Reduced production rates in the economic lot scheduling problem

The economic lot scheduling problem where the item’s production rates can be reduced from the current or nominal production rates is considered. Management may be interested in reducing production rates to avoid a rapid accumulation of inventories. The instances of the problem where reducing the production rates leads to a decrease in a sharp lower bound of the average cost are characterized. These instances include problems where the independent solution (strictly) satisfies the capacity constraint. The independent solution is likely to satisfy the capacity constraint in facilities with nominal production rates that are high relative to the demand rates, or in facilities with small setup times. It is shown that, in minimizing a sharp lower bound on the average cost, it is optimal to reduce the rate of at most one item. A simple test identifies the item, typically the slowest, with potential for production rate reduction. If a reduction is warranted a line search, on the dual variable of the capacity constraint, determines the item’s production rate, the order intervals of all the items, and a sharp lower bound on the average cost. This information is fed into a time-varying heuristic to obtain a near-optimal schedule. Additional savings are possible if rates can be reduced by inserting arbitrary idle times between the production of consecutive units of the same item without incurring additional setup costs. These savings are obtained by first producing at the demand rate and then resuming at nominal rate.