ارزیابی استراتژی های تعیین اندازه دسته تولید تحت مشوقهای قیمت محدود به زمان : حد پایین کارآمدی

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.

It is commonly observed that vendors occasionally offer buyers some incentives that will remain effective only for a limited time. Such incentives may take several forms such as (i) a limited time reduction in the item’s price, (ii) an interest-free delayed-payment privilege, or (iii) an advance notification of an imminent price increase. Vendors offer such incentives for various reasons such as a need to reduce excess inventories or to take up the slack in their production facility. Although a temporary price reduction, an advance notification of a price increase, and a temporary delayed-payment privilege are different types of limited-time price incentives, these are all conceptually the same and their analysis is similar. The importance and the wide range of interest in this problem are clearly evident from the extensive body of literature one finds on this topic. See Silver et al. (1998) for a detailed description of the problem.

In this paper we addressed the problem of determining optimal lot sizes when the vendor offers a temporary price advantage. An optimum solution methodology based on the conceptually rigorous discounted cash flow approach is available to this problem. However, the complexity of the mathematical analysis and the computational burden associated with the optimum solution is likely to deter its adoption in managerial decision-making and policy implementation. Recognizing this, we developed an intuitively appealing and easy-to-compute “lower bound”, which can serve as a surrogate for the minimum cost associated with the optimal solution. We demonstrated that it is very close to the total cost associated with the optimal lot sizes. The implication of our findings for policy implementation is immediately apparent. Managers interested in adopting policies that include lot sizes based on heuristics or ad hoc considerations would find it useful to know how the total costs of these policies compare with the total costs from an optimal policy derived from a mathematically rigorous analysis. Since our lower bound is simple to compute and it is almost equal to the cost associated with the optimum policy, managers can use the lower bound as a benchmark for the evaluation of any heuristic or ad hoc lot-sizing policies. They may consider for evaluation a number of different heuristic policies and adopt a policy with costs acceptably close to the lower bound, which in turn is very close to the true optimum minimum cost.