1. NEW MEXICO INSTITUTE OF MINING AND TECHNOLOGY Department of Management Management Science for Engineering Management (EMGT 501) Fall, 2005 Instructor : Toshi Sueyoshi (Ph.D.) HP address : www.nmt.edu/~toshi E-mail Address : toshi@nmt.edu Office : Speare 143-A

2. 1. Course Description: The purpose of this course is to introduce Management Science (MS) techniques for manufacturing, services, and public sector. MS includes a variety of techniques used in modeling business applications for both better understanding the system in question and making best decisions.

3. MS techniques have been applied in many situations, ranging from inventory management in manufacturing firms to capital budgeting in large and small organizations. Public and Private Sector Applications

4. The main objective of this graduate course is to provide engineers with a variety of decisional tools available for modeling and solving problems in a real business and/or nonprofit context. In this class, each individual will explore how to make various business models and how to solve them effectively.

5. 2. Texts -- The texts for this course: (1) Anderson, Sweeney and Williams An Introduction to Management Science, South-Western (2) Chang Yih-Long, WinQSB, John Wiley&Sons

6. 3. Grading: In a course, like this class, homework problems are essential. We will have homework assignments. Homework has significant weight. The grade allocation is separated as follows: Homework 20% Mid-Term Exam 40% Final Exam 40% The usual scale (90-100=A, 80-89.99=B, 70- 79.99=C, 60-69.99=D) will be used. Please remember no makeup exam.

7. 4. Course Outline: Week Topic(s) Text(s) 1 Introduction and Overview Ch. 1&2 2 Linear Programming Ch. 3&4 3 Solving Linear Programming Ch. 5 4 Duality Theory Ch. 6 5 No Class 6 Project Scheduling: PERT-CPM Ch. 10 7 Inventory Models Ch. 11 8 Review for Mid-Term EXAM

8. Week Topic(s) Text(s) 9Waiting Line Models Ch. 13 10Waiting Line Models Ch. 13 11Decision Analysis Ch. 14 12Multi-criteria Decision Ch. 15 13No Class 14Forecasting Ch. 16 15Markov Process Ch. 17 16Review for FINAL EXAM

9. Linear Programming (LP): A mathematical method that consists of an objective function and many constraints. LP involves the planning of activities to obtain an optimal result, using a mathematical model, in which all the functions are expressed by a linear relation.

10. Maximize subject to A standard Linear Programming Problem Applications: Man Power Design, Portfolio Analysis

11. Simplex method: A remarkably efficient solution procedure for solving various LP problems. Extensions and variations of the simplex method are used to perform postoptimality analysis (including sensitivity analysis).

12. (0) (1) (2) (3) (0) (1) (2) (3) (a) Algebraic Form (b) Tabular Form Coefficient of: Right Side Basic Variable Z Eq. 1 -3 -5 0 0 0 0 0 1 0 1 0 0 0 0 2 0 0 1 0 12 0 3 2 0 0 1 18

13. Duality Theory: An important discovery in the early development of LP is Duality Theory. Each LP problem, referred to as ” a primal problem” is associated with another LP problem called “a dual problem”. One of the key uses of duality theory lies in the interpretation and implementation of sensitivity analysis.

14. PERT (Program Evaluation and Review Technique)-CPM (Critical Path Method): PERT and CPM have been used extensively to assist project managers in planning, scheduling, and controlling their projects. Applications: Project Management, Project Scheduling

15. A 2 B C E M N START FINISH H G D J I F L K 4 10 4 7 6 7 9 8 54 6 2 5 0 0 Critical Path 2 + 4 + 10 + 4 + 5 + 8 + 5 + 6 = 44 weeks

16. Decision Analysis: An important technique for decision making in uncertainty. It divides decision making between the cases of without experimentation and with experimentation. Applications: Decision Making, Planning

17. Oil 0.5 0.3 Favorable 0.75 Dry 0.85 Dry a e d c b f g h Drill Sell Drill Sell Drill Oil 0.14 Oil 0.25 0.5 Dry Do seismic survey Unfavorable 0.7 No seismic survey decision fork chance fork

18. Markov Chain Model: A special kind of a stochastic process. It has a special property that probabilities, involving how a process will evolve in future, depend only on the present state of the process, and so are independent of events in the past. Applications: Inventory Control, Forecasting

19. Queueing Theory: This theory studies queueing systems by formulating mathematical models of their operation and then using these models to derive measures of performance.

20. This analysis provides vital information for effectively designing queueing systems that achieve an appropriate balance between the cost of providing a service and the cost associated with waiting for the service.

