Inventory Management of Platelets in Hospitals: Optimal Inventory Policy for Perishable Products with Emergency Replenishments

Platelets are short-life blood components used in hospital blood transfusion centers. Excluding time for transportation, testing, and arrangement, clinically transfusable platelets have a mere three-day life-span. This paper analyzes a periodic review inventory system for such perishable products under two replenishment modes. Regular orders are placed at the beginning of a cycle. Within the cycle, the manager has the option of placing an emergency order, characterized by an order-up-to level policy. We prove the existence and uniqueness of an optimal policy that minimizes the expected cost. We then derive the necessary and sufficient conditions for the policy, based on which a heuristic algorithm is developed. A numerical illustration and a sensitivity analysis are provided, along with managerial insights. The numerical results show that, unlike typical inventory problems, the total expected cost is sensitive to the regular order policy. It also shows that the optimal policy is sensitive to changes in the expected demand, suggesting to decision makers the significance of having an accurate demand forecast

Optimal allocation of blood products

The high cost of collection and the short shelf life of apheresis platelets demand efficient inventory management to reduce outdates and shortages. Apheresis platelets are licensed for seven days, and blood centers are keen on knowing the consequences of various product collection and distribution strategies. To reduce outdates, inventory managers typically distribute the older units first, thereby following first-in first-out (FIFO) policy; however, hospital blood banks would prefer that the blood center issues out the freshest units first, equivalent to a last-in first-out (LIFO) policy. This study addresses the optimal distribution policy to achieve a desired outdate, shortage and average age of apheresis platelets. A comprehensive literature review was conducted on previous models studied to efficiently distribute blood products. However, most of the research on blood inventory management has been restricted to the hospital blood bank level in terms of ordering policies and inventory levels. This study takes the approach from the perspective of the inventory manager at the regional blood center. The inventory manager needs a reliable forecast of the quantity and timing of future blood supply (collection from donors) and blood demand from hospital blood banks to make an effective decision on blood inventory control. A forecasting method is used in this study to predict collection and demand for Single Donor Platelets (SDPs), and solves the blood inventory problem using a heuristic method and a Linear Programming (LP) with a rolling horizon method to find the near optimal issuing policy, the expected average age, outdate rate, and shortage rate of a blood product from the perspective of the blood center. It is concluded that regional blood centers can distribute with a ‘mixed’ FIFO/LIFO strategy and not significantly affect outdates or ability to cover shortages. For the LP model with a rolling horizon schedule, the inventory manager at the blood center would have to use forecast windows of five to achieve good issuing policies. A simulation study comparing the heuristic method and an LP-based with a rolling horizon method indicated that LP models with forecast windows of five and heuristics methods with a ‘mixed’ FIFO/LIFO strategy can be used to optimize this inventory problem

A Metaheuristic-Based Simulation Optimization Framework For Supply Chain Inventory Management Under Uncertainty

The need for inventory control models for practical real-world applications is growing with the global expansion of supply chains. The widely used traditional optimization procedures usually require an explicit mathematical model formulated based on some assumptions. The validity of such models and approaches for real world applications depend greatly upon whether the assumptions made match closely with the reality. The use of meta-heuristics, as opposed to a traditional method, does not require such assumptions and has allowed more realistic modeling of the inventory control system and its solution. In this dissertation, a metaheuristic-based simulation optimization framework is developed for supply chain inventory management under uncertainty. In the proposed framework, any effective metaheuristic can be employed to serve as the optimizer to intelligently search the solution space, using an appropriate simulation inventory model as the evaluation module. To be realistic and practical, the proposed framework supports inventory decision-making under supply-side and demand-side uncertainty in a supply chain. The supply-side uncertainty specifically considered includes quality imperfection. As far as demand-side uncertainty is concerned, the new framework does not make any assumption on demand distribution and can process any demand time series. This salient feature enables users to have the flexibility to evaluate data of practical relevance. In addition, other realistic factors, such as capacity constraints, limited shelf life of products and type-compatible substitutions are also considered and studied by the new framework. The proposed framework has been applied to single-vendor multi-buyer supply chains with the single vendor facing the direct impact of quality deviation and capacity constraint from its supplier and the buyers facing demand uncertainty. In addition, it has been extended to the supply chain inventory management of highly perishable products. Blood products with limited shelf life and ABO compatibility have been examined in detail. It is expected that the proposed framework can be easily adapted to different supply chain systems, including healthcare organizations. Computational results have shown that the proposed framework can effectively assess the impacts of different realistic factors on the performance of a supply chain from different angles, and to determine the optimal inventory policies accordingly

