A Lot-Sizing Model for a Multi-State System with Deteriorating Items, Variable Production Rate, and Imperfect Quality

Abstract

Conventional production systems assume that during the manufacturing processes, machines operate without breakdown over an infinite planning horizon and manufacture only products of good quality. Imperfect production processes as a result of machine degradation are common in manufacturing. This paper deals with a problem that concerns the modelling and evaluation of the performance of a multi-state production system that is subject to degradation and its effect on lot sizing. Here, we consider that the cycle starts with a particular production rate until a point when the inventory reaches a certain level after which the failure mode is activated due to the deterioration of certain components, leading to a reduction in the production rate in order to ensure the continuity of supply until the maximum inventory level is reached. Production then stops to restore the machine and the cycle starts again. We have assumed that the rate at which inventory deteriorates is exponential and that demand is constant. A numerical example is used to illustrate the model application, followed by sensitivity analysis. This paper contributes to lot sizing in the area of machine reliability by considering a production system in a degraded state with a non-increasing production rate for deteriorating items with imperfect quality and partial backlogging.

A Lot Sizing Model for a Deteriorating Product with Shifting Production Rates, Freshness, Price, and Stock-Dependent Demand with Price Discounting

“…This paper introduces an extended inventory model for deteriorating items that specifically incorporates the influence of product freshness on demand. The model builds upon the work of Tshinangi et al (2022) and extends this research by considering the dynamic relationship between the concept of shifting production rates in a deteriorating process and both freshness condition and deterioration of products, guided by Banerjee and Agrawal (2017). Initially, the demand for the product (e.g., meat) is determined solely by its selling price and its displayed stock level when it is fresh.…”

“…They demonstrated that process deterioration could be the result of minor stoppages and speed losses, which in practice may affect the efficiency of the process. Tshinangi et al (2022) conducted a study focusing on a degrading production system that incorporates shifting production rates, imperfect quality, and partial backlogging of demand along with lost sales to understand the impact of these factors on system performance, such as inventory levels, cycle time, shortage levels and overall cost incurred.…”