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

Two perishable inventory systems with one-way substitution

Motivated by the ABO issue of the blood banks system, in which the portions stored have constant shelf life, we consider two subsystems of perishable inventory. The two Perishable Inventory Subsystems -- PIS A and PIS B, are correlated to each other through a so-called one-way substitution of demands. Specifically, the input streams and the demand streams applied to each subsystem are four Poisson processes which are independent of one another. However, if the shelf of PIS A (blood of type O) is empty of items an arriving demand of type A is unsatisfied, since demand of type A cannot be satisfied by an item of type B (blood portions of type AB), but if the shelf of PIS B is empty of items an arriving demand of type B is applied to PIS A, since demands of type B can be satisfied by both types. Such a one-way substitution of the issuing policy generates for PIS A a modulated Poisson demand process operating in a two-state non-Markovian environment. The performance analysis of PIS B is known from previous work. Hence, in this study we focus on the marginal performance analysis of PIS A. Based on a fluid formulation and a Markovian approximation for the one-way substitution demands process, we develop a unified approach to efficiently and accurately approximate the performance of PIS A. The effectiveness of the approach is investigated by extensive numerical experiments

Pricing perishable products with compound poisson demands

2011-2012 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Perishable inventories with random input:a unifying survey with extensions

This paper is devoted to the theory of perishable inventory systems. In such systems items arrive and stay ‘on the shelf’ until they are either taken by a demand or become outdated. Our aim is to survey, extend and enrich the probabilistic analysis of a large class of such systems. A unifying principle is to consider the so-called virtual outdating process V , where V(t) is the time that would pass from t until the next outdating if no new demands arrived after t. The steady-state density of V is determined for a wide range of perishable inventory systems. Key performance measures like the rate of outdatings, the rate of unsatisfied demands and the distribution of the number of items on the shelf are subsequently expressed in that density. Some of the main ingredients of our analysis are level crossing theory and the observation that the V process can be interpreted as the workload process of a specific single server queueing system.</p

Data-Driven Algorithms for Stochastic Supply Chain Systems: Approximation and Online Learning

In the era of Big Data, with new and emerging technologies, data become easily attainable for companies. However, acquiring data is only the first step for the company. The second and more important step is to effectively integrate the data through the learning process (mining the data) in the decision-making process, and to utilize the information extracted from data to improve the efficiency of the company’s supply chain operation. The primary focus of this dissertation is on multistage stochastic optimization problems arising in the context of supply chains and inventory control problems, and on the design of efficient algorithms to solve the respective models. This dissertation can be categorized into two broad areas as follows. The first part of this dissertation focuses on the design of non-parametric learning algorithms for complex inventory systems with censored data. We address two challenging stochastic inventory control models: the periodic-review perishable inventory system and the periodic-review inventory control problem with lost-sales and positive lead times. We assume that the decision maker has no demand distribution information available a priori and can only observe past realized sales (censored demand) information to optimize the system's performance on the fly. For each of the problems, we design a learning algorithm that can coverage to the best base-stock policy with tight regret rate. The second part of this dissertation focuses on the design of approximation algorithms for stochastic perishable inventory systems with correlated demand. In this part, we consider the perishable inventory system from the optimization perspective. Different from traditional perishable inventory literature, we allow demands to be arbitrarily correlated and nonstationary, which means we can capture the seasonality nature of the economy, and allow the decision makers to effectively incorporate demand forecast. For this problem, we develop two approximation algorithms with worst-case performance guarantees. Through comprehensive numerical experiments, we have shown that the numerical performances of the approximation algorithms are very close to optimal.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138697/1/zhanghn_1.pd