Decision Making Process

Management ScienceIntroduction

Management Science/Operations Research

Synonyms: Operations Research, Management Science, Quantitative Analysis, Decision Science

History: Early 1900s:Frederic Taylor provided the

foundation for the use of quantitative methods in management.

About 1947: Modern development of OR/MS during world war II

Summer 1947: George Dantzig developed the simplex method to solve linear programming problems.

First conference on linear programming

First book of operations research

Management Science: is a scientific approach for solving management problems.

Applications:OrganizationNature of

ApplicationAnnual Saving

United AirlinesSchedule shift work at reservation offices and airports to meet customer needs with minimum cost

$6 millions

CaltransUsed operations research to complete the repair process of the 405 freeway in shorter time after the 1994 earthquake

San Francisco Police Department

A system was designed to schedule police officers in such a way that minimize the cost of police operation, and maintain a high level of citizen safety.

11 millions +

$3 millions increase in the traffic citation revenue

IBMDevelop a Spare parts inventory system to improve service support

$750 millions

Citgo Petroleum

Corp.

Optimize refinery operations and the supply distribution

$70 millions

HP Redesign the sizes and locations of buffers in a printer production line to meet production goals

$280 millions

Research workDetermining the optimal fiber orientations that maximizes the strength of a composite material

Taco BellSchedule employees to provide desired customer service at minimum cost

$13 millions

Current Professional Organizations:

• The Institute for Operations Research and Management Science (Informs)

• The Decision Science Institute (DSI)

• Colleges offering degrees in Operations Research/Management Science

Jobs available for the graduates of OR/MS:• Operations Research analyst is one of the

fastest growing occupations for careers requiring B.Sc. degrees. The Bureau of Labor Statistics predicts growth from 57,000 jobs in 1990 to 100,000 in 2005, i.e. 73% increase.

What can management ScienceWhat can management ScienceTechniques do?Techniques do?

1. System Design– capacity– location– arrangement of departments– product and service planning– acquisition and placement of

equipment

Decision MakingDecision Making2. System operation– personnel– Inventory– Scheduling– Project management

Quality assurance–

ModelsModels

A model is an abstraction of reality.

– Iconic– Analog– Mathematical

What are the pros and cons of models?

Tradeoffs

Types of Models

Iconic Models: Examples - scale model of airplane, toy truck etc.

Analog Models: models do not have the same physical appearance of the object. Examples – The speedometer is an analog model representing the speed of the automobile, a thermometer is an analog model representing temperature.

Mathematical Model: A system of mathematical relationships.

Models Are Beneficial

• Easy to use, less expensive

• Increase understanding of the problem

• Enable “what if” questions

• Consistent tool

• Power of mathematics

Quantitative ApproachesQuantitative Approaches

• Linear programming

• Integer programming

• Nonlinear programming

• Goal programming

• Queuing Techniques

• Project models

• Statistical models

Systems ApproachSystems Approach

“The whole is greater than the sum of the parts.”

SuboptimizationSuboptimization

Pareto PhenomenonPareto Phenomenon

• A few factors account for a high percentage of the occurrence of some event(s).

• 80/20 Rule - 80% of problems are caused by 20% of the activities.

How do we identify the vital few?

Quantitative Analysis Approach

1. Identify Problem

2. Problem definition/Problem Statement

3. Model development (Problem Formulation)

4. Model Solution

5. Data Preparation

Quantitative Analysis Approach (continued)

6. Model Solution-Graphical Approach

-Computer Approach

7. Report Generation

8. Result implementation

Mathematical Model Development:

• Step 1: Understand the problem.

• Step 2: Define the controllable inputs (decision variables)

• Step 3: Identify and model the Criterion (objective function)

• Step 4: Identify and model the restrictions (constraints)

• Step 5: Identify the upper/lower bounds.

Product Mix

Example- Problem # 13- Pg. 41 The Electrotech Corporation manufactures twoindustrial-

sized electrical devices: generators and alternators. Both of the products require wiring and testing during the assembly process. Each generator requires 2 hours of wiring and 1 hour of testing and can be sold for a $250 profit. Each alternator requires 3 hours of wiring and 2 hours of testing and can be sold for a $150 profit. There are 260 hours of wiring time and 140 hours of testing time available in the next production period and Electrotech would like to maximize profit.

a) Formulate an LP model for this problem.

b) Sketch the feasible region for this problem.

c) Determine the optimal solution to this problem.

Example – 2.5 – Pg. 20 Blue Ridge Hot Tubs manufactures and sells two models

of hot tubs: the Aqua-Spa and the Hydro-Lux. Howie Jones, the owner and manager of the company, needs to decide how many of each type of hot tub to produce during his next production cycle. Howie buys prefabricated fiberglass hot tub shells form a local supplier and adds the pump and tubing to the shells to create his hot tubs. (This supplier has the capacity to deliver as many hot tub shells as Howie needs.) Howie installs the same type of pump into both hot tubs. He will have only 200 pumps available during his next production cycle. From a manufacturing standpoint, the main difference between two models of hot tubs is the amount of tubing and labor required. Each Hydro-Lux requires 6 hours of labor and 16 feet of tubing available during the next production cycle. Howie earns a profit of $350 on each Aqua-Spa he sells and $350 on each Aqua-Spa he sells and $300 on each Hydro-Luxes should Howie produces if he wants to maximize his profits during the next production cycle?

Example 3-1/Practical MSCI

The Monet Company produces four type of picture frames, which we label 1, 2, 3, 4.

• The four types of frames differ with respect to size, shape and materials used.

