LP (Linear Program) and LDR (Linear Decision Rule) Model of Aggregate Production Planning (APP): Inclusion of Aggregate Shortage

In this paper we give two methods to allow aggregate shortages in the LP approach to APP. We give two approaches to handle this. It will be worthwhile to explore which approach is better. In the next part of the paper we give a method to handle shortages in the LDR model of APP. Here we give new aggregate flow balance equation and dualize it to be included in quadratic objective function. After partial differentiation w.r.t. each variable involved, we get a system of linear equations that is solved to get optimal solution. If some decision variable is negative, we use a procedure to get a good feasible solution.