Nonlinear Programming Model for Aggregate Planning

The LP model, illustrated in Section 2.15, can be extended to solve a more general aggregate planning problem. For the development of the general model, we use the following notations  

T Total number of time periods in the planning horizon D, Forecasted demand in period t = 1,2,. ..,T r, Amount produced in period f = 1, 2,. .., T y, An unrestricted variable (positive or negative) denoting the 

Objective function We consider three types of cost for the objective function. 

Production cost Let C,(xJ represent the nonlinear cost of producing Xf units in period t. For example, C,(x,) could be a convex, piece-wise linear, cost function with per unit cost increasing depending on whether the units are produced in regular time, over time, or obtained through outsourcing. Fixed cost can also be included as part of the production cost. 

Cost of changing production Production quantities can be changed by changing the workforce level (hiring, firing, lay off, etc.). Let P( X() represent the cost of changing production from period (f - 1) to period t. Note that X( Xt y if the workforce level is increased and X( X( i, if there is a reduction in the workforce. 

---