Random Replenishment Research Articles

Be the Match: Optimizing Capacity Allocation for Allogeneic Stem Cell Transplantation

Problem definition: Treating many blood-related diseases requires transplantation of genetically compatible hematopoietic stem cells (HSCs) extracted from the bone marrow (BM) of live donors or the umbilical cord blood (CB) of babies. To facilitate the search for HSCs, institutions known as BM registries collect the details of potential donors and CB banks store units of CB. This paper focuses on the problem of joint optimization of the capacity of these two institutions. Academic/practical relevance: With more than 10 million genetic variants, limited inventory relative to this variety, and random replenishment, BM registry and CB bank compositions are random, interdependent, and change nondeterministically over time. Furthermore, BM and CB differ in their supply, costs, genetic matching criteria, and influences on medical outcomes, giving rise to important tradeoffs such that neither is preferred exclusively to the other. Jointly determining the optimal capacity of both sources is therefore both technically challenging and has immediate policy implications. Methodology: We develop a simulation-based approach to estimate the temporal variation in matching probabilities before incorporating the associated regression parameters into a mathematical model closely matching the research context. Results are contrasted against a simplified mathematical model, highlighting the importance of the dynamic setup. Results: Inventories of 17.5 million registered BM donors and 335,000 CB units are estimated as optimal for the U.S. population under reasonable assumptions. Expanding capacity to these levels would satisfy 33% of the currently unmet demand, increasing the transplantation rate to 98.7% and delivering $770 million of extra social surplus annually. Managerial implications: Rigorous policy analyses are imperative for designing evidence-based, cost-effective policies that deliver societal benefits. To this end, we provide quantitative evidence in support of calls for further expansion of the national BM registry and CB banks in the United States. We also propose annual recruitment targets for BM donors and CB units to maintain the two institutions at their suggested levels.History: This paper has been accepted for the Manufacturing & Service Operations Management Special Section on Responsible Research in Operations Management.Supplemental Material: The e-companion is available at https://doi.org/10.1287/msom.2022.1093 .

Queuing-Inventory Models with MAP Demands and Random Replenishment Opportunities

Combining the study of queuing with inventory is very common and such systems are referred to as queuing-inventory systems in the literature. These systems occur naturally in practice and have been studied extensively in the literature. The inventory systems considered in the literature generally include (s,S)-type. However, in this paper we look at opportunistic-type inventory replenishment in which there is an independent point process that is used to model events that are called opportunistic for replenishing inventory. When an opportunity (to replenish) occurs, a probabilistic rule that depends on the inventory level is used to determine whether to avail it or not. Assuming that the customers arrive according to a Markovian arrival process, the demands for inventory occur in batches of varying size, the demands require random service times that are modeled using a continuous-time phase-type distribution, and the point process for the opportunistic replenishment is a Poisson process, we apply matrix-analytic methods to study two of such models. In one of the models, the customers are lost when at arrivals there is no inventory and in the other model, the customers can enter into the system even if the inventory is zero but the server has to be busy at that moment. However, the customers are lost at arrivals when the server is idle with zero inventory or at service completion epochs that leave the inventory to be zero. Illustrative numerical examples are presented, and some possible future work is highlighted.

Be the Match: Optimizing Capacity Allocation for Allogeneic Stem Cell Transplantation

