- MNG 2201 – M ANAGEMENT S CIENCE Troy J Wishart

A SSUME THE P OSITION

M ANAGEMENT S CIENCE  Lecture Times  Mondays 5:15 – 7:10  Wednesdays 8:15 – 9:10  Tutorial Times – 5 hours

M ANAGEMENT S CIENCE  Lecture Notes  Main Text - Taylor, W.B. (2007) Introduction to Management Science. 9 th edition. Pearson Prentice Hall.  Power Point Presentations  Can be downloaded from: 

Death and Life is in the Power of the Tongue… I am getting an ‘A’ in this Course We Believe that

I NTRODUCTION TO Lecture 1 M ANAGEMENT S CIENCE

D EFINITION  Management Science (MS), an approach to managerial decision making that is based on the scientific method and makes extensive use of quantitative analysis.

D EFINITION  A Scientific Approach to solving management problems  Help managers make better decisions.  Known as Operations Research (OR)  Both terms are used interchangeably.

H ISTORY  The Scientific Management Revolution began in the early 1900s,  Initiated by Frederic W. Taylor,  It provided the foundation for MS/OR.

H ISTORY  Both originated during the World War II period.  Operations Research Teams were formed to deal with Strategic And Tactical Problems faced by the military.

H ISTORY  These teams, which often consisted of people with Diverse Specialties  (e.g. Mathematicians, Engineers, And Behavioural Scientists),  After the war, - continued their research on quantitative approaches to decision making.

P ROBLEM S OLVING  Problem Solving can be defined as the process of identifying a difference between some actual and some desired state of affairs and then taking action to resolve the difference.

P ROBLEM S OLVING Steps to Problem Solving… 1. Identify and Define the Problem 2. Determine the set of alternative solutions 3. Determine the criterion or criteria that will be used to evaluate the alternatives 4. Evaluate the alternatives

P ROBLEM S OLVING Steps to Problem Solving… 5. Choose an alternative 6. Implement the selected alternative 7. Evaluate the results, and determine if a satisfactory solution had been obtained.

D ECISION M AKING  Decision Making is the term generally associated with the first five steps of the problem-solving process.  Decision making ends with the choosing of an alternative, which is the act of making a decision.

D ECISION M AKING P ROBLEM S OLVING &

D ECISION M AKING P ROBLEM S OLVING Example – Step 1 & 2  Problem: Graduated & looking for a job - satisfying career  Alternatives: Job Offers..  Company located in Rochester, New York  Company located in Dallas, Texas  Company located in Greensboro, North Carolina.  Company located in Pittsburgh, Pennsylvania &

 Step 3 - determine the Criterion or Criteria to evaluate alternatives  S ingle Criterion Decision Problems - Problems in which the objective is to find the best solution with respect to one criterion  Multi-criteria Decision Problems – Problems that involve more than one criterion. D ECISION M AKING P ROBLEM S OLVING &

D ECISION M AKING P ROBLEM S OLVING Example – Criterion Criteria  Single Criterion - “Best” criterion is the starting salary of the each job.  Multi-Criteria - Location of Job & potential for advancement &

D ECISION M AKING P ROBLEM S OLVING Example – Step 4 Evaluation & Alternatives Starting Salary Potential for Advancement Job Location Rochester$28,500AverageFair Dallas$26,000ExcellentAverage Greensboro$26,000GoodExcellent Pittsburg$26,000AverageGood

D ECISION M AKING P ROBLEM S OLVING Example – Step 5 – Choose  It is now time to make a choice among the alternatives – Decision.  Alternative 3 seems the best and is therefore referred to as the decision  This completes the decision making process. &

D ECISION M AKING P ROBLEM S OLVING & Define Problem Identify the Alternatives Determine the Criteria Evaluate the Alternatives Choose an Alternative Implement the Decision Evaluate the Results Decision Making Problem Solving

D ECISION M AKING Q UANTITATIVE A NALYSIS &

D ECISION M AKING Q UANTITATIVE A NALYSIS  The decision-making process may take on two basic forms: 1.Quantitative 2.Qualitative. &

D ECISION M AKING Q UANTITATIVE A NALYSIS  Qualitative Analysis - based primarily on the manager’s judgement and experience;  It includes the manager’s intuitive “feel” for the problem  It is more an Art than a Science.  It used when the problem is Relatively Simple. &

