Managing a sustainable integrated inventory model for imperfect production process with type one and type two errors

Novrianty Rizky,Wakhid Ahmad Jauhari,Hui Ming Wee,Ivan Darma Wangsa

doi:10.1007/s10098-021-02194-w

Abstract

Unlike previous research, this study develops an integrated inventory model for controllable lead time with defective items, errors in inspection, and variable lead time considering sustainability. The research investigates the effect of controlling lead time and capital investment in the setup cost. We assume that the buyer receives a lot size that may contain some defective items with a known defective probability. The buyer’s inspector conducts a 100% quality inspection and may incorrectly classify a non-defective item as a defective item (type one (I) error) or incorrectly classify a defective item as a non-defective item (type two (II) error). The mathematical inventory model considering carbon emission cost is developed, and the solution procedure is designed using the heuristic algorithm to derive the optimal or near optimal solution. Finally, numerical examples and sensitivity analysis are given to illustrate the results. The results show that the defective rate, and type I type II inspection errors, have a significant impact on the shipment lot. This leads to the changes in the total cost, lead time, and the carbon emissions. Our study provides cost savings of 4.39% and carbon emission savings of 28.44%.Graphic abstract

Highlights

In recent years, the issues of economics and sustainability in the supply chain have attracted considerable attention from governments, universities, and other non-profit organizations
We develop a sustainable integrated inventory under a vendor-buyer system taking into account the crashing lead time, defective items, inspection errors, freight cost, and investment for setup cost reduction
Conclusions and future research directions In this study, type I and II errors are considered for a single vendor-single buyer system with defective items, setup cost reduction and controllable lead time

Summary

Introduction

The issues of economics and sustainability in the supply chain have attracted considerable attention from governments, universities, and other non-profit organizations. The earliest research of the EOQ model with defective items was made by Salameh and Jaber (2000) They assumed a perfect inspection to screen out and dispose of the defective items. Jauhari et al (2017) developed an unequal-sized shipment policy for a single-vendor and a single-buyer integrated inventory model with deterministic demand, defective items, and errors in the inspection. Khan et al (2017) proposed a mathematical inventory model for a supply chain system with stochastic lead time. Jauhari et al (2018) developed a two-echelon inventory model with stochastic demand, defective items, and carbon emissions cost. Tiwari et al (2018a) proposed a vendor-buyer inventory model considering carbon emissions, deteriorating, and imperfect quality items. Tiwari et al (2020) investigated the impact of human errors, variable lead time, and capital investment

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