## QM350: Operations Research

Course Syllabus QM350

Textbook

An Introduction to Management Science, Quantitative Approaches to Decision Making, By  Anderson, D.R., Sweeney, D. J., Williams, T.A., and Martin, K, 2009 edition, Cengage Learning (http://cws.cengage.co.uk/aswims/)

Software

Course Intended Learning Outcomes (CILOs)

1. Demonstrate an understanding of the theory behind the standard OR formulae and algorithms presented.
2. Formulate and solve elementary problems requiring the use of these formulae and algorithms, both analytically and using appropriate software.
3. Develop a report that describes the model and the solving technique, analyze the results and propose recommendations in language understandable to the decision-making.
4. Simulate a real system by experimenting.
5. Understand various important concepts in forecasting and different approaches for modeling trend, seasonality.
6. Develop critical thinking and objective analysis of decision problems.

Course Chapters

1. INTRODUCTION: Introduction to Management Science / Where did MS Come From / Management Science Applications / The MS approach  (pp. 2-5 and 10-14)
2. AN INTRODUCTION TO LINEAR PROGAMMING: Models /A maximization problem / Graphical solution procedure / Extreme points and the optimal solution / Computer Solution / A simple minimization problem / Special cases / General linear programming notation (pp. 33-67)
3. LINEAR PROGRAMMING APPLICATIONS: The process of problem formulation / Production Management / Marketing and media applications / Financial Applications/ Transportation Problem (PPTs only)
Excel files: Example 2
4. LINEAR PROGRAMMING: THE SIMPLEX METHOD: An algebraic overview of the simplex method / Tableau form/ Setting up the initial simplex tableau / Improving the solution/ Calculating the next tableau / Tableau form: The general case /Solving a minimization problem / special cases (pp. 223-256) Simplex Tableau
5. SIMPLEX-BASED SENSITIVITY ANALYSIS AND DUALITY: Sensitivity analysis with the simplex tableau (continued) / Duality (pp. 267-277, 279-285)
6. SIMULATION: Risk analysis/ Queuing simulation (pp. 563-577, 583-590)
Excel files: ComputerWorld Simulation ExamplePortaCom Project ExampleWaiting Line Simulation Example
7. FORECASTING: Components of a time Series / Moving Averages / Trend and Seasonal Components / Qualitative approaches (pp. 715-723, 732-740, 753-755)
8. DECISION ANALYSIS: Problem formulation / Decision making without probabilities / Decision making with probabilities/ Risk analysis and Sensitivity analysis  (pp. 613-630)
9. MARKOV PROCESS: Market Share Analysis (On CD 2-10)

Homework assignment

Videos

• Resource title: The origins of operations research with Kenneth Arrow (Chapter 1)
Resource description: Nobel Prize-winning economist Kenneth Arrow is the Joan Kenney Professor of Economics and a professor emeritus of Management Science and Engineering at Stanford University. He won the 1972 Nobel Prize in Economics (with Sir John Hicks) for pioneering contributions to general equilibrium theory and welfare theory — theories underlying assessment of business risk, and government economic and welfare policies. In March, Arrow earned another career accolade when he was named a Stanford Engineering Hero. In this interview during a visit to campus for his induction ceremony, Arrow discusses the origins of operations research.
Channel: Youtube
• Resource title: Operations what? (Chapter 1)
Resource description: In a nutshell, Operations Research is the discipline of applying advanced analytics to help you make better business decisions. But why o why should any manager care about algorithms? Because these days many major corporation, such as UPS, and Proctor and Gamble, are using Operations Research to solve their complex business problems. The good news: You don’t have to be a mathematician to use OR. The bad news: If you don’t use it, your competitors most likely will — and the competition could eat you alive!
Channel: Youtube
• Resource title: Introduction to a linear program (Chapter 1)
Resource description: This video examines how two businesses can make decisions that help maximise profits as a result of using the mathematical technique of linear programming. Belgian chocolates are famous the world over. But there are many different kinds of chocolate that can be made. How can the producer pick the best combinations within the various constraints imposed on the business? We see how the mathematics of linear programming can help to give an insight into this question.
Channel: Youtube
• Resource title: Graphical Solution (Chapter 2)
Resource description: In the previous video we established what is possible and what is not if our chocolatier is to meet the constraints imposed on his business. How do we find the best combination that produces the maximum profit. We now follow the final two steps in solving the linear program using the graphical solution procedure.
Channel: Youtube
• Resource title: Production Management (Chapter 3)
Resource description: Hugh and his partners at Wight Salads grow tomatoes exclusively. Although they grow many varieties, tomatoes are all that they produce for leading supermarket chains in the UK. Should they diversify into related products such as lettuce? Linear Programming helps them arrive at an answer.
Channel: Youtube

