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Constraint Left and Right Hand Sides

In the simplest cases, constraint left hand sides are single cell references, and the right hand sides are constants entered in the Add Constraint dialog. But the Solver permits more general forms for both the left and right hand sides of constraints.

The constraint left hand side, entered in the Cell Reference edit box, may be any cell range, such as a column, row, or rectangular area of cells. The cells you reference must be on the active worksheet. In the example shown earlier, we could have entered all five constraint left hand sides at once, as B1..B5 (as long as we entered the five right hand sides at the same time).

The constraint right hand side may be any of the following:

1. A numeric constant such as 1.

2. A cell reference such as C1.

3. A cell range such as C1..C5.

4. An arbitrary formula such as +A:C1+1 or +A:C2/B:D2.

5. Either "integer" or "binary" for integer constraints

Option 5 is for integer constraints only and is discussed below under "Using Integer Constraints." When entering a formula (Option 4), be sure to include an explicit sheet reference such as A:C1. This is the only context where you can refer to cells on sheets other than the active worksheet. If you use option 3 -- a selection of more than one cell -- the number of cells selected must match the number of cells you selected for the constraint left hand side. The two selections need not have the same "shape:" For example, the left hand side could be a column and the right hand side a row. You may also use rectangular areas of cells. In any case, when you use this form you are specifying several constraints at once, and the constraint left hand sides correspond element-by-element to the right hand sides. In the example shown earlier, you could have entered the right hand side values 400, 200, 800, 400 and 600 into cells C1 to C5, and entered a single constraint such as B1..B5 <= C1..C5. You can see examples of this form in nearly all of the sample worksheets included with the Solver, as well as throughout this Helpfile. It is by far the most useful form.

If the constraint right hand side is a cell reference, cell selection or formula, the Solver needs to know whether the contents of those cells, or the value of the formula is constant in the problem, or variable (i.e. dependent on the values of the decision variables). If the right hand side depends on any of the decision variables, the Solver transforms a constraint such as "LHS >= RHS" into "LHS - RHS >= 0" internally. Both the linear and nonlinear Solvers work internally with constant bounds on the constraint functions.

Related Topics:

Implicit Non-Negativity Constraints

Efficiency of Constraint Forms

Using Integer Constraints