Impact of carbon emission on imperfect production inventory system with advance payment base free transportation

¹ Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, WB, India
² Department of Mathematics, Sidho-Kanho-Birsha University, Purulia, WB, India
³ The Logistics Institute – Asia Pacific, National University of Singapore, 21 Heng Mui Keng Terrace, #04-01, 119613, Singapore

^* Corresponding author: akmanna1987@gmail.com

Received: 26 September 2018
Accepted: 23 January 2019

Abstract

Most of the works in EPQ model considered that retailer’s purchasing cost of an order should be paid to the manufacturer at the time of its delivering. In the real world situations, few manufacturers may be expect to receive full or a fraction of the purchasing cost in advance and sometimes allow to prepayment into several equal instalments. Also, in classical inventory models it is assumed that no defective items are produced, but real production process may shift from in-control state to out-of-control state due to occurrence of some assignable causes, which results in the quality loss of items. To make the study more realistic, we develop an imperfect production inventory model that incorporates random carbon emissions under consecutive prepayments. Also, production processes are assumed to be imperfect, so they can produce some defective items and some portion of them are reworked in the same cycle. In addition, it is assumed that manufacturer offers an advanced payment based free transportation to the retailer. Carbon emissions are associated with the decisions of production and transportation from manufacturer to retailer. A carbon emission tax is need to pay by the manufacturer due to the environmental regulations. Numerical examples illustrate the proposed models and sensitivity analysis provides some managerial insights for managers.