Mathematical Techniques for Aggregate Planning:

Linear Programming

The general model of linear programming is appropriate to aggregate planning if the cost and variable relationships are linear and demand may be treated as deterministic. For the special case where hiring and firing are not considerations, the more easily formulated transportation model may be applied in a manner similar to the location problems.

The application of a transportation matrix to aggregate planning is depicted by the solved problem shown in Table. This formulation is termed a period model because it relates production demand to production capacity by periods. In this case, there are four sub periods with demand forecasts as 800 units in each. The total capacity available is 3950 or an excess capacity of 750 (3950 - 3200). Although, the bottom row of the matrix indicates a desire for 500 units in inventory at the end of the planning period, so unused capacity is reduced to 250. The left side of the matrix mentioned the mean by which production is made available over the planning period (that is, beginning inventory and regular and overtime work during each period). An X shows a period where production cannot be backlogged. That is we can't produce in; say period 3 to meet demand in period 2. At last, costs in each cell are incremented by a holding cost of Rs 225 for each period. Therefore, if one produces on regular time in period 1 to satisfy demand for period 4, there will be a Rs. 675 holding cost. Overtime is of course, more costly to start with, but holding cost in this example is not affected by whether production is on regular time or overtime. The solution shown is an optimal one.