Integrated model in one vendor-one customer situation when costs are fuzzy and lot sizes are deterministic

An integrated inventory model considering one‐vendor, one‐customer in the presence of uncertainties in cost functions which can be characterised by fuzzy numbers is presented. The vendor seeks to minimise his total annual cost subject to the maximum costs, which buyers are prepared to incur. To find the optimal solution a joint economic lot size (JELS) model is developed for the one‐vendor, one‐customer case, in which the demand/production lot sizes are deterministic and the costs are fuzzy. A fuzzy JELS model in one‐vendor, one‐customer situation has been developed on the basis of extended Wilson‐Harris deterministic model to fuzzy environment, in which setup/ordering costs, the holding/carrying costs and shortage cost of both the vendor and the customer are fuzzy and the demand or usage of inventory item and the order or production lot sizes of the parties are deterministic. In this paper, costs are to be assumed as L‐R fuzzy numbers. The model is expressed in terms of L‐R fuzzy. The effective ways for a compromise between the vendor and customer at a common lot size with certain amount of price adjustment and methodology are explained through a numerical example.