Effect of inspection errors on imperfect production inventory model with warranty and price discount dependent demand rate

¹ Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, 721102 Midnapore, West Bengal, India
² Department of Mathematics, Mahishadal Raj College, 721628 Mahishadal, West Bengal, India

^* Corresponding author: akmanna1987@gmail.com

Received: 22 February 2019
Accepted: 6 May 2019

Abstract

This paper deals with selling price-discount and warranty period dependent demand in an imperfect production inventory model under the consideration of inspection errors and time dependent development cost. Normally, due to long-run, a production process deteriorates with time and here we assume that the process shifts from "in-control" to "out-of-control" state at any random time. A time dependent development cost has been constructed to increase the reliability of the production system i.e., to decrease the deterioration of the system during the production process. As a result, a few items are rejected. Here, two types of inspection errors such as Type-I error and Type-II error, have been considered during the period of product inspection process. In Type-I error, an inspector may choose falsely a defective item as non-defective and in Type-II error an inspector may choose falsely a non-defective item as defective. Due to these phenomena, the inspection process would consist of the following costs: cost of inspection, cost of inspection errors. The purpose of this paper is to investigate the effects of time dependent development cost on the defective items, selling price-discount and warranty policy on the market demand and finally optimize the expected average profit under consideration of such inspection costs in infinite time horizon. Some numerical examples along with graphical illustrations and sensitivity analysis are provided to test the feasibility of the model.