Integration of Multi-State Systems in a series of EPQ models for deteriorating products

Abstract

This thesis contains a collection of problems dealing with the modelling and optimisation of multi-state production systems, hence addressing challenges within the broader category of flexible manufacturing. These systems are often subjected to random degradations, failures, age of machines, human errors, power supply disruptions, or changes in demand.

In literature, many inventory models have been developed under the assumption that the lifetime of systems is infinite, meaning the performance of a system or equipment remains unchanged and is fully usable for satisfying future demand. Some other models have extended this assumption by considering the functioning of systems (or equipment) under binary modelling conditions in which two states are considered: operational state and failure state. However, a growing body of literature is beginning to take into consideration the numerous scenarios that may occur during the lifetime of an equipment. These situations contribute to the multiplicity of the possible states of systems. Such systems are called multi-state systems (MSS). MSS are generally subject to several failure modes, in particular degradation and age of the systems, with various effects on their performance. The operational characteristics of MSS allow them to continue to function; however, they have a reduced level of performance, demonstrating the adaptability and scalability of the equipment. In the literature, techniques to increase the performance of binary systems are often based on strategies including redundancy or preventive maintenance. In the case of multi-state systems (MSS), continuity of service is ensured by reconfiguration.

The objective of this research is to develop models for managing inventory models for deteriorating items in a multi-state manufacturing environment. In many research based on the binary modelling conditions, ensuring the continuity of the production is an important issue. These models assume complete shutdowns of production systems upon failure of manufacturing resources, which can be extremely costly and lead to substantial manufacturing losses. By addressing these limitations that are present in many of the current literature, the models proposed in this thesis are more practical and thus beneficial for operations management practitioners when making decisions involving multi-state systems in manufacturing processes. For such systems, the breakdown or failure of any component only minimally or at least partially disrupts their performance. In this way, the system can continue to provide service with an acceptable level of degradation. The contribution of this thesis is the development of three mathematical models to optimise a series of Economic Production Quantity (EPQ) systems for deteriorating products.

The first model deals with A lot-sizing model for a deteriorating product with shifting production rates, freshness-, price-, and stock-dependent demand with price discounting. The system consists of one machine producing a single type of product. When the component of the machine breaks down, the system is minimally or at least partially disrupted. Thus, it may continue to operate at a rate lower than the initial rate until a specific inventory level is reached. Initially, demand is influenced by its selling price and the level of stock displayed. As freshness declines, demand then depends on the product's freshness condition. As production continues, there is also a shift in production rate over time. To account for declining freshness affecting consumer interest and purchasing behaviour, discounts are applied after a certain period. The optimisation problem was solved using numerical methods and supported by sensitivity analysis to demonstrate its practical implications. However, at this stage, the model does not explore how raw materials with imperfect quality could impact this system.

The second scenario presents a two-echelon supply chain inventory model for perishable products, incorporating a shifting production rate, stock-dependent demand rate, and imperfect quality raw material. This novel model extends the classic EPQ as well as the first novel developed in this thesis to account for the use of raw materials with imperfect quality in the production process. Two scenarios are formulated within this framework: one involves selling imperfect raw materials at a discounted price after a screening period, while the other entails keeping imperfect items in stock until they are returned to the supplier at the end of an inventory cycle. Both scenarios consider product deterioration as well as shifts in production rate. Numerical solutions were derived for these scenarios. The findings indicate that maximising profit may involve selling the proportion of imperfect raw material rather than retaining it until a new lot arrives from the supplier. This approach is particularly crucial in manufacturing systems where imperfect products appear in both the raw materials and finished goods. The results were validated through a sensitivity analysis.

The third model expands previous novels by considering the scenario of a production system that continually declines, leading to an increasing rate of defects over time. It takes into consideration various elements including deterioration of finished products, stock levels, product quality, and the influence of corporate social responsibility (CSR). CSR plays a critical role in enhancing the reputation of the company, building customer loyalty, and increasing sales by demonstrating a commitment to ethical practices and societal well-being. The objective of the model presented in this scenario is to identify the optimal inventory level and cycle time that minimise the total cost per cycle. To illustrate the effectiveness of this model, numerical examples are provided along with sensitivity analysis.

The findings show that the profit generated can increase by as much as 14 % if manufacturers integrate a setup cost policy and selling price decisions. Extending product shelf life by 60 % can increase the net profit by as much as 7 %. In another model involving a two-echelon supply chain system, the profit can be increased by as much as 360 % and 386 %, respectively, if the selling price and the demand enhancement parameter for inventory level increase by 20 %. Furthermore, the unit selling price can decrease the total cost by as much as 34 %. Operations managers can use all these mechanisms to increase profits in their production systems. Under reasonable conditions, other industrial fields like automotive, mineral processing plants, assembly lines, as well as the production of mechanical components, may also also benefit from the results obtained.