21. S S Service S facility S CCCCCCCC Served customers C C C Queueing system Customers Queue Applications: Waiting Line Design, Banking, Network Design

22. Inventory Theory: This theory is used by both wholesalers and retailers to maintain inventories of goods to be available for purchase by customers. The just-in-time inventory system is such an example that emphasizes planning and scheduling so that the needed materials arrive “just-in-time” for their use. Applications: Inventory Analysis, Warehouse Design

23. Economic Order Quantity (EOQ) model Time t Inventory level Batch size

24. Forecasting: When historical sales data are available, statistical forecasting methods have been developed for using these data to forecast future demand. Several judgmental forecasting methods use expert judgment. Applications: Future Prediction, Inventory Analysis

25. 1/99 4/99 7/99 10/99 1/00 4/00 7/00 The evolution of the monthly sales of a product illustrates a time series Monthly sales (units sold) 10,000 8,000 6,000 4,000 2,000 0

26. Introduction to MS/OR MS: Management Science OR: Operations Research Key components: (a) Modeling/Formulation (b) Algorithm (c) Application

27. Management Science (MS) (1) A discipline that attempts to aid managerial decision making by applying a scientific approach to managerial problems that involve quantitative factors. (2) MS is based upon mathematics, computer science and other social sciences like economics and business.

28. General Steps of MS Step 1: Define problem and gather data Step 2: Formulate a mathematical model to represent the problem Step 3: Develop a computer based procedure for deriving a solution(s) to the problem

29. Step 4: Test the model and refine it as needed Step 5: Apply the model to analyze the problem and make recommendation for management Step 6: Help implementation

30. Linear Programming (LP)

31. [1] LP Formulation (a) Decision Variables : All the decision variables are non-negative. (b) Objective Function : Min or Max (c) Constraints s.t. : subject to

32. [2] Example A company has three plants, Plant 1, Plant 2, Plant 3. Because of declining earnings, top management has decided to revamp the company’s product line. Product 1: It requires some of production capacity in Plants 1 and 3. Product 2: It needs Plants 2 and 3.

33. The marketing division has concluded that the company could sell as much as could be produced by these plants. However, because both products would be competing for the same production capacity in Plant 3, it is not clear which mix of the two products would be most profitable.

34. The data needed to be gathered: 1. Number of hours of production time available per week in each plant for these new products. (The available capacity for the new products is quite limited.) 2. Production time used in each plant for each batch to yield each new product. 3. There is a profit per batch from a new product.

35. Production Time per Batch, Hours Production Time Available per Week, Hours Plant Product Profit per batch 123123 4 12 18 1 2 1 0 0 2 3 2 $3,000 $5,000

36. : # of batches of product 1 produced per week : # of batches of product 2 produced per week : the total profit per week Maximize subject to

37. 0 2 4 6 8 2 4 6 8 10 Graphic Solution Feasible region

38. 0 2 4 6 8 2 4 6 8 10 Feasible region

39. 0 2 4 6 8 2 4 6 8 10 Feasible region

40. 0 2 4 6 8 2 4 6 8 10 Feasible region

41. 0 2 4 6 8 10 2 4 6 8 Maximize: The optimal solution The largest value Slope-intercept form:

42. Maximize s.t. [4] Standard Form of LP Model

43. [5] Other Forms The other LP forms are the following: 1. Minimizing the objective function: 2. Greater-than-or-equal-to constraints: Minimize

44. 3. Some functional constraints in equation form: 4. Deleting the nonnegativity constraints for some decision variables: : unrestricted in sign

45. [6] Key Terminology (a) A feasible solution is a solution for which all constraints are satisfied (b) An infeasible solution is a solution for which at least one constraint is violated (c) A feasible region is a collection of all feasible solutions

46. (d) An optimal solution is a feasible solution that has the most favorable value of the objective function (e) Multiple optimal solutions have an infinite number of solutions with the same optimal objective value

47. and Maximize Subject to Example Multiple optimal solutions:

48. 0 2 4 6 8 10 2 4 6 8 Feasible region Every point on this red line segment is optimal, each with Z=18. Multiple optimal solutions

49. (f) An unbounded solution occurs when the constraints do not prevent improving the value of the objective function.

50. Case Study - Personal Scheduling UNION AIRWAYS needs to hire additional customer service agents. Management recognizes the need for cost control while also consistently providing a satisfactory level of service to customers. Based on the new schedule of flights, an analysis has been made of the minimum number of customer service agents that need to be on duty at different times of the day to provide a satisfactory level of service.

51. * * * * * * * * * * Shift Time Period Covered Minimum # of Agents needed Time Period 6:00 am to 8:00 am 8:00 am to 10:00 am 10:00 am to noon Noon to 2:00 pm 2:00 pm to 4:00 pm 4:00 pm to 6:00 pm 6:00 pm to 8:00 pm 8:00 pm to 10:00 pm 10:00 pm to midnight Midnight to 6:00 am 1 2 3 4 5 48 79 65 87 64 73 82 43 52 15 170 160 175 180 195 Daily cost per agent

52. The problem is to determine how many agents should be assigned to the respective shifts each day to minimize the total personnel cost for agents, while meeting (or surpassing) the service requirements. Activities correspond to shifts, where the level of each activity is the number of agents assigned to that shift. This problem involves finding the best mix of shift sizes.

53. : # of agents for shift 1 (6AM - 2PM) : # of agents for shift 2 (8AM - 4PM) : # of agents for shift 3 (Noon - 8PM) : # of agents for shift 4 (4PM - Midnight) : # of agents for shift 5 (10PM - 6AM) The objective is to minimize the total cost of the agents assigned to the five shifts.

54. Min s.t. all

55. Total Personal Cost = $30,610