cab Company has 70 drivers that it must schedule in three 8-hour shifts. However, the demand for cabs in the metropolitan area varies dramatically according to the time of day. The slowest period is between midnight and 4:00 A.M. The dispatcher receives few calls, and the calls that are received have the smallest fares of the day. Very few people are going to the airport at that time of night or taking other long-distance trips. It is estimated that a driver will average $80 in fares during that period. The largest fares result from the airport runs in the morning. Thus, the drivers who start their shift during the period from 4:00 A.M. to 8:00 A.M. average $500 in total fares, and drivers who start at 8:00 A.M. average $420. Drivers who start at noon average $300, while drivers who start at 4:00 P.M. average $270. Drivers who start at the beginning of the 8:00 P.M. to midnight period earn an average of $210 in fares during their 8-hour shift.
To retain customers and acquire new ones, Rowntown must maintain a high customer service level. To do so, it has determined the minimum number of drivers it needs working during every 4-hour time segment10 from midnight to 4:00 A.M., 12 from 4:00 to 8:00 A.M., 20 from 8:00 A.M. to noon, 25 from noon to 4:00 P.M., 32 from 4:00 to 8:00 P.M., and 18 from 8:00 P.M. to midnight. 1. Formulate and solve an integer programming model to help Rowntown Cab schedule its drivers. 2. If Rowntown has a maximum of only 15 drivers who will work the late shift from midnight to 8:00 A.M., reformulate the model to reflect this complication and solve it.3. All the drivers like to work the day shift from 8:00 A.M. to 4:00 P.M., so the company has decided to limit the number of drivers who work this 8-hour shift to 20. Reformulate the model in (b) to reflect this restriction and solve it.
Do the case study called "NEW OFFICES AT ATLANTIC MANAGEMENT SYSTEMS". DON'T SUBMIT
Downloads
Lectures L1 & L2 below. Please use the password you were given to open the pdf. It is straightforward. Just click the arrow pointing down (on right of the pdf document) to download. Then enter the password I gave you in class to open it
Just Attempt the ff at home, Don't submit:
1: The Munchies Cereal Company makes a serial from several ingredients. Two of the ingredients, oats and rice, provide vitamins A and B. the company wants to know how many ounces of oats and rice it should include in each box of cereal to meet the minimum requirements of 48 milligrams of vitamin A and 12 milligrams of vitamin B while minimizing cost. An ounce of oats contributes 8 milligrams of vitamin A and 1 milligram of vitamin B, whereas an ounce of rice contributes 6 milligrams of A and 2 milligrams of B. An ounce of oats costs GH₵0.05, and an ounce of rice costs GH₵0.03. Formulate an LP model for this problem. Solve this model by using excel spreadsheet
2: The Elixir Drug Company produces a drug from two ingredients. Each ingredient contains the same three antibiotics, in different proportions. One gram of ingredient 1 contributes 3 units, and one gram of ingredient 2 contributes 1 unit of antibiotic 1; the drug requires 6 units. At least 4 units of antibiotic 2 are required, and the ingredients contribute 1 unit each per gram. At least 12 units of antibiotic 3 are required; a gram of ingredient 1 contributes 2 units, and a gram of ingredient 2 contributes 6 units. The cost for a gram of ingredient 1 is GH₵80, and the cost for a gram of ingredient 2 is GH₵50. The company wants to formulate a linear programming model to determine the number of grams of each ingredient that must go into the drug in order to meet the antibiotic requirements at the minimum cost. Formulate a linear programming model for this problem and Solve this model by using excel.
3: Turbo produces multiblade impellers. George has to schedule the production of two special impellers, designated the homeowner and the professional. Production resources are limited and it is critical that profit from these two products be maximized. Each impeller is machined in the machining department and then heat treated for additional strength. Each homeowner requires 1 hour of machining time and each professional requires 2 hours. Each homeowner must be heat treated for 4 hours and each professional for 3 hours. Current production control figures show there are 80 hours of machining time available per day and the equivalent of 180 hours of oven time for heat treating. The professional also requires a special Teflon hub liner. Turbo can obtain a maximum of 36 of these Teflon liners per day. The accounting department has informed George that each Homeowner contributes $15 per unit toward profit while each professional contributes $12 per unit. George must use this information to decide how many of each impeller to produce.
4: As a supervisor of a production department, you must decide the daily production totals of a certain product that has two models, the Deluxe and the Special. The profit on the Deluxe model is $12 per unit, and the Special's profit is $10. Each model goes through two phases in the production process, and there are only 100 hours available daily at the construction stage and only 80 hours available at the finishing and inspection stage. Each Deluxe model requires 20 minutes of construction time and 10 minutes of finishing and inspection time. Each Special model requires 15 minutes of construction time and 15 minutes of finishing and inspection time. The company has also decided that the Special model must comprise at most 60 percent of the production total. Formulate this as a linear programming problem.
5: Two advertising media are being considered for promotion of a product. Radio ads cost $400 each, while newspaper ads cost $600 each. The total budget is $7,200 per week. The total number of ads should be at least 15, with at least 2 of each type, and there should be no more than 19 ads in total. The company does not want the number of newspaper ads to exceed the number of radio ads by more than 25 percent. Each newspaper ad reaches 6,000 people, 50 percent of whom will respond; while each radio ad reaches 2,000 people, 20 percent of whom will respond. The company wishes to reach as many respondents as possible while meeting all the constraints stated. Develop the appropriate LP model for determining the number of ads of each type that should be placed.
News:
Please, you are strongly encouraged to bring your laptops to class every time. Course outline & Lecture slides are below
Downloading Instructions:
All the documents are password-protected. Students have been given the passwords. To download, click on the arrow (to the right of the file) pointing downwards.