Linear Programming using Whats Best

A convenient way of creating models to solve linear programming problems is to use the What's Best! add-in for Microsoft Excel. A demo version of What's Best! is available from Lindo Systems. After installation, the What's Best! toolbar becomes available in Excel (Fig. 1.1). Decision, uncontrolled, or endogenous variables are called adjustable cells in What's Best!. The value of the objective function is called the best cell.

A linear programming model can be constructed by transcribing the standard LP form described by Equation (1.1) and its restrictions into Excel, as shown in Figure 1.2. We will use this representation throughout the book.

A

B

C

D

E

F

G

1

Endogenous variables

varl

var2

varn

2

Outcome

*1

*2

xn

3

4

Objective Function

C1

C2

Cn

Z

5

6

Constraint 1

^11

a12

a1n

< =

b1

7

Constraint 2

a21

a22

a2n

< =

b2

8

9

Constraint m

am1

am2

amn

< =

bm

Figure 1.2 The standard LP form represented in Excel with What's Best!

A handy way of quickly building a model is by following this ABC:

A. Define the Adjustable cells. These are the cells in the worksheet of which What's Best! is allowed to change the values. Simply select the cells that hold these variables and click the 'Make Adjustable' button on the toolbar. The contents of these cells turn blue as a visual reminder.

B. Define the Best cell. This is the cell that holds the outcome of the objective function. Select the cell that holds this value and then click on the 'Minimize' or 'Maximize' button on the toolbar. This cell is then named WBMAX or WBMIN depending on whether you have chosen to minimise or maximise. The cell turns blue to indicate that it is to be optimised by What's Best!.

C. Define the Constraints that have to be met. These are the cells that define the relationship between cells that hold required resources and available resources in the model. The mathematical relationships are set with the 'Constraint Less Than', 'Constraint Greater Than', and 'Constraint Equal To' buttons on the toolbar.

We will illustrate this procedure in detail with the exercises that follow.

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