### International Journal of Mathematical, Engineering and Management Sciences

#### ISSN: 2455-7749 . Open Access

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

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

Kapya Tshinangi
Department of Industrial and Systems Engineering, University of Pretoria, Pretoria, Gauteng, South Africa.

Department of Industrial and Systems Engineering, University of Pretoria, Pretoria, Gauteng, South Africa.

Department of Industrial and Systems Engineering, University of Pretoria, Pretoria, Gauteng, South Africa.

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Accepted on July 28, 2022

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.

Keywords- Multi-state systems; Inventory; Shortages; Deteriorating process; Variable production rate.

Citation

Tshinangi, K., Adetunji, O., & Yadavalli, V. S. S. (2022). A Lot-Sizing Model for a Multi-State System with Deteriorating Items, Variable Production Rate, and Imperfect Quality. International Journal of Mathematical, Engineering and Management Sciences, 7(5), 730-748. https://doi.org/10.33889/IJMEMS.2022.7.5.048.