An optimal solution policy to an integrated manufacturer-retailers problem with normal distribution of lead times of delivering equal and unequal-sized batches

Abstract

In this paper a single-manufacturer multi-retailer integrated model is developed by extending the ideas of two single-vendor single-buyer integrated models, where Normal distribution of lead times of delivering equal- and/or unequal- sized batches of a lot was considered. In the original models, the mean lead time of delivering batches was assumed to be equal to sum of the times of setting up the used machine, processing of the first batch and inspection, loading, transfer and unloading of that batch. However, delivery time of each of the batches from the second to the last of the same lot is only concerned with the time of inspection, loading, transfer and unloading of that batch, not on the additional time of setting up the machine and processing of the first batch. As a result, extra inventories are accumulated during delivering those batches. In our model the mean lead time is assumed to be the mean of the times of inspection, loading, transfer and unloading of a batch. The supply chain flow is synchronized by transferring the lot either only with equal-sized batches or only with unequal-sized batches, and generating a notification point to the manufacturer to start processing of a next lot in time so that the mean lead times of batches is maintained. Then an optimal solution policy to that model is presented along with an algorithm and it is illustrated with numerical example problems. The benefit of this policy is highlighted by comparative studies on numerical example problems and significant reduction in the minimal total cost for a single-manufacturer 5-retailer numerical problem is found.