Abstract
In the general framework for modeling production proposed by Hackman and Leachman [1989], the model with noninteger leadtime and unequal length time periods are accurate under the assumption of constant production rate between two time grids, but not real optimal in practical application. In Hung’s research [2000] has proved that the real optimum can be obtained by converting the formulation using the greatest common divider (G.C.D.) of all the leadtimes as a time unit and planning period, but the problem size of this model will be huge and requires long computation time. Hence, Hung developed variable partition procedures to improve the objective function value under reasonable computation times. The partition rules were developed by considering product inventory levels and resources capacity constraints. The procedure break up the original production variables at time epochs between original time grid in order to give the flexibility for improving the objective value. The result of the Hung’s experiment show that the partition rules improved the objective value but computation time did not decrease as well as we expect. One possible reason is that, in Hung’s formulation, the inventory balance constraints are built by cumulative flow in and flow out form time 0 to time . This generates a huge number of nonzero coefficients and,thus, increases the computation time. The purpose of this study is to modify the inventory balance constraints and hopefully, to decrease the computation time substantially. In our modified inventory balance constraints, we use a recursive procedure. The inventory at time is equal to the inventory at former time grid, plus the flow in in the interval (, ), and minus the flow out in the interval (, ). By doing this, we will be able to decrease the number of nonzero coefficients and, thus, reduce the computation time.