Transshipment in supply chain networks with perishable items

Supply chain management is an efficient approach to managing the flow of information, goods, and services in fulfillment of customer demand. The implementation of supply chain management significantly affects the cost, benefit level, and quality. Over the past decades, multiple strategies for effective supply chain management have been developed in both academia and industry. One such strategy is named lateral transshipment which allows movement of stock between locations at the same echelon level or even across different levels. Although transshipment has been considered in the literature for a long time, there has been limited studies of transshipment for perishable items, most likely because of the complex structure of perishable inventories. The analysis of perishable-inventory systems has been considered in numerous articles because of its potential application in sectors such as chemicals, food, photography, pharmaceuticals, and blood bank management. Blood services in Australia rely on voluntary, non-remunerated donors to satisfy the demand for blood. Blood services confront ongoing challenges in providing an adequate supply of blood and blood products. One of the powerful tools that could improve the efficiency of the blood supply chain is lateral transshipment. This thesis presents three models that have application in the transshipment of perishable items such as blood. The first model (presented in Chapter 2) outlines the development of a new transshipment policy for perishable items, to enhance supply chain performance. A Poissondistributed customer demand is assumed and the effect of reactive transshipment on expected costs are evaluated. A heuristic solution is developed, using partial differential equations to compute performance measures and cost function. The performance of this model is evaluated through a numerical study. The results indicate that this transshipment policy is effective under lost-sale and backordering scenarios. In addition, the performance of the suggested transshipment policy is compared with the current transshipment policy that is practiced in some Australian hospitals. The results suggest that by setting the optimal threshold, a significant cost saving could be obtained with the same average issuing age of the current policy. The second model (presented in Chapter 3) considers a finite-horizon multi-period inventory system with one main hospital connected to several smaller hospitals. The hospitals face random demand and small hospitals are allowed to transship to the big hospital to mitigate their wastage. The problem is formulated as an infinite-horizon dynamic programming model. The objective of this model is to determine an optimal ordering and transshipment policy that minimizes the total expected cost. An approximate dynamic programming (ADP) model is used to approximate the value function with a linear combination of basis functions, using column generation to cope with the course of dimensionality. The numerical results suggest that considerable cost saving can be achieved by using an ADP model. The third model (presented in Chapter 4) proposes a proactive transshipment policy for a network of hospitals with uncertain demand. At the beginning of each review period, each hospital makes decisions on the quantity to order from a central blood bank and to transship to other hospitals. The problem is formulated as a two-stage stochastic programming model where the Quasi-Monte Carlo (QMC) sampling approach is used to generate scenarios and the optimal number of scenarios is determined by conducting stability tests. The performance of the developed model is evaluated through numerical experiences. The numerical results indicate significant potential cost savings in comparison with the current policy in use and the no-transshipment policy

Ensuring blood is available when it is needed most

The provision of blood to patients in need is an imperative faced by all countries.  Red blood cells (RBCs) are perishable with a life of 42 days.  Inventory managers at hospitals need to know how many RBCs to order so that the probability of experiencing shortages or outdates is minimised.  This is complicated by demand for RBCs being doubly stochastic.  Both the number of patients that need RBCs and quantity of RBCs they will need are random.  For centralised blood banks not only are the orders they receive from hospitals apparently random, the supply of blood is also random. This thesis shows that, in addition to the previously mentioned sources of volatility, the structure of the supply chain induces further volatility.  This occurs due to the presence of delivery delays and negative feedback loops in two locations within the supply chain.  It is shown how this volatility can be addressed with some simple structural changes.  But simply removing system induced volatility does not imply that the supply chain is optimised.  To address optimality the problem is formulated as a Markov decision process (MDP).  A solution to this process uses Stochastic Dynamic Programming (SDP), but this results in a combinatoric explosion making the computation of an exact solution within a reasonable time impossible.  Instead, Stochastic Average Approximation (SAA) is used to derive an approximate solution.  Repeated, sequential application of this is an exercise in Discrete Time Stochastic Control.  A working control solution is provided in python.  This solution can be arranged so as to mimic the two echelon supply chain found in blood inventories.  It is general enough to apply to any discrete perishable inventory system with random demand and/or supply. The approach for blood inventories requires credible estimates of demand for RBCs.  It is shown, using hierarchical Bayesian modelling and Discrete Phase-Type (DPH) distributions, that credible estimates of demand at hospitals of any size can be derived from publicly available information.  In particular a new method for obtaining the parameters of a DPH distribution is formulated and applied to estimating transfusion quantities from publicly available sources. An application of the proposed solution is presented for RBC inventories at both hospitals and at the blood bank.  For the blood bank in particular it is shown how this can be used to determine the quantity of donors needed to meet demand within a desired probability of adequacy

