MANAGEMENT SCIENCE LINEAR PROGRAMMING APPLICATIONS LP APPLICATIONS In

MANAGEMENT SCIENCE LINEAR PROGRAMMING APPLICATIONS

LP APPLICATIONS In a recent survey of Fortune 500 firms, 85% of those responding said that they used linear programming. LP models that are most often applied to real applications. purchase television ads schedule postal workers manage Pension Funds. Management Science Modeling, Albright, Winston, 4 th Ed.

Advertising Models Many companies spend enormous amounts of money to advertise their products. Reaching large numbers of various groups of potential customers Keeping their advertising costs as low as possible. Management Science Modeling, Albright, Winston, 4 th Ed.

CASE 1 ADVERTISING PLAN Management Science Modeling, Albright, Winston, 4 th Ed.

The General Flakes Company sells a brand of low-fat breakfast cereal that appeals to people of all age groups and both genders. The company advertises this cereal in a variety of 30 second television ads, and these ads can be placed in a variety of television shows. The ads in different shows vary by cost— some 30 -second slots are much more expensive than others— and by the types of viewers they are likely to reach. The company has segmented the potential viewers into six mutually exclusive categories: males age 18 to 35, males age 36 to 55, males over 55, females age 18 to 35, females age 36 to 55, and females over 55. A rating service can supply data on the numbers of viewers in each of these categories who will watch a 30 -second ad on any particular television show. Each such viewer is called an exposure. The company has determined the required number of exposures it wants to obtain for each group. It wants to know how many ads to place on each of several television shows to obtain these required exposures at minimum cost. The data on costs per ad, numbers of exposures per ad, and minimal required exposures are listed in the table(the next slide), where numbers of exposures are expressed in millions, and costs are in thousands of dollars. What should the company do? Management Science Modeling, Albright, Winston, 4 th Ed.

The General Flakes Company Game of Thrones Walking The Sports The Real Dead Simpsons Center World Lifetime movie CNN Min Required Black exposure Mirror s Men 18 -35 5 6 5 0. 7 0. 1 3 60 Men 36 -55 3 5 2 0. 5 0. 2 0. 1 0. 2 5 60 Men >55 Women 1835 Women 3655 1 3 0 0 0. 3 4 28 6 1 4 0. 1 0. 9 0. 6 0. 1 3 60 4 1 2 0. 1 1. 3 0. 2 5 60 Women >55 2 1 0 0. 4 0. 3 4 28 Cost per ad 140 100 80 9 13 15 8 140 Company wants to know how many ads to place on each of several television shows to obtain these required exposures at

Worker Scheduling Models Many organizations must determine how to schedule employees to provide adequate service. Management Science Modeling, Albright, Winston, 4 th Ed.

CASE 2 WORKER SCHEDULING Management Science Modeling, Albright, Winston, 4 th Ed.

Post Office 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 the table (next slide). Union rules state that each full-time employee must work five consecutive days and then receive two days off. For example, an employee who works Monday to Friday must be off on 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. Management Science Modeling, Albright, Winston, 4 th Ed.

Post Office Minimum Number of Employees Day of week Required Mon 17 Tue 13 Wed 15 Thu 19 Fri 14 Sat 16 Sun 11 Mon Tue Wed Thu Fri Sat Sun Union rules state that each full-time employee must work five consecutive days and then receive two days off. For example, an employee who works Monday to Friday must be off on Saturday and Sunday. Mon Tue Wed Thu Fri Sat Sun * * * * * * * * *

Financial Models The majority of optimization examples described in management science textbooks are in the area of operations: scheduling, blending, logistics, aggregate planning, and others. Optimization and other management science methods have also been applied successfully in a number of financial areas, and they deserve recognition. Capital Budgeting Revenue Management Fund Management Portfolio Management Science Modeling, Albright, Winston, 4 th Ed.

CASE 3 FINANCIAL MODEL EXAMPLE: Managing a Pension Fund Management Science Modeling, Albright, Winston, 4 th Ed.

Armco Inc. James Judson is the financial manager in charge of the company pension fund at Armco Inc. James knows that the fund must be sufficient to make payments listed in the table. Each payment must be made on the first day of each year. James is going to finance these payments by purchasing bonds. It is currently January 1, 2010, and three bonds are available for immediate purchase. The prices and coupons for the bonds are given in the following table. James must decide how much cash to allocate to meet the initial $11000 payment and buy enough bonds to make future payments. He knows that any excess cash on hand can earn an annual rate of 4% in a fixed-rate account. How should he proceed? Management Science Modeling, Albright, Winston, 4 th Ed.

Armco Inc. PAYMENTS 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 $11, 000 $12, 000 $14, 000 $15, 000 $16, 000 $18, 000 $20, 000 $21, 000 $22, 000 $24, 000 $25, 000 $30, 000 $31, 000 PRICES OF BOND AND EARNINGS BY YEAR Year 2010 (price) 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 Bond 1 $980 $60 $60 $1, 060 Bond 2 $970 $65 $65 Bond 3 $1, 050 $75 $75 He knows that any excess cash on hand can earn an annual rate of 4% in a fixed-rate account 2021 2022 2023 2024 $65 $1, 065 $75 $75 $75 $1, 075

The End of WEEK 4