A partial backlogging production-inventory lot-size model for deteriorating items with time-varying production and demand rate over a finite time horizon

Abstract

In this article, I extend Balkhi ((2001), ‘On a Finite Horizon Production Lot Size Inventory Model for Deteriorating Items: An Optimal Solution’, European Journal of Operational Research, 132, 210–223), by considering a generalised mathematical production-inventory model for deteriorating items with partial backlogging. The demand, production and backlogging rates are assumed to be continuous and varying with time. The objective is to find the optimal production restarting and stopping time to keep the total relevant cost as low as possible. To ascertain the optimal solution exists, the conditions for the total relevant cost in the system which attains its global minimum are provided. In addition, based on the minimum total relevant cost, an alternative among the proposed four cases is also suggested. Finally, a numerical example and sensitivity analysis is illustrated and some management insights are presented.