An intelligent computational approach to the optimization of inventory policies for single company

This study develops and tests a computational approach for determining optimal inventory policies for single company. The computational approach generally comprises of two major components: a meta-heuristic optimizer and an event-driven inventory evaluation module. Meta-heuristic is a powerful search technique, under the intelligent computational paradigm. The approach is capable of determining optimal inventory policy under various demand patterns regardless their distribution for a variety of inventory items. Two prototypes of perishability are considered: (1) sudden deaths due to disasters and (2) outdating due to expirations. Since every theoretical model is specially designed for a certain type of inventory problem while the real world inventory problems are numerous, it is desirable for the newly proposed computational approach to cover as many inventory problems/models as possible. In a way, the proposed meta-heuristic based approach unifies many theoretical models into one and beyond. Experimental results showed that the proposed approach provides comparable results to the theoretical model when demand follows their assumption. For demands not well conformed to the assumption, the proposed approaches are able to handle it but the theoretical approaches do not. This makes the proposed computational approach advantageous in that it can handle various types of real world demand data without the need to derive new models. The main motivation for this work is to bridge the gap between theory and practice so as to deliver a user-friendly and flexible computational approach for rationalizing the inventory control system for single company

Perishable Items in Multi-Level Inventory Systems

This master thesis studies a two-echelon distribution system for perishable items with two non identical retailers. Each location is managed following a standard continuous (R, Q) ordering policy. The demand occurs solely at the retailers and follows independent Poisson processes. Customers are backordered when the retailer is out of stock. The items are considered as fixed lifetime perishables. Whenever an item perished, it is discarded from the stock. The model includes fix transportation time and the allocation policy at the central warehouse is a First-Come-First-Serve one. This kind of system is very complicated and therefore hard to study. In this master thesis, we focus on a simulation study of 48 different problems with both a FIFO and a LIFO issuing policy at the retailers. The goal of this study is therefore to optimize the values of R in (R, Q) ordering policies considering that the items are perishables. To do so, we try to optimize the values of the reorder points at every location. We also try to find some general behaviour of the system and we compare the FIFO and the LIFO best found solution. More than 1000 hours of computer-time were used for this study. For every problem, we conducted an optimization process to find better values of the reorder points at every location. For the FIFO case, an average cost reduction of more than 20% was found. It exists a good opportunity in term of cost savings while taking into account the perishable characteristic of the items. Another finding of our study is that the LIFO case has good performance comparing to what expected. On average, the costs increase is only 7% while considering a LIFO issuing policy instead of a FIFO one. Moreover, the values of the reorder points for the FIFO best found solution are still the same than the LIFO best found solution in 70% of the problems studied

Modelling and Determining Inventory Decisions for Improved Sustainability in Perishable Food Supply Chains

Since the introduction of sustainable development, industries have witnessed significant sustainability challenges. Literature shows that the food industry is concerned about its need for efficient and effective management practices in dealing with perishability and the requirements for conditioned storage and transport of food products that effect the environment. Hence, the environmental part of sustainability demonstrates its significance in this industrial sector. Despite this, there has been little research into environmentally sustainable inventory management of deteriorating items. This thesis presents mathematical modelling based research for production inventory systems in perishable food supply chains. In this study, multi-objective mixed-integer linear programming models are developed to determine economically and environmentally optimal production and inventory decisions for a two-echelon supply chain. The supply chain consists of single sourcing suppliers for raw materials and a producer who operates under a make-to-stock or make-to-order strategy. The demand facing the producer is non-stationary stochastic in nature and has requirements in terms of service level and the remaining shelf life of the marketed products. Using data from the literature, numerical examples are given in order to test and analyse these models. The computational experiments show that operational adjustments in cases where emission and cost parameters were not strongly correlated with supply chain collaboration (where suppliers and a producer operate under centralised control), emissions are effectively reduced without a significant increase in cost. The findings show that assigning a high disposal cost, limit or high weight of importance to perished goods leads to appropriate reduction of expected waste in the supply chain with no major cost increase. The research has made contributions to the literature on sustainable production and inventory management; providing formal models that can be used as an aid to understanding and as a tool for planning and improving sustainable production and inventory control in supply chains involving deteriorating items, in particular with perishable food supply chains.the Ministry of Science and Technology, the Royal Thai Government