Evaluating lot-sizing strategies under limited-time price incentives: An efficient lower bound

Determination of the optimal lot sizing strategy when the vendor offers limited time price incentives, such as pre-announcement of a price increase that will take effect after a finite time or a price discount that is valid for a limited time, is a common problem that has been extensively researched. A review of the literature indicates that the mathematical analysis and solution of this problem are quite complex. This complexity may deter managers from using the optimal strategy although an optimal lot sizing strategy results in the lowest cost. Managers generally prefer simple heuristic or rule-of-thumb strategies that are easy to understand and to implement, provided the total relevant cost associated with such strategies compares well with that of the optimal strategy. Therefore, it would be of significant value to managers if the cost associated with the optimal strategy can be deduced easily without recourse to complex mathematical analysis so that the simpler strategies can be quickly and easily evaluated. In this paper, we present an intuitively appealing and easy-to-compute method to determine a tight lower bound, whose value is very close to the total cost of the optimal strategy. We demonstrate, through extensive computational analysis, the adequacy of our lower bound by comparing it with the total cost associated with an optimal strategy over a wide range of operating parameters. Thus, managers can use it as a surrogate for the cost of the optimal strategy while evaluating heuristic strategies. We illustrate the application of our lower bound with numerical examples.