Example 15.1

Static Workforce Scheduling

Example 15.2

Blending Models

Example 15.3

Logistics Model

• The optimal solution of the model is illustrated graphically. A minimum cost of $1020 is incurred by using the shipments listed. Except for these six routes listed, no other routes are used.

Example 15.4

Logistics Model

• The RedBrand Company produces tomato products at three plants.

• These products can be shipped directly to their two customers or they can first be shipped to the company’s two warehouses and then to the customers.

To Node

1 2 3 4 5 6 7

1 - 5 3 5 5 20 202 9 - 9 1 1 8 153 0.4 8 - 1 0.5 10 12

From Node 4 - - - - 1.2 2 125 - - - 0.8 - 2 126 - - - - - - 17 - - - - - 7 -

• The cost of shipping (in thousands of dollars) between each pair of points is given below. A dash indicates that RedBrand cannot ship across that arc.

Example 15.5

Aggregate Planning Models

• During the next 4 months the SureStep Shoe Company must meet (on time) the following demands for pairs of shoes: 3000 in month 1; 5000 in month 2; 2000 in month 3; and 1000 in month 4.

• At the beginning of month 1, 500 pairs of shoes are inventory, and SureStep has 100 workers. Each worker is paid $1500 per month and can work up to 160 hours a month before he or she receive overtime. (This amounts to about $9.38 per hour.)

• A worker can be forced to work up to 20 hours of overtime per month at an overtime rate of $13 per hour.

Example 15.6

A Dynamic Financial Model

Background Information

• A small toy store, Tyco, projects the monthly cash inflows listed below (in thousands of dollars) during the year 2000.

Cash Inflow Cash InflowJanuary -12 July -7February -10 August -2March -8 September 15April -10 October 12May -4 November -7June 5 December 45

Example 15.7

Integer Programming Models

• The Tatham Company is considering four investments. • The cash required for each investment and the net present value

(NPV) each investment adds to the firm are given in the table below.

Cash Required NPV AddedInvestment 1 $5,000 $16,000Investment 2 $7,000 $22,000Investment 3 $4,000 $12,000Investment 4 $3,000 $8,000

Example 15.9

Integer Programming Models

• Western wants to determine the smallest number of hubs it will need to cover all of these cities, where a city is “covered” if it is within 1000 miles of at least one hub. The table below lists which cities are within 1000 miles of other cities.

Cities Within 1000 Miles

Atlanta (AT) AT, CH, HO, NO, NY, PIBoston (BO) BO, NY, PIChicago (CH) AT, CH, NY, NO, PIDenver (DE) DE, SLHouston (HO) AT, HO, NOLos Angeles (LA) LA, SF, SLNew Orleans (NO) AT, CH, HO, NO, NYPittsburgh (PI) AT, BO, CH, NY, PISalt Lake City (SL) DE, LA, SL, SF, SESan Francisco (SF) LA, SL, SF, SESeattle (SE) SL, SF, SE

WESTERN.XLS• This file provides the setup to develop

the model seen below.

Example 15.11

Portfolio Optimization

• The investment company RB Flury can invest in three stocks.

• From past data the means and standard deviations of annual returns have been estimated as shown in the table below.

Mean Standard Deviation

Stock 1 0.14 0.20Stock 2 0.11 0.15Stock 3 0.1 0.08

Combination Correlation

Stocks 1 and 2 0.60Stocks 1 and 3 0.4Stocks 2 and 3 0.7