D ECISION M AKING Q UANTITATIVE A NALYSIS  Quantitative Analysis is used if the problem is sufficiently complex.  Analyst will:  Concentrate on the quantitative facts or data associated with the problem  Develop mathematical expressions -  that describe the objectives, constraints, and other relationships that exist in the problem  Make a recommendation using one or more quantitative methods,. &

D ECISION M AKING Q UANTITATIVE A NALYSIS  The manager must be:  Knowledgeable of both in qualitative and quantitative decision-making sources of recommendations  Able to ultimately combine the two sources and to make the best possible decision. &

D ECISION M AKING Q UANTITATIVE A NALYSIS Reasons why the quantitative approach might be used in decision making: 1. The Problem is Complex  The manager cannot develop a good solution without the aid of quantitative analysis. 2. The Problem is Very Important  (e.g. a great deal of money is involved), and the manager desires a thorough analysis before attempting to make a decision. &

D ECISION M AKING Q UANTITATIVE A NALYSIS Reasons why the quantitative approach might be used in decision making: 3. The Problem is New,  The manager has no previous experience to draw on. 4. The Problem is Repetitive,  the manager saves time and effort by relying on quantitative procedures to make routine decision recommendations. &

D ECISION M AKING Q UANTITATIVE A NALYSIS &  Qualitative Analysis

D ECISION M AKING Q UANTITATIVE A NALYSIS &  Quantitative Analysis

M ODEL D EVELOPMENT Q UANTITATIVE A NALYSIS &

M ODEL D EVELOPMENT Q UANTITATIVE A NALYSIS  Models are representations of real objects or situation. The various forms are: 1. Iconic Models – physical replicas of real objects.  E.g. scale model of an airplane or a child’s toy truck. 2. Analog Models – Models that are physical in form but do not have the same physical appearance as the object being modeled.  E.g. the speedometer & thermometer &

Q UANTITATIVE A NALYSIS 3. Mathematical Models – a model that represents a problem by a system of symbols and mathematical relationships or expressions.  It is a critical part of quantitative approach to decision making.  E.g. A profit function for the sale of a product $10: - P = 10x & M ODEL D EVELOPMENT

Q UANTITATIVE A NALYSIS Purpose of Models  It enables us to make inferences about the real situation by studying and analyzing the model. Example…  An iconic model of a new airplane can tested in a wind tunnel,  A mathematical model can be used to calculate profit with specified quantity of a product.  P = 10x for 3 units - P = 10(3) = $30 & M ODEL D EVELOPMENT

Q UANTITATIVE A NALYSIS Advantages of Models 1. Requires less time and is less expensive than experimenting with the real object or situation. 2. It reduces the risk associated with experimenting with the real situation,  E.g. A Large Investment. & M ODEL D EVELOPMENT

Q UANTITATIVE A NALYSIS  However, the value of model-based conclusions is dependent on how well the model represents the real situation.  The Problem Definition phase leads to a:  Specific Objective, such as Maximization of Profit or Minimization of Cost,  Restrictions or Constraints, such as Production Capacities. & M ODEL D EVELOPMENT

Q UANTITATIVE A NALYSIS  The success of a mathematical model and quantitative approach will depend heavily on accurately expressing :  The Objective and Constraints in terms of a mathematical equations or relationships.  A Mathematical Expression that describes a problem’s objective is referred to as the Objective Function, & M ODEL D EVELOPMENT

Q UANTITATIVE A NALYSIS  Example - P = 10x.  A production capacity constraint could be that 5 hours are required to produce each unit and there are only 40 hours available per week.  Let x indicate the number of units produced each week so that: 5x≤40. & M ODEL D EVELOPMENT

Q UANTITATIVE A NALYSIS  A complete mathematical model for this production problem is  Maximize P = 10x  Subject to (s.t.)  5x≤40  x≥0  This model is an example of linear programming & M ODEL D EVELOPMENT Constraints Objective Function

Q UANTITATIVE A NALYSIS  Models can contain environmental factors that are Controllable or Uncontrollable:  Controllable Inputs – Inputs that are controlled or determined by the decision maker – e.g. Quantity x.  Controllable inputs are the decision alternatives specified by a manager and are also referred to as Decision variables. & M ODEL D EVELOPMENT

Q UANTITATIVE A NALYSIS  Uncontrollable Inputs – Environmental factors which can affect both the objective function and the constraints.  E.g. Profit per unit $10, 5 hours and production capacity -40hrs per week.  Uncontrollable inputs can either be known exactly or be uncertain and subject to variation. & M ODEL D EVELOPMENT

