Two-warehouse production inventory model for a deteriorating item with time-varying demand and shortages: a genetic algorithm with varying population size approach

A production-inventory model for a deteriorating item with time-varying demand and fully backlogged shortages is developed for a two warehouse system. For display and storage of inventory, management hires one warehouse of finite capacity at the market place, called own warehouse abbreviated as OW and another warehouse with large capacity as it may be required at a distance place from the market, called rented warehouse abbreviated as RW. Though the time of transporting items from RW to OW is ignored the transportation cost for transporting items is taken to be dependent on the transported amount. Here the objective is to minimize the total cost for a finite planning horizon. A genetic algorithm (GA) is designed to determine the optimum number of production cycles and the cycle times within a finite planning horizon. In this GA a subset of better children is included with the parent population for next generation and size of this subset is a percentage of the size of its parent set. Performance of this GA with respect to some other GAs is compared. Two particular cases (i) with non-deteriorating items and (ii) without shortages are also investigated. Finally, to illustrate the model and to show the effectiveness of the proposed approach, a numerical example is provided. With respect to the demand parameters, a sensitivity analysis is performed and presented. In this paper, we have pointed out that the expression of Lee and Hsu (2009) can be obtained as a particular case.