An optimal solution policy to an integrated manufacturer-retailers problem with normal distribution of lead times of del
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An optimal solution policy to an integrated manufacturer‑retailers problem with normal distribution of lead times of delivering equal and unequal‑sized batches M. A. Hoque1 Accepted: 22 October 2020 © Operational Research Society of India 2020
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. Keywords Mean lead time · Normal distribution · Notification point · Minimal total cost
* M. A. Hoque [email protected]; [email protected] 1
BRAC Business School, BRAC University, Dhaka 1212, Bangladesh
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1 Introduction Nowadays, integrated systems of producing products and delivering them to buyers play an important role in the management of operations cost of these systems [7–10, 14, 15, 17, 19, 23]. Variation in delivery lead times of an integrated production–distribution system is common in practice, which is usually resulted due to variation in times of setting up of a production process, inspection, loading, transportation and unloading of batches. Variable lead times greatly affect the production and ordering decisions made by all types of firms. It interacts with other sources of inefficiencies in supply chains, such as the variability of consumer demand, and managing inventories becomes much more complex. Larger and highly variable lead times entail dealing with a greater degree of uncertainty [18]. Thus variability in lead times leads to an uncertainty in a supply chain system. Barron and Baron [2] revealed that va
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