A Fuzzy EOQ Model for Deteriorating Items With Allowable Shortage and Inspection Under the Trade Credit

Introduction

Since the development of the first economic order quantity (EOQ) and economic production quantity (EPQ) models, many manufacturing organizations widely used these basic models to manage their inventory processes. After that, many researchers have tried to improve and modify them through relaxing unrealistic assumptions such as considering varying demand, deterioration, backordering, trade credit, to name a few. In this context, one of the essential and impractical assumptions is that all the inventory scenarios occur under a certain and deterministic environment. However, in today's competitive and dynamic business world, it is not possible to access to all the necessary information. Hence, the information related to the inventory system is not well-defined as assumed in the traditional models. One of the effective methods to overcome these drawbacks is using fuzzy set theory (FST), developed by Zadeh (1965), making possible to transform ill-defined information to mathematical expressions. In today’s competitive business environment, it is quite common for the supplier to offer the retailer a permissible delay in payments in order to stimulate the demand of the retailer. The retailer can either pay off all accounts at the end of the credit period or delay incurring interest charges on the unpaid and overdue balance due to the difference between interest earned and interest charged. The existing literature has thoroughly discussed the inventory problem with delayed payments. Goyal (1985) first developed an economic order quantity (EOQ) model under the condition of permissible delay in payments, in which he calculated interest income based on the purchasing cost of goods sold within the permissible delay period. Shah (1993), Aggarwal and Jaggi (1995) and Hwang and Shinn (1997) extended Goyal’s (1985) model by incorporated the case of deterioration. Jamal et al. (1997) extended Aggarwal and Jaggi (1995) model to allow for shortages. Fisman (2001) indicated that trade credit is an important form of financing for businesses in a broad range of industries and economies. Chang and Dye (2001) extended the model of Jamal et al. (1997) for time dependent deterioration. Abad and Jaggi (2003) first offered a supplier-retailer integrated model following a lot-for-lot shipment policy under permissible delay in payment. Teng et al. (2005) developed an optimal pricing and ordering policy under permissible delay in payments. Teng et al. (2007) developed an economic order quantity model with trade credit financing in which the supplier offers the retailers the permissible delay period M, and the retailer in turn provides the trade credit period N (with N ≤ M) to customers. Jaggi et al. (2008) determined a retailer’s optimal replenishment decisions with trade credit-linked demand under permissible delay in payments. Mahata and Mahata (2009) developed optimal retailer’s ordering policies in the EOQ model for deteriorating items under trade credit financing in supply chain. Soni et al. (2010) summarized the work on permissible delay in payment. Tripathi and Misra (2010) developed EOQ model credit financing in economic ordering policies of non- deteriorating items with time-dependent demand rate in the presence of trade credit using a discounted cash-flow (DCF) approach. Taheri-Tolgari et al. (2012) discussed about the inspection error in the inventory model under inflation. Cheng et al. (2012) discussed an economic order quantity model with trade credit policy in different financial environment. They discussed the model under the conditions that the interest earned is higher than the interest charged and the interest earned is lower than the interest charged. Su and Ouyang (2014) developed an integrated inventory model with imperfect items under inspection for two-level trade credit strategy. Consumers' demand is dependent on length of credit period allowed by retailer. Setiawan (2016), presented an inventory model for imperfect quality items with inspection error where shortages are allowed and lead time can be controlled. Jauhari et al. (2016) discussed inventory model for imperfect quality and inspection error for single manufacturer and single retailer.