International Journal of Japan Association for Management Systems
Online ISSN : 2188-2460
Print ISSN : 1884-2089
ISSN-L : 1884-2089
Combination Sale Problem for a Perishable Product with Fuzzy shortage cost
Hiroaki ISHII
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2019 Volume 11 Issue 1 Pages 25-28


Several researchers have been interested in inventory control for a perishable product. Here we introduce a combinatorial sale in order to reduce the outdating quantities. Here we consider the following problem: (1) Single perishable product with two life time period. That is, for a period, an amount of old one (remaining life time period is 1) in the stock is given as ๐‘ฅใ€“ and under this condition we should determine an ordering quantity ๐‘ฅใ€“of the fresh one (remaining life time period is 2 (2) Ordering takes a place at the start of the period. The unit purchasing cost of the product is ๐‘. (3) Issuing policy is LIFO, that is, customer buys fresh one first and if fresh one is sold out, only some percent of customers overflowed from purchase of the fresh one buy the old one. This percentage is at most 100๐‘ž. Unit selling price of the fresh one is ๐‘Ÿใ€“ and that of old one is ๐‘Ÿใ€“ satisfying ๐‘Ÿใ€“ใ€“๐‘Ÿใ€“ใ€“๐‘ (4)Prominent feature of our model is a combination sale, that is, we sell a set of products consisting of the fresh and old ones at the discount unit price ๐‘Ÿใ€“ satisfying ๐‘Ÿใ€“ใ€“๐‘ใ€“๐‘Ÿใ€“ใ€“๐‘Ÿใ€“ใ€“๐‘Ÿใ€“, At most 100๐‘ percent of the customers purchasing the fresh one accept the promotion set, that is, buy the old one with the fresh one at the same time but ๐‘ใ€“๐‘ž. (5)The old one that is not purchased by the customer and remained outdates and is discarded at the unit cost ๐œƒ. The fresh one not purchased by the customer is stocked at the unit cost โ„Ž and we assume that unit shortage costs is ๐ฟ fuzzy number. (6)The demand ๐ท of the customer: nonnegative random variable. Its cumulative distribution function and density function: ๐นใ€“๐ทใ€“,๐‘“ใ€“๐ทใ€“ใ€“. We introduce ๐ฟ fuzzy order and we seek some non-dominated ordering quantities considering pessimistic case, most possible case and optimistic case of shortage cost.

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