Inventory model of a deteriorating item with price and credit linked fuzzy demand : A fuzzy differential equation approach

This paper deals with an inventory model for a deteriorating item. Here the demand is considered as fuzzy in nature which depends on unit selling price as well as credit period offered by the retailer. Here wholesaler/producer offers a delay period of payment to its retailer to capture the market. At the same time retailer also offers a fixed credit period to its customers to boost the demand. Due to impreciseness of demand, the model is formulated using fuzzy differential equation (FDE). Fuzzy-Riemann integration method is followed to find α-cuts of fuzzy inventory costs and fuzzy average profit. The goal is to find the optimal cycle length, unit selling price and credit period offered by retailer to maximize the average profit. Combining the features of Particle Swarm Optimization (PSO) and Genetic Algorithm (GA), a hybrid algorithm named Interval Compared Hybrid Particle Swarm GA (ICHPSGA) is developed and used to find marketing decision for the retailer. Different ranking methods of intervals are used in this algorithm to find fitness of a solution. The model is also solved using Fuzzy Genetic Algorithm (FGA), Multi-Objective GA (MOGA) and results are compared with those obtained using the proposed algorithm (ICHPSGA). Moreover, several non-linear test functions are also tested with the present developed algorithm, conventional MOGA and FGA. Numerical experiments are performed to illustrate the model and some sensitivity analyses have been made. For statistical support, analysis of variance (ANOVA) is performed with the sample of runs for the test functions using the presented algorithm.

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