Reference no: EM132217834

A manager of a factory needs to make a production plan to satisfy demands over next T time periods. For each time period t -1,2,...,T, let dt be the demand of a single product, ct be the unit production cost. After shipping all the demand, if we still have left over, we charge ht dollars for each unit left for t-1, 2, . . . ,T, we can also delay the production and have shortage (or backlog), for each unit of which we charge bt for t-1, 2, , T. We want to minimize the total cost of production, inventory, and backlog. Assume that we start with both inventory and shortage being zero and our production line has infinite production capacity. (a) Formulate this problem as a linear program. (b) Suppose that we have a budget of N that we can spend on total production, inventory, and backlogging costs. In order to smooth production levels, a new objective is set to minimize the difference between the largest and smallest production levels in any period. Formulate this problem variant as a linear program.