Buyer–seller fuzzy inventory model for a deteriorating item with discount

Multi-objective economic lot size models of deteriorating items for both the buyer and the seller are developed in crisp and fuzzy environments. A buyer tries to minimize total average cost and at the same time the seller maximizes the total average revenue allowing discount on bulk purchase with the restricted material cost of the buyer. Here, the total average expenditure for the buyer, the estimated total average revenue for the seller and the resource for the material purchase are assumed to be crisp (Model 1) and fuzzy (Model 2) in nature. The impreciseness in the above objectives and constraint have been expressed by fuzzy linear membership functions. It has been solved by the additive goal and fuzzy additive goal programming methods with different weights. Also, to ensure the achievement level, thresholds are considered in crisp and fuzzy models. All the models are illustrated with numerical examples and the results are compared.