Inventory models for production systems with constant/linear demand, time value of money, and perishable/non-perishable items

This research considers inventory systems for economic production models where the objective is to find the optimal cycle time, which minimizes the total cost, and optimal amount of shortage if it is allowed. Several aspects such as time value of money, inflation, constant and linear demand rates, shortages, and deterioration are considered in developing different models. Closed formulas are obtained for the optimal policy in one model. For others, more complex models where closed formulas cannot be obtained, search techniques are used to find the optimal solution.;First, a deterministic inventory control problem is considered for determination of optimal production quantities for an item with constant demand rate, while considering the effect of time value of money. Closed formulas are obtained to calculate the optimal cycle time and corresponding production quantity for the model without shortage. However, search procedures are used to find the optimal cycle time and maximum amount of shortage allowed for the models where shortage is allowed.;In the next inventory control problem, a deterministic model for items with linear demand rate over time, for a finite planning horizon, while considering the effect of time value of money, is considered. Search techniques are developed to find the optimal cycle time for the models without shortage, and the optimal cycle time and maximum amount of shortage for the models where shortage is allowed. A proof of the existence of a unique optimal point for the cost function is presented for the model without shortage.;A deterministic inventory control problem is also considered for items with constant rate of demand and exponentially decaying inventory over an infinite planning horizon, while considering the effect of time value of money. Two different search techniques are developed to find the optimal cycle time for the models without shortage, and the optimal cycle time and maximum amount of shortage allowed for the models where shortage is allowed. A proof of the existence of a unique optimal point for the cost function is presented for the model without shortage

Imperfect quality items in inventory and supply chain management

The assumption that all items are of good quality is technologically unattainable in most supply chain applications. Moreover, inventory theories are often built upon the assumption that the rates of demand, screening, deterioration and defectiveness are constant and known, even though this is rarely the case in practice. In addition, the classical formulation of a two-warehouse inventory model is often based on the Last-In-First-Out (LIFO) or First-In-First-Out (FIFO) dispatching policy. The LIFO policy relies upon inventory stored in a rented warehouse (RW), with an ample capacity, being consumed first, before depleting inventory of an owned warehouse (OW) that has a limited capacity. Consumption works the other way around for the FIFO policy. This PhD research aims to advance the current state of knowledge in the field of inventory mathematical modelling and management by means of providing theoretically valid and empirically viable generalised inventory frameworks to assist inventory managers towards the determination of optimum order/production quantities that minimise the total system cost. The aim is reflected on the following six objectives: 1) to explore the implications of the inspection process in inventory decision-making and link such process with the management of perishable inventories; 2) to derive a general, step-by-step solution procedure for continuous intra-cycle periodic review applications; 3) to demonstrate how the terms “deterioration”, “perishability” and “obsolescence” may collectively apply to an item; 4) to develop a new dispatching policy that is associated with simultaneous consumption fractions from an owned warehouse (OW) and a rented warehouse (RW). The policy developed is entitled “Allocation-In-Fraction-Out (AIFO)”; 5) to relax the inherent determinism related to the maximum fulfilment of the capacity of OW to maximising net revenue; and 6) to assess the impact of learning on the operational and financial performance of an inventory system with a two-level storage. Four general Economic Order Quantity (EOQ) models for items with imperfect quality are presented. The first model underlies an inventory system with a singlelevel storage (OW) and the other three models relate to an inventory system with a two-level storage (OW and RW). The three models with a two-level storage underlie, respectively, the LIFO, FIFO and AIFO dispatching policies. Unlike LIFO and FIFO, AIFO implies simultaneous consumption fractions associated with RW and OW. That said, the goods at both warehouses are depleted by the end of the same cycle. This necessitates the introduction of a key performance indicator to trade-off the costs associated with AIFO, LIFO and FIFO. Each lot that is delivered to the sorting facility undergoes a 100 per cent screening and the percentage of defective items per lot reduces according to a learning curve. The mathematical formulation reflects a diverse range of time-varying forms. The behaviour of time-varying demand, screening and deterioration rates, defectiveness, and value of information (VOI) are tested. Special cases that demonstrate application of the theoretical models in different settings lead to the generation of interesting managerial insights. For perishable products, we demonstrate that LIFO and FIFO may not be the right dispatching policies. Further, relaxing the inherent determinism of the maximum capacity associated with OW, not only produces better results and implies comprehensive learning,but may also suggest outsourcing the inventory holding through vendor managed inventory