1 1 slide chapter 4 linear programming applications in marketing, finance, and operations marketing...

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Chapter 4 Linear Programming Applications

in Marketing, Finance, and Operations

Marketing Applications: Media selection

Financial Applications: Portfolio selection

Operations Management Applications

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Media Selection• One application of linear programming in

marketing is media selection.• LP can be used to help marketing managers

allocate a fixed budget to various advertising media.

• The objective is to maximize reach, frequency, and quality of exposure.

• Restrictions on the allowable allocation usually arise during consideration of company policy, contract requirements, and media availability.

Marketing Applications

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The Camden County Chamber of Commerce (CCCC) would like to promote the region to area businesses. Advertising alternatives include television, radio and internet. Estimates of audience reached and costs per advertisement and maximum media usage limitations are shown below:

Television Radio InternetAudience/adv. 100,000 18,000 40,000Cost/adv. $2,000 $300 $600 Maximum usage 10 20 10

To ensure a balance use of advertisement media, television advertisements must not exceed 50% of the total number authorized. In addition, internet ads should account for at least 10% of the total advertisements used. CCCC has a total budget of $18,000. Determine the number of each type of media to use such that the number of audience reached is maximized.

If CCCC had an additional $100, what is the net increase of audience reached. Would the allocation of the media stay the same?

Marketing Applications: Media Selection

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Media Selection

TV = number of television advertisements to use

RA = number of radio advertisements to use

IN = number of internet advertisements to use

Define the Objective Function

Define the Decision Variables

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Media Selection

Define the Constraints

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Financial Applications

LP can be used in financial decision-making that involves capital budgeting, make-or-buy, asset allocation, portfolio selection, financial planning, and more.

Portfolio selection problems involve choosing specific investments – for example, stocks and bonds – from a variety of investment alternatives.This type of problem is faced by managers of banks, mutual funds, and insurance companies.The objective function usually is maximization of expected return or minimization of risk.

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Portfolio Selection

Willie Maykit, who recently inherited $1,000,000 from his late aunt, would like to invest all his inheritance in a mix of 4 investment instruments, each with characteristics as listed below:Investment Price Annual Return Maximum Risk Type /unit /unit Investment Factor A $60 $3 $500,000 0.7 B $25 $5 $200,000 0.8

C $20 $5 $300,000 1.2

D $40 $8 $250,000 1.4

Due to its low risk, Willie would like to invest at least 30% of the total dollar investments in Type A. Furthermore, he specified that the dollar average weighted risk factor of his investments should not exceed 1.1Determine the number of units of each investment type to buy so that Willie will maximize his investment returns. How many dollars should Willie invest in each of the 4 types of investments?

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Portfolio Selection


A =B =C =D =


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Portfolio Selection

Define the ConstraintsTotal investment amount limited to principal

30% of the total dollar investments in Type A

Risk factor of his investments should not exceed 1.1

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Portfolio Selection

Define the Constraints (continued)

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Operations Management Applications

LP can be used in operations management to aid in decision-making about product mix, production scheduling, staffing, blending, inventory control, capacity planning, and other issues.An important application of LP is multi-period planning such as production scheduling.Usually the objective is to establish an efficient, low-cost production schedule for one or more products over several time periods.Typical constraints include limitations on production capacity, labor capacity, storage space, and more.

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A MANUFACTURER HAS TWO PRODUCTS, BOTH OF WHICH ARE MADE IN TWO STEPS BY MACHINES 1 AND 2. THE PROCESS TIMES FOR THE TWO PRODUCTS ON THE TWO MACHINES ARE AS FOLLOWS:PRODUCT MACHINE A (hrs). MACHINE B (hrs) 1 4 5 2 5 2FOR THE COMING PERIOD, MACHINE A HAS 100 HOURS AVAILABLE AND MACHINE B HAS 80 HOURS AVAILABLE. THE PROFIT FOR PRODUCT 1 IS $10 PER UNIT AND PRODUCT 2 IS $5 PER UNIT. DEFINE THE DECISION VARIABLES AND FORMULATE THE LP PROBLEM.

