9781118041581

732 Chapter 17 Linear Programming

TABLE 17.1

Linear Programming

Solution for Police

Staffing Problem

The department

meets its

hourly staffing

requirements at

minimum total

cost.

ABCDEFGHIJ

1

2 8 A.M.–12 12–4 P.M. 4–8 P.M.8 P.M.–12 12–4 A.M. 4–8 A.M.

3

4 Shift Costs 1 1.125 1.25 1.375 1.5 1.25 Total Cost

5 1,150

6 # of Officers 150 175 75 325 175 0

7

8 # per 8-Hour Shift 150 325 250 400 500 175

9

10 Officers Required 150 100 250 400 500 175

11

12 Extra Officers 0 225 0 0 0 0

13

14 Shadow Price 1.0 0 1.125 0.125 1.25 0.25

Set Target Cell:

Solver Parameters?

$I$5

$B$6 : $G$6

Equal to:

By Changing Cells:

Subject to Constraints:

Add

Change

Delete

Solve

Close

Options

Max Min

$B$12 : $G$12 ≥ 0

$B$6 : $G$6 ≥ 0

To direct the computer to solve the LP problem, one must complete the

Solver menu (shown below the spreadsheet in Table 17.1). In the menu, we have

entered target cell I5 (total cost) to be minimized by varying cells B6 to G6 (the

numbers hired beginning in each time period). The constraints specify that cells

B12 through G12 must be greater than or equal to zero, so there cannot be a

shortage of officers (i.e., a negative number of extra officers) on any shift. The

final constraint states that all decision variables must be nonnegative.

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