Constraints :: SAS/OR(R) 13.1 User's Guide: Mathematical Programming Examples

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Constraints

The following constraints are used in this example:

bounds on variables
for $\text {retailer} \in \text {RETAILERS}$ ,

$\sum _{\text {division} \in \text {DIVISIONS}} \Variable{Assign[retailer,division]} = 1$
for $\text {division} \in \text {DIVISIONS}$ ,

$\Variable{MarketShare[`delivery,division]} = \frac{\sum \limits _{\text {retailer} \in \text {RETAILERS}} \Argument{delivery[retailer]} \cdot \Variable{Assign[retailer,division]}}{\sum \limits _{\text {retailer} \in \text {RETAILERS}} \Argument{delivery[retailer]}}$
for $\text {division} \in \text {DIVISIONS}$ ,

$\Variable{MarketShare[`spirit,division]} = \frac{\sum \limits _{\text {retailer} \in \text {RETAILERS}} \Argument{spirit[retailer]} \cdot \Variable{Assign[retailer,division]}}{\sum \limits _{\text {retailer} \in \text {RETAILERS}} \Argument{spirit[retailer]}}$
for $\text {reg} \in \text {REGIONS}$ and $\text {division} \in \text {DIVISIONS}$ ,

$\Variable{MarketShare[`oil||reg,division]} = \frac{\sum \limits _{\text {retailer} \in \text {RETAILERS\_ region[reg]}} \Argument{oil[retailer]} \cdot \Variable{Assign[retailer,division]}}{\sum \limits _{\text {retailer} \in \text {RETAILERS\_ region[reg]}} \Argument{oil[retailer]}}$
for $\text {group} \in \text {GROUPS}$ and $\text {division} \in \text {DIVISIONS}$ ,

$\Variable{MarketShare[`growth||group,division]} = \frac{\sum \limits _{\text {retailer} \in \text {RETAILERS\_ group[group]}} \Variable{Assign[retailer,division]}}{\left|\text {RETAILERS\_ group[group]}\right|}$
for $\text {category} \in \text {CATEGORIES}$ and $\text {division} \in \text {DIVISIONS}$ ,

$\Variable{MarketShare[category,division]} - \Variable{Surplus[category,division]} + \Variable{Slack[category,division]} = \Argument{target[division]}$
for $\text {category} \in \text {CATEGORIES}$ and $\text {division} \in \text {DIVISIONS}$ ,

$\Variable{MinMax} \ge \Variable{Surplus[category,division]} + \Variable{Slack[category,division]}$