PRODUCT MIX

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PRODUCT MIX


Objective Function

Constraints

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PRODUCT MIX

A MANUFACTURER HAS TWO PRODUCTS, BOTH OF WHICH ARE CAN BE MADE BY EITHER BY MACHINES 1 AND 2. THE PROCESS TIMES FOR THE TWO PRODUCTS ARE AS FOLLOWS:PRODUCT MACHINE A (hrs). MACHINE B (hrs) 1 4 5 2 5 2FOR THE COMING PERIOD, MACHINE A HAS 100 HOURS AVAILABLE AND MACHINE B HAS 80 HOURS AVAILABLE. THE PROFIT FOR PRODUCT 1 IS $10 PER UNIT AND PRODUCT 2 IS $5 PER UNIT. DEFINE THE DECISION VARIABLES AND FORMULATE THE LP PROBLEM.

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PRODUCT MIX


Objective Function

Constraints

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Workforce Assignment

Due to recent budget cuts, Gotham City Police department would like to better utilize its police force. The minimum required number of police officers for each time period is as follows: Time Period Minimum Patrol OfficersMidnight-4 a.m 64-8 a.m. 48-noon 1412-4 p.m. 84-8 p.m. 128-midnight 16

Police officers report for duty at midnight or each of the following 4 hour intervals and they work continuously fir 8 hours. What is the minimum number of officers needed per day?

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Define the Constraints (continued)

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Blending Problem

BURN-CLEAN OIL COMPANY PRODUCES REGULAR AND PREMIUM GASOLINE. BOTH TYPES OF GASOLINE ARE PRODUCED BY BLENDING TWO TYPES OF CRUDE OILS. THE CRUDE OILS CONTAIN TWO INGREDIENTS, NAMELY A AND B. THE PERCENTAGES OF INGREDIENTS A AND B, AND THE COST PER GALLON OF EACH TYPE OF THE CRUDE OIL ARE AS FOLLOWS: CRUDE OIL COST INGREDIENT A INGREDIENT B

1 $0.20 20% 60% 2 $0.30 50% 30%

EACH GALLON OF REGULAR MUST CONTAIN AT LEAST 40% OF INGREDIENT A, AND EACH GALLON OF PREMIUM CAN CONTAIN AT MOST 50% OF INGREDIENT B. THE DAILY DEMAND FOR REGULAR AND PREMIUM GASOLINE ARE 800,000 GALLONS AND 500,000 GALLONS, RESPECTIVELY. FORMULATE THE LP PROBLEM.

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Blending Problem

Define the decision variables

Define the objective function

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Blending Problem

Define the constraints

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MULTIPERIOD PRODUCTION PLANNING MODEL

XYZ CO. USES A 3 MONTH PLANNING HORIZON TO PLAN THE PRODUCTION OF WIDGETS. INVENTORY AT THE END OF MARCH IS 500 UNITS. MANAGEMENT WANTS AT LEAST 300 UNITS IN INVENTORY AT THE END OF JUNE. THE INVENTORY HOLDING COST IS $2.00/UNIT/MONTH. PRODUCTION RATE IS 2 UNITS / HOUR. EACH WIDGET REQUIRES 5 SQ FT. AND THE WAREHOUSE STORAGE CAPACITY IS 10,000 SQ FT. USE THE FOLLOWING DATA TO FORMULATE THE LP MODEL TO FIND THE OPTIMAL PRODUCTION SCHEDULE THAT MEETS THE DEMAND.Month Demand Prod cost/unit Prod. capacityApril 600 units $ 10 1000 hrsMay 1500 15 800June 2500 15 600

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Define the decision variables

Define the objective function

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Define the constraints

1 1 slide chapter 4 linear programming applications in marketing, finance, and operations marketing...

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