A lot sizing model for a multi-state system with deteriorating items, variable production rate and imperfect quality

Abstract

The management and control of inventory has become a core part of management, which plays a significant role through achieving efficient and profitable operations of a business organization. Hence, considerable efforts have been made to develop models that can be implemented to optimize inventory systems without compromising customer needs. The classic Economic Production Quantity (EPQ) model is the most widely used of these models; however, this model presents certain limitations, leading researchers to extend some of the assumptions to increase its applicability to present-day organizations. In manufacturing, studies of the functional state of equipment have, for a long time, been based on binary modelling conditions where two states were considered: the operational state and the complete failure state. However, a growing literature takes into consideration the numerous scenarios that may occur during the lifetime of some equipment. Such systems are called Multi-State Systems (MSS). Thus, in this dissertation, a perishable replenishment policy is developed based on the MSS concept to optimize an EPQ model that operates in a degraded state, producing both perfect and imperfect products, under constant demand and backlog dependent-demand. The cycle was assumed to start with a particular production rate until a point when the inventory reached a certain level, and after which the failure mode was activated due to the deterioration of certain components, and the production rate was reduced to a lower rate to ensure the continuity of supply until the maximum inventory level was reached. Production then stopped to restore the machine and the cycle started again. The model assumed that inventory was subject to deterioration, the demand rate was constant, and partial backlogging was allowed. The work done included an exploration of the modelling methods, analysis and evaluation of the performance of the multi-state system in which the level of service relies on the state of the equipment during the production cycle. An evaluation and optimization of the system’ performance indicators such as inventory levels, backorder level, cycle time and the total cost function were carried out. Due to model complexity, the Newton-Raphson approach was used to solve the model and numerical examples are provided to illustrate the solution procedure. Based on the results, the presence of imperfect quality outputs forced the system to produce more items to meet the needs for perfect quality items. As the proportion of imperfect quality items produced increased, the proportional increase in cost seems to have grown more quickly. As the production rate in the first production-consumption cycle increased, the total cost function increased; this was mainly due to higher production cost, holding and disposal costs incurred. However, as the inventory holding cost rate increased, the optimal inventory levels decreased, the cycle time decreased, but the shortage and the total cost increased. The decrease in production rate during the second production-consumption cycle was shown to have increased the cycle time and the inventory level in the first cycle, but decreased the inventory level in the second cycle and the total cost. Sensitivity analysis showed that working with low values of cost parameters provided better results in terms of optimizing the total cost.

The EPQ model presented in this research can be used by production managers, working in industries such as assembly lines, steel factories, hydrometallurgical plants under different operational scenarios, as a guideline when making production decisions