Q UANTITATIVE A NALYSIS  Deterministic Model If all uncontrollable inputs to a model are known and cannot vary, e.g. Corporate Income Tax.  The distinguishing feature of a deterministic model is that the uncontrollable inputs are known in advance. & M ODEL D EVELOPMENT

Q UANTITATIVE A NALYSIS  Stochastic or Probabilistic Model, If any of the uncontrollable inputs are uncertain or subject to variation e.g. Demand.  The distinguishing feature of a stochastic model is that the value of the output cannot be determined even if the value of the controllable input is known, because the specific values of the uncontrollable inputs are unknown. In this respect, stochastic models are often more difficult to analyze. & M ODEL D EVELOPMENT

Q UANTITATIVE A NALYSIS & M ODEL D EVELOPMENT Flowchart showing the process of transforming (Production) Model Inputs into Output

D ATA P REPARATION Q UANTITATIVE A NALYSIS

 Data in this sense refer to the values of the uncontrollable inputs to the model.  All uncontrollable inputs must be specified before analyzing model and recommend decision/solution.  E.g. $10 per unit, 5 hours per unit for production time, and 40 hours for production capacity.  Analysts combines model development and data preparation into one step if the model is relatively small and the uncontrollable inputs are few. D ATA P REPARATION

 If the uncontrollable inputs or data is unavailable the analyst will usually develop a General Notation: c = profit per unit a = production time in hours per unit b = production capacity in hours  As such the following general model is developed: Max cx s.t. ax ≤ b x ≥ 0 D ATA P REPARATION

M ODEL S OLUTION Q UANTITATIVE A NALYSIS

 The analyst will attempt to identify the values of the decision variables that provide the “best” output for the model.  This is referred to as the Optimal Solution for the model. M ODEL S OLUTION

 To determine the best value of x :  Trial-and-Error approach where the model is used to test and evaluate various decision alternatives.  Infeasible - If a particular decision alternative does not satisfy one or more of the model constraints.  Feasible If all constraints are satisfied, it becomes a candidate for the “best” solution or recommended decision. M ODEL S OLUTION

 The disadvantage of the trial-and-error approach is that it may not necessarily and being inefficient in terms of requiring numerous calculations if many decision alternatives are tried. M ODEL S OLUTION

R EPORT G ENERATION Q UANTITATIVE A NALYSIS

 An important part of the quantitative analysis process.  It is essential that the results of the model appear in a managerial report  The Report should be easily understood by the decision maker. R EPORT G ENERATION

 The report should include:  The recommended decision  Other pertinent information about the model results that can help to the decision maker. R EPORT G ENERATION

I MPLEMENTATION Q UANTITATIVE A NALYSIS

 It is the responsibility of the manager to integrate the quantitative solution with qualitative considerations.  The manager should oversee implementation and follow-up evaluation of the decision. I MPLEMENTATION

 User Involvement is one of the most effective ways to ensure a successful implementation.  If the user feels he/she has been involved they are much more likely to enthusiastically implement the results. I MPLEMENTATION

M ODELS OF C OST, R EVENUE, AND P ROFIT

 Volume Models are some of the most basic quantitative models  E.g those involving the relationship between a volume variable-such as production volume or sales volume-and cost, revenue, or profit. M ODELS OF C OST, R EVENUE, AND P ROFIT

 Financial planning, production planning, sales quotas, and other areas of decision making can benefit from such cost, revenue and profit models. M ODELS OF C OST, R EVENUE, AND P ROFIT

C OST AND V OLUME M ODELS

 The cost of manufacturing or producing a particular product is a function of the volume produced. C OST AND V OLUME M ODELS

 This cost can usually be defined as a sum of two costs:  Fixed Cost – the portion of the total cost that does not depend on the production volume.  Variable Cost – the portion of the total cost that is dependent on and varies with the production volume. C OST AND V OLUME M ODELS

 Example, the setup cost for a production line is $3,000 (fixed cost), variable labour and material costs are $2 for each unit produced.  The cost-volume model for producing ( x ) units would be written as  C( x ) = x  Where  x = production volume in units  C( x ) = total cost of producing x units C OST AND V OLUME M ODELS

 Marginal Cost is the rate of change of the total cost with respect to volume.  It is the cost increase associated with a one-unit increase in the production volume. E.g. $2 as per model. C OST AND V OLUME M ODELS

R EVENUE AND V OLUME M ODELS

 Projected Revenue associated with selling a specified number of units can be determined through a model relationship between revenue and volume. R EVENUE AND V OLUME M ODELS