• Resource title: Excel – Solver Add In (Chapter 2/3)
Resource description: Video to add the solver add-in to Excel.
Channel: Youtube
• Resource title: Excel – Use the Solver Add In to solve Linear programs (Chapter 2/3)
Resource description: Video for Using Excel Solver to find the solution to a maximization problem.
Channel: Youtube
• Resource title: Excel – Using the sumproduct formula (Chapter 2/3)
Resource description: Using sumproduct formula in MS Excel Solver for Linear Programming.
Channel: Youtube
• Resource title: Simulation – ATM Queue Simulation (Chapter 6)
Resource description: Simulation demonstrating ATM queuing assuming variable arrival times and different types of transaction used at the machine.
Channel: Youtube
• Resource title: Simulation – Excel functions RAND and VLOOKUP  (Chapter 6)
Resource description: A simulation using cumulative probabilities, vlookup, and random numbers..
Channel: Youtube
• Resource title: Simulation –Simulate Stock Price Changes with Excel  (Chapter 6)
Resource description: Simulate stock price changes in Excel using the NORMINV & RAND functions and the Data Table feature. Make a basic Monte Carlo simulation to develop a range within which prices should fall over a specific time frame.
Channel: Youtube
• Resource title: Excel –Intro to Moving Average in Excel  (Chapter 7)
Resource description: Introduction to using excel for the Moving Average Forecasting Technique.
Channel: Youtube
• Resource title: Excel -Finding slope and intercept for Trend Forecast  (Chapter 7)
Resource description: Finding slope and intercept for Trend Forecast using excel.
Channel: Youtube
• Resource title: Excel -Trend Forecasting in Excel (Chapter 7)
Resource description: Final development of a Trend Forecast in Excel. Use to develop a demand forecast over several time periods.
Channel: Youtube
• Resource title: Excel – Time Series Forecasting   (Chapter 7)
Resource description: This video examines how to calculate the Seasonal indexes and how to use the multiplicative model for forecasting.
Channel: Youtube

Project Details: Sensitivity Analysis

The task is to be attempted individually. Evidence of collusion will result in no marks!

In the following problem, each student should replace D1 by the first two digits (from the right) of your registration ID (00 < D1 < 99). Similarly, D2 replaced by the third and fourth digits (from the right) of your registration ID (00 < D2 < 99), and D3 by the fifth and sixth digits of your registration ID. (D4) represents the total of all digits in the student ID.

Suppose student ID=20 0670 21 à 1st 2-digits D1=21, 2nd 2-digits D2=70, 3rd 2-digits D3=06, total of all digits D4= (2+0+0+6+7+0+2+1) =18

A firm is contracted to make (D4+80) K.G’s of cattle feed. The mixture consist of 3 substances A, B, and C. “A” costs \$3/K.G “B” costs \$4/ K.G and “C” costs \$6/K.G.

(0.5D2+50) K.G’s of “A” and (D1+90) K.G’s of “B” are available. There is an unlimited amount of “C” available. The firm can convert 1.5 tons of substance A to 1 ton of substance C at an extra cost of 50 cents per ton of C produced. Each K.G of these substances has some nutrition units (grams). Substance A has 9 grams/K.G of the nutrition, 7 grams/ K.G for “B’, and 4 grams/ K.G for C. The total mixture must have average nutrition grams of no more than or equal to (D3) grams/ K.G. The firm wishes to minimize its costs.

The Assignment:

1. Solve the L.P. Model below using “Excel Solver” software using the simplex method to find the optimal solution. Comment on the optimal solution.
2. Without reformulating the problem, explain how you can determine from the final optimal solution (Use the Sensitivity report produced by Excel):
• The difference in total cost caused by one more K.G of “B” substance being available than there was available.
• The range of values for the amount of substance “A” available, for which the optimal solution contains the same basic variables.
• If the cost of substance “A” decreases to \$2.2/ K.G, will the same variables be in the basis.
• The range of values for the cost of “B” substance, for which the optimal solution will remain optimal.

Evidence of calculations and computer software are required.