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Production inventory model with disruption considering shortage and time proportional demand

This paper is an attempt to develop an economic production quantity model using optimization method for deteriorating items with production disruption. We obtained optimal production time before and after the system gets disrupted. We have also devised the model for optimizing the shortage of the products. | Yugoslav Journal of Operations Research 28 (2018), Number 1, 123–139 DOI: https://doi.org/10.2298/YJOR161118008K PRODUCTION INVENTORY MODEL WITH DISRUPTION CONSIDERING SHORTAGE AND TIME PROPORTIONAL DEMAND U. K. KHEDLEKAR Dr.Harisingh Gour Vishwavidyalaya, Department of Mathematics and Statistics, A Central University Sagar M.P. India - 470003, uvkkcm@yahoo.co.in A. NAMDEO Dr.Harisingh Gour Vishwavidyalaya, Department of Mathematics and Statistics, A Central University Sagar M.P. India - 470003 A. NIGWAL Department of Mathematics, Government Engineering College, Ujjain MP-India Received: November 2016 / Accepted: May 2017 Abstract: The disruption in a production system occurs due to labor problem, machines breakdown, strikes, political issue, and weather disturbance, etc. This leads to delay in the supply of the products, resulting customer to approach other dealers for the products. This paper is an attempt to develop an economic production quantity model using optimization method for deteriorating items with production disruption. We obtained optimal production time before and after the system gets disrupted. We have also devised the model for optimizing the shortage of the products. This research is useful to determine the time for start and stop of the production when system gets disrupted. The optimal production and inventory plan are provided, so that the manufacturer can reduce the loss occurred due to disruption. Finally a graph based simulation study has been given to illustrate the proposed model. Keywords: Inventory, Disruption, Deterioration, Preservation Cost, Shortage. MSC: 90B05, 90B30, 90B50. 124 U.K.Khedlekar, et al. / Production Inventory Model 1. INTRODUCTION The production system can always be affected by labor problem, political crises, machine breakdown, strike, political issue, and undetermined weather. If the production disruption appears, this leads us to a big loss because we are unable to fulfill the demand and new orders are still