Supply Chain Model with Two Storage Facility for Stock Dependent Demand Incorporating Learning and Inflationary Effect under Crisp and Fuzzy Environment

1. Introduction

One of the fertile areas in the field of supply chain is that the shortcoming of production/ handling facilities can be overcome through a human phenomenon known as learning effect. Although different types of learning effects have been studied in various areas, it has been studied rarely in the context of supply chain problems. Kuo and Yang (2006) developed a single machine scheduling problem with a time-dependent learning effect in order to minimize the total completion time. Roy et al. (2009) discussed a production inventory model with stock dependent demand incorporating leaning and inflationary effect in a random planning horizon to determine the economic production quantities using fuzzy genetic algorithm with varying population size approach. Khan et al. (2010) developed an inventory model for items with imperfect quality with learning in inspection to determine the economic ordering quantities. Yadav et al. (2011) discussed an inventory model with imprecise demand rate under the effects of learning in order to determine the optimal ordering policy.

In realistic world, there usually exist various factors that induce the retailer to order more items than the capacity of his Own-warehouse (OW). Therefore, for the retailer, it is very practical to determine whether or not to rent other warehouse and what order policy to adopt if other warehouse is indeed needed. Baker and Urban (1988) discussed deterministic inventory system with an inventory-level-dependent demand rate. Yang (2006) developed two-warehouse partial backlogging inventory model. Vishnoi and Shon (2010) discussed an inventory model for non-instantaneous deteriorating items for two levels of storage. Liang and Zhou (2011) find the optimal replenishment policies for minimizing the total relevant inventory costs for two-warehouse inventory model for deteriorating items with constant demand under conditionally permissible delay in payment. Liao et al. (2012) determined economic order quantity for deteriorating items with two-storage facilities (one is owned warehouse and the other is a rented warehouse) where trade credit is linked to order quantity. Wang et al. (2012) consider a single-manufacturer–single-buyer supply chain problem in which the manufacturer produces a single deteriorating product and delivers it to the buyer on the basis of a consignment policy with buyer's warehouse capacity constraint. Singh and Singh (2013) derived optimal ordering policy for two-warehouse storage facility with power-form stock dependent demand.