ILOG OPL Development Studio Language Reference Manual

Piecewise-linear functionsPiecewise-linear functions are important in many applications. They are often specified bygiving a set of slopes, a set of breakpoints at which the slopes change, and the value of thefunctions at a given point. Consider, for instance, a transportation problem in which thetransportation cost between two locations o and d depends on the size of the shipment ship[o][d]. The piecewise-linear expression The piecewise-linear expressionpiecewise{10 -> 100;20 -> 200;40}(0,0) ship[o][d];describes the piecewise-linear function of ship[o,d] depicted in A Piecewise-linear function.The function has slopes 10, 20, and 40, breakpoints 100 and 200, and evaluates to 0 at point0.A Piecewise-linear function.In other words, the piecewise-linear expression is equivalent to the expression:10 * ship[o][d]whenship[o,d]