 For instance if the product above sells for $5 per unit then: R( x ) = 5 x Where x = sales volume in units R( x ) = total revenue associated with selling x units R EVENUE AND V OLUME M ODELS

 Marginal Revenue is defined as the rate of change of total revenue with respect to sales volume.  It is the increase in total revenue resulting from one-unit increase in sales volume. E.g. $5 R EVENUE AND V OLUME M ODELS

 Profit is one of the most important criteria for managerial decision making. P ROFIT V OLUME M ODELS

P ROFIT AND V OLUME M ODELS

 If only what is produce what is sold, the production volume and sales volume will be equal.  As such a profit-volume model can be developed to determine profit associated with a specified production-sales volume. P ROFIT A ND V OLUME M ODELS

 Since the total profit is total revenue minus total cost, the following model is associated with producing and selling ( x ) units: P( x ) = R( x ) – C( x ) = 5 x – ( x ) = x P ROFIT A ND V OLUME M ODELS

B REAK - EVEN A NALYSIS

 The volume that results in total revenue equaling total cost (providing $0 profit) is called the break-even point. B REAK - EVEN A NALYSIS

 If the break-even point is known a manager can quickly infer :  That a volume above the break-even point will result in profit,  While volume below the point will result in loss. B REAK - EVEN A NALYSIS

 The break-even point can be found by setting the profit expression equal to zero and soling for the production volume. P( x ) = x = 0 3 x = 3000 X = 1000  Production and sales of the product must be at least 1000 units before a profit can be expected B REAK - EVEN A NALYSIS

M ANAGEMENT S CIENCE T ECHNIQUES

 Linear Programming –  is a problem-solving approach  has been developed for situations involving maximizing or minimizing linear function  subject to linear constraints that limit the degree to which the objective can be pursued. M ANAGEMENT S CIENCE T ECHNIQUES

 Integers Linear Programming –  is an approach used for problems that can be set up as linear programs  with the additional requirement that some or all of the decision recommendations be integer values. M ANAGEMENT S CIENCE T ECHNIQUES

 Network Models – A network is a graphical description of a problem consisting of circles called nodes that are interconnected by lines called arcs.  Solves managerial problems such as transportation system design, information system design, and project scheduling. M ANAGEMENT S CIENCE T ECHNIQUES

 Project Management: PERT/CPM – The PERT (Program Evaluation and Review Technique) and CPM (Critical Path Method) techniques help managers carry out their project scheduling responsibilities. M ANAGEMENT S CIENCE T ECHNIQUES

 Inventory Models –  are used by managers faced with the dual problem of maintaining sufficient inventories to meet demand for goods  and, at the same time, incurring the lowest possible inventory holding costs. M ANAGEMENT S CIENCE T ECHNIQUES

 Waiting-Line or Queuing Models –  have been developed to help managers understand  and make better decisions concerning the operation of systems involving waiting lines. M ANAGEMENT S CIENCE T ECHNIQUES

 Computer Simulation –  is a technique used to model the operation of a system over time.  This technique employs a computer program to model the operation of systems involving waiting lines. M ANAGEMENT S CIENCE T ECHNIQUES

 Decision Analysis –  can be used to determine optimal strategies in situations involving several decisions alternatives  and an uncertain or risk filled pattern of events. M ANAGEMENT S CIENCE T ECHNIQUES

 Goal Programming –  is a technique for solving multi-criteria decision problems, usually within the framework of linear programming. M ANAGEMENT S CIENCE T ECHNIQUES

 Analytic Hierarchy Process –  A multi-criteria decision making technique that permits the inclusion of subjective factors in arriving at a recommended decision. M ANAGEMENT S CIENCE T ECHNIQUES

 Forecasting –  forecasting methods are techniques that can be used to predict future aspects of a business operation. M ANAGEMENT S CIENCE T ECHNIQUES

 Markov-Process Models –  Markov-process models are useful in studying the evolution of certain systems over repeated trials.  For example, Markov have been used to describe the probability that a machine that is functioning in one period will continue to function or break down in another period. M ANAGEMENT S CIENCE T ECHNIQUES

 Dynamic Programming –  is an approach that allows us to break up a large problem in such a fashion that once all the smaller problems have been solved, we are left with an optimal solution to the large problem. M ANAGEMENT S CIENCE T ECHNIQUES

 Calculus-Based Procedures –  are used to solve problems that involve a nonlinear objective function and/or constraints involving nonlinear functions of the decision variables. M ANAGEMENT S CIENCE T ECHNIQUES