Assignment:
1. Consider the planning problem faced by a facility that produces a single product with periodic demands d1, d2.,dr over a planning horizon given by periods 1,2...,T. The production capacity in number of units and unit production cost are denoted by ut, ct and respectively, for each period t= 1,..., T. Holding inventory carries a cost of h per unit held, per period. Since the warehouse roduction in period t) should not exceed w units. Formulate an LP to find an optimal production schedule space is limited, the maximum inventory stored in any period t (not including p that minimizes the total cost under each of the following assumptions.
a. Product is perishable and any month's demand may be fulfilled by that month's production and the previous month's production- not older. Assume that ending and beginning inventories must be zero; back-ordering and shortages are not allowed.