Unequal shipment policy in a sustainable production inventory system considering defective items and multi-level price breaks

Abstract

In this time and age, sustainability is a global phenomenon. This article represents a vendor–buyer integrated inventory system considering defective products. A multi-level quantity flexibility contract with unequal shipment policy is used here to achieve better productivity. Carbon emission for inventory holding and transportation is also considered to make the model sustainable. The vendor provides a multi-level quantity flexibility scheme to encourage the buyer to order additional quantities and deliver it in several unequal sized shipments. There are some imperfect products in each lot due to the unreliable production process, and those products are rejected after the inspection at the buyer's end. An algorithm is proposed to optimise the overall expense of the proposed system. We examine several shipment policies and determine the optimal shipment policy to minimise the system expenditure. Through detailed numerical analysis, we have validated our findings and the soundness of our model. The aim of this study is to bridge the gap between the existing literature and provide insights to industrial practitioners and academic researchers alike. We obtain the optimal order quantity, shipment policy and shipment frequency that minimise overall expenses considering carbon emission costs.