Two-Level Trade Credit in Supply Chain Management Quadratic With Fix Life Under Quadratic Demand

Two-Level Trade Credit in Supply Chain Management Quadratic With Fix Life Under Quadratic Demand

Manavi Gilotra (Banasthali University, India) and Sarla Pareek (Banasthali University, India)
DOI: 10.4018/978-1-5225-3232-3.ch009

Abstract

In this paper, supply chain inventory models are formulated with quadratic demand. The demand increases linearly for times when a product is launched and when with new substitute available demand decreases exponentially. The inventory of every player is subject to deteriorate after a fixed life time. The deterioration rate under the retailer is lower in comparison to manufacturer. Under two level trade credit, manufacturer offers delay period to settle the account to the distributor and the distributor also offers some credit period to the retailer. Interest is charged if the account is not settled in a given stipulated time period. The cost of the integrated inventory system is minimized with respect to a number of shipments from the manufacturer to the distributor and the distributor to the retailer and each player's replenishment times. A solution procedure is worked out to obtain the best possible decision for the player of the supply chain. The results are validated with the numerical examples for different scenarios. Managerial decisions are suggested.
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Introduction

In business transactions, the offer for settling the dues against the purchases without any interest charges from the supplier revenue and incur interest on it by depositing in the bank or financial firms. During this permissible delay period, the retailer can sell the item and generate the revenue and incur interest on it by depositing in the bank or financial firms. Goyal (1977) was the first author who initiated the joint optimization concept for vendor and buyer. Banerjee (1986) extended this concept for the vendor with a finite production rate to order for a buyer on a lot-for-lot basis where the operating cost of the manufacturer and buyer is considered. He assumed that the shipment can only be made when the production has been completed. The coordination between three players of the supply chain viz manufacturer, wholesaler and retailer was advocated by Ishii, Takashi, and Muramatsu (1988). The work of Abad (1996) under the conditions of perishability and partial backordering was more realistic and applicable in practice. Chang and Dye (1999) studied an EOQ model for deteriorating items with time varying demand and partial backlogging. Woo, Hsu and Wu (2001) discussed inventory policies for one manufacturer and multiple buyers. Hangs, Raafat and Paul (2006) discussed a methodology to compute joint economic lot-size in a distribution system with multiple shipments. The effect of deterioration in any system is very important. It is necessary to manage product’s deterioration as instances fruits and vegetables which deteriorate over time. Ghare and Schrader (1963) investigated a model for exponentially decaying inventory model. Chang et al. (2001) determined the optimal cycle time for deteriorating items under trade credit policy. Duan et al. [2010] extended Luo’s [2007] model with quality discount incentive for fixed lifetime products. Mandal (2010) gave an EOQ inventory model for Weibull-distributed deteriorating items under ramp-type demand and shortages. Mishra et al. (2013) developed an inventory model for deteriorating items with time-dependent demand and time-varying holding cost under partial backlogging. Manna and Chaudhari (2014) discussed an order level inventory model for deteriorating item with quadratic time-varying demand, shortages and partial backlogging. Pahl and Voß [2014] surveyed about deteriorating and lifetime constraints in production and supply chain planning.

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