Exploring a production-inventory model with optimal reliability of the production in a parallel-series system

In this study, a production-reliability-inventory system has been formulated and discussed. Here, different types of components, i.e., raw materials are purchased from a supplier in some cycles of equal length. Purchased raw materials have been stored in a warehouse and used in a parallel-series system to produce items with system reliability dependent production cost. Also, the demand rate of the items has been considered to be linearly dependent on reliability and selling price of those items. The main goal of this study is to find the optimal number of transportation cycles and components, which maximize the total business profit and system reliability with volume, weight and cost of the system as constraints. Multi-objective genetic algorithm (MOGA) has been applied to solve the proposed problem. A numerical example has discussed that how this model is applicable in real life situations. Finally, some sensitivity analyses have been performed to study the model.