NEW MEXICO INSTITUTE OF MINING AND TECHNOLOGY

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

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.

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

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.

2. Texts -- The texts for this course: (1) Anderson, Sweeney, Williams & Martin An Introduction to Management Science: Quantitative Approaches to Decision Making, Thomson South-Western (Required)

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.

4. Course Outline: WeekTopic(s)Text(s) 1 Introduction and Overview Ch. 1&2 2 Linear Programming Ch. 3&17 3 Solving LP and Dual Ch. 4&18 4 DEA Ch. 5 5 Game Theory Ch.5 6 Project Scheduling: PERT-CPM Ch. 9 7 Inventory Models Ch. 10 8 Review for Mid-Term EXAM

WeekTopic(s)Text(s) 9 Waiting Line Models Ch. 11 10 Waiting Line Models Ch. 11 11 Decision Analysis Ch. 13 12 Multi-criteria Decision Ch. 14 13 Forecasting Ch. 15 14 Markov Process Ch. 16 15 Slack (for Class Delay) 16 Review for FINAL EXAM

Assessment • Please indicate the current level of your knowledge. (1: no idea, 2: little, 3: considerable, 4: very well). • TopicYour Assessment • (1) Linear Programming • (2) Dual and Primal Relationship • (3) Simplex Method • (4) Data Envelopment Analysis • (5) PERT/CPM • (6) Inventory • Return the assessment by Sep 1 (noon) to toshi@nmt.edu

Model Development • Models are representations of real objects or situations • Mathematical models - represent real world problems through a system of mathematical formulas and expressions based on key assumptions, estimates, or statistical analyses

Advantages of Models • Generally, experimenting with models (compared to experimenting with the real situation): • requires less time • is less expensive • involves less risk

Mathematical Models • Cost/benefit considerations must be made in selecting an appropriate mathematical model. • Frequently a less complicated (and perhaps less precise) model is more appropriate than a more complex and accurate one due to cost and ease of solution considerations.

Mathematical Models • Relate decision variables (controllable inputs) with fixed or variable parameters (uncontrollable inputs) • Frequently seek to maximize or minimize some objective function subject to constraints • Are said to be stochastic if any of the uncontrollable inputs is subject to variation, otherwise are deterministic • Generally, stochastic models are more difficult to analyze. • The values of the decision variables that provide the mathematically-best output are referred to as the optimal solution for the model.

Body of Knowledge • The body of knowledge involving quantitative approaches to decision making is referred to as • Management Science • Operations research • Decision science • It had its early roots in World War II and is flourishing in business and industry with the aid of computers

Transforming Model Inputs into Output Uncontrollable Inputs (Environmental Factors) Output (Projected Results) Controllable Inputs (Decision Variables) Mathematical Model

Example: Project Scheduling Consider the construction of a 250-unit apartment complex. The project consists of hundreds of activities involving excavating, framing, wiring, plastering, painting, land-scaping, and more. Some of the activities must be done sequentially and others can be done at the same time. Also, some of the activities can be completed faster than normal by purchasing additional resources (workers, equipment, etc.).

Example: Project Scheduling • Question:What is the best schedule for the activities and for which activities should additional resources be purchased? How could management science be used to solve this problem? • Answer: Management science can provide a structured, quantitative approach for determining the minimum project completion time based on the activities' normal times and then based on the activities' expedited (reduced) times.

Example: Project Scheduling • Question: What would be the decision variables of the mathematical model? The objective function? The constraints? • Answer: • Decision variables: which activities to expedite and by how much, and when to start each activity • Objective function: minimize project completion time • Constraints: do not violate any activity precedence relationships and do not expedite in excess of the funds available.

Example: Project Scheduling • Question: Is the model deterministic or stochastic? • Answer: Stochastic. Activity completion times, both normal and expedited, are uncertain and subject to variation. Activity expediting costs are uncertain. The number of activities and their precedence relationships might change before the project is completed due to a project design change.

Example: Project Scheduling • Question: Suggest assumptions that could be made to simplify the model. • Answer: Make the model deterministic by assuming normal and expedited activity times are known with certainty and are constant. The same assumption might be made about the other stochastic, uncontrollable inputs.

Data Preparation • Data preparation is not a trivial step, due to the time required and the possibility of data collection errors. • A model with 50 decision variables and 25 constraints could have over 1300 data elements! • Often, a fairly large data base is needed. • Information systems specialists might be needed.

Model Solution • The “best” output is the optimal solution. • If the alternative does not satisfy all of the model constraints, it is rejected as being infeasible, regardless of the objective function value. • If the alternative satisfies all of the model constraints, it is feasible and a candidate for the “best” solution.

Computer Software • A variety of software packages are available for solving mathematical models. • a) Management Scientist Software (attached to the text book) • b) QSB and Spreadsheet packages such as Microsoft Excel

Model Testing and Validation • Often, goodness/accuracy of a model cannot be assessed until solutions are generated. • Small test problems having known, or at least expected, solutions can be used for model testing and validation. • If the model generates expected solutions, use the model on the full-scale problem. • If inaccuracies or potential shortcomings inherent in the model are identified, take corrective action such as: • Collection of more-accurate input data • Modification of the model

Report Generation • A managerial report, based on the results of the model, should be prepared. • The report should be easily understood by the decision maker. • The report should include: • the recommended decision • other pertinent information about the results (for example, how sensitive the model solution is to the assumptions and data used in the model)

Implementation and Follow-Up • Successful implementation of model results is of critical importance. • Secure as much user involvement as possible throughout the modeling process. • Continue to monitor the contribution of the model. • It might be necessary to refine or expand the model.

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.

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

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).

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

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.

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

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

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

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

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

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

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.

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

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

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

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

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

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

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.

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

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

Linear Programming (LP)

Linear Programming (LP) Problem • The maximization or minimization of some quantity is the objective in all linear programming problems. • All LP problems have constraints that limit the degree to which the objective can be pursued. • A feasible solution satisfies all the problem's constraints. • An optimal solution is a feasible solution that results in the largest possible objective function value when maximizing (or smallest when minimizing). • A graphical solution method can be used to solve a linear program with two variables.

Linear Programming (LP) Problem • If both the objective function and the constraints are linear, the problem is referred to as a linear programming problem. • Linear functions are functions in which each variable appears in a separate term raised to the first power and is multiplied by a constant (which could be 0). • Linear constraints are linear functions that are restricted to be "less than or equal to", "equal to", or "greater than or equal to" a constant.

NEW MEXICO INSTITUTE OF MINING AND TECHNOLOGY