• Each type requires a certain amount of skilled labor, metal, and glass as shown in this table. The table lists the unit selling price Monet charges for each type of frame.


Labor

hr

Metal

ounces

Glass

Ounces

Sale

Price

Frame 124628.50

Frame 212212.50

Frame 331129.25

Frame 422221.50

Example 3-1/Practical MSCI• During the coming week Monet can

purchase up to 4000 hours of skilled labor, 6000 ounces of metal, and 10,000 ounces of glass.

• The unit costs are $8.00 per labor hour, $0.50 per ounce of metal, and $0.75 per ounce of glass.

• Also, market constraints are such that it is impossible to sell more than 1000 type 1 frames, 2000 type 2, frames, 500 type 3 frames, and 1000 type 4 frames.

• The company wants to maximize its weekly profit.


• In the traditional algebraic solution method we first identify the decision variables.

• In this problem they are the number of frames of type 1, 2, 3, and 4 to produce. We label these x1, x2, x3, x4.

• Next we write total profit and the constraints in terms of the x’s.

• Finally, since only nonnegative amounts can be produced, we add explicit constraints to ensure that the x’s are nonnegative.

Example 3-1/Practical MSCI• The resulting algebraic formulation is

shown below:Maximize 6x1 + 2x2 + 4x3 + 3x4 (profit objective)Subject to 2x1 + x2 + 3x3 + 2x4 4000 (labor constraint)

4x1 + 2x2 + x3 + 2x4 10,000 (glass constraint)

x1 1000 (frame 1 sales constraints)




x1, x2, x3, x4 0 (nonnegativity constraint)

A Multiperiod Production Problem

Example 3.3 Winston/Albright Page 91

• The Pigskin Company produces footballs.• Pigskin must decide how many footballs to

produce each month. It has decided to use a 6-month planning horizon.

• The forecasted demands for the next 6 months are 10,000, 15,000, 30,000, 35,000, 25,000 and 10,000.

• Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given month’s production to help meet the demand for that month.

Example 3.3• During each month there is enough

production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred.

• The forecasted production costs per football for the next 6 months are $12.50, $12.55, $12.70, $12.80, $12.85, and $12.95, respectively.

• The holding cost per football held in inventory at the end of the month is figured at 5% of the production cost for that month.

Example 3.3• In the traditional algebraic

formulation, the decision variables are the production quantities for the 6 months, labeled P1 through P6.

• It is convenient to let I1 through I6 be the corresponding end-of-month inventories (after the demand has occurred).

• For example, I3 is the number of footballs left over at then end of month 3. Therefore, the obvious constraints are on production and inventory storage capacities: Pj 300 and Ij 100 for each month j, 1 j 6.

Example 3.3

• In addition to these constraints, we need balance constraints that relate the P ’s and I ’s.

• In any month the inventory from the previous month plus the current production must equal the current demand plus leftover inventory.

• If Dj is the forecasted demand for month j, then the balance equation for month j is Ij-1 + Pj = Dj + Ij.

Example 3.3

• The first of these constraints, for month j = 1, uses the known beginning inventory, 50, for the previous inventory (the Ij-1 term)

• By putting all variables (P’s and I’s) on the left and all known values on the right (a standard LP convention), these balance constraints become

P1 – I1 = 100-50

I1 + P2 – I2 = 150

I2 + P3 – I3 = 300

I3 + P4 – I4 = 350

I4 + P5 – I5 = 250

I5 + P6 – I6 = 100

Employee SchedulingExample 4.1 Winston/Albright

• A post office requires different numbers of full-time employees on different days of the week.

• The number of full-time employees required each day is given in this table.

Employee Requirements for Post Office

Monday 17

Tuesday 13

Wednesday 15

Thursday 19

Friday 14

Saturday 16

Sunday 11

Example 4.1 Winston/Albright

• Union rules state that each full-time employee must work 5 consecutive days and then receive 2 days off.

• For example, an employee who works Monday to Friday must be off Saturday and Sunday.

• The post office wants to meet its daily requirements using only full-time employees.

• Its objective is to minimize the number of full-time employees that must be hired.

• To model the Post Office problem with a spreadsheet, we must keep track of the following:– Number of employees starting

work on each day of the week– Number of employees working

each day– Total number of employees

• It is important to keep track of the number of employees starting work each day, because this is the only way to incorporate the fact that workers work 5 consecutive days.

Aggregate Planning Models


• During the next four months the SureStep Company must meet (on time) the following demands for pairs of shoes: 3,000 in month 1; 5,000 in month 2; 2,000 in month 3; and 1,000 in month 4.

• At the beginning of month 1, 500 pairs of shoes are on hand, and SureStep has 100 workers.

• A worker is paid $1,500 per month. Each worker can work up to 160 hours a month before he or she receives overtime.

• A worker is forced to work 20 hours of overtime per month and is paid $13 per hour for overtime labor.

Example 4.2 Winston/Albright• It takes 4 hours of labor and $15 of

raw material to produce a pair of shoes.

• At the beginning of each month workers can be hired or fired. Each hired worker costs $1600, and each fired worker cost $2000.

• At the end of each month, a holding cost of $3 per pair of shoes left in inventory is incurred.Production in a given month can be used to meet that month’s demand.

• SureStep wants to us LP to determine its optimal production schedule and labor policy.


• To model SureStep’s problem with a spreadsheet, we must keep track of the following:– Number of workers hired, fired,

and available during each month.– Number of pairs of shoes

produced each month with regular time and overtime labor

– Number of overtime hours used each month

– Beginning and ending inventory of shoes each month

– Monthly costs and the total costs

Decision Making Process

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