Problem definition: Treating many blood-related diseases requires transplantation of genetically compatible hematopoietic stem cells (HSCs) extracted from the bone marrow (BM) of live donors or the umbilical cord blood (CB) of babies. To facilitate the search for HSCs, institutions known as BM registries collect the details of potential donors and CB banks store units of CB. This paper focuses on the problem of joint optimization of the capacity of these two institutions. Academic: With over 10 million genetic variants, limited inventory relative to this variety, and random replenishment, BM registry and CB bank compositions are random, inter-dependent, and change nondeterministically over time. Furthermore, BM and CB differ in their supply, costs, genetic matching criteria, and influenc s on medical outcomes, giving rise to important trade-offs such that neither is preferred exclusively to the other. Jointly determining the optimal capacity of both sources is therefore both technically challenging and has immediate policy implications. Methodology: We develop a simulation-based approach to estimate the temporal variation in matching probabilities before incorporating the associated regression parameters into a mathematical model closely matching the research context. Results are contrasted against a simplified mathematical model, highlighting the importance of the dynamic setup. Results: Inventories of 17.5 million registered BM donors and 335 thousand CB units are estimated as optimal for the U.S. population under reasonable assumptions. Expanding capacity to these levels would satisfy 33% of the currently unmet demand, increasing the transplantation rate to 98.7% and delivering $770 million of extra social surplus annually. Managerial Implications: Rigorous policy analyses are imperative for designing evidence-based, cost-effective policies that deliver societal benefits. To this end, we provide quantitative evidence in support of calls for further expansion of the national BM registry and CB banks in the U.S. We also propose annual recruitment targets for BM donors and CB units to maintain the two institutions at their suggested levels.

PERISHABLE INVENTORY MODEL WITH FINITE RATE OF REPLENISHMENT HAVING GENERALIZED PARETO DECAY

In this paper an EPQ model for deteriorating items is developed and analyzed an inventory model for deteriorating items with the assumptions that the lifetime of the community is random and follows a Generalized Pareto distribution, having constant demand rate with shortages. The total cycle length in this model is divided into our non-over lapping intervals depending on the decrease of stock. Assuming that shortages are allowed and fully back backlogged, the differential equations governing the instantaneous state of inventory are developed and solved for I(t). The loss due to deterioration, the total backlogged demand, the ordering quantity is also derived with suitable cost consideration. The total profit per unit time is developed and optimized with respect to the time at which production is to be started, time at which shortages occur, the time at which production is to be restated. The optimal ordering quantity, Q is also obtained for given values of the parameters. A numerical illustration is presented. This model also includes some of the earlier models as particular cases for specific values of the parameters. KEYWORDS: Random Replenishment; Generalized Pareto Decay; Constant Demand; Shortages.

Time-based service constraints for inventory systems with commitment lead time

We consider a firm which targets a certain level of customer responsiveness with a minimum operational cost. The firm employs a preorder strategy, in which customers place their orders before their actual need based on a predefined time window called commitment lead time and, in turn, they receive a bonus. The firm aims to determine the optimal control policy, which consists of the optimal commitment lead time and the optimal base-stock level, such that the total operational cost is minimized subject to a time-based service level target. We formulate two time-based service criteria to measure the firm’s responsiveness in terms of average customer waiting time and individual customer waiting time in two constraint optimization models called ACO and CCO, respectively. We derive the exact probability distribution of customer waiting time, and we propose exact and heuristic optimization algorithms to solve the ACO and CCO models. We show that the commitment lead time not only increases the firm’s responsiveness level but also decreases the customers’ maximum waiting time. We find that when the firm targets a high level of responsiveness, the value of commitment lead time is more highlighted. We study multiple interesting extensions with two customer classes, random replenishment lead times and a combined model with two time-based service level targets.

Studies on inventory model for deteriorating items with Weibull replenishment and generalised Pareto decay having time dependent demand

Inventory models play an important role in determining the optimal ordering and pricing policies. Much work has been reported in literature regarding inventory models with finite or infinite replenishment. But in many practical situations the replenishment is governed by random factors like procurement, transportation, environmental condition, availability of raw material, etc. Hence, it is needed to develop inventory models with random replenishment. In this paper an EPQ model for deteriorating items is developed and analysed with the assumption that the replenishment is random and follows a Weibull distribution. It is further assumed that the life time of a commodity is random and follows a generalised Pareto distribution and demand is a function of time. Using the differential equations the instantaneous state of inventory is derived. With suitable cost considerations the total cost function is obtained. By minimising the total cost function the optimal ordering policies are derived. Through numerical illustrations the sensitivity analysis is carried. The sensitivity analysis of the model reveals that the random replenishment has significance influence on the ordering and pricing policies of the model. This model also includes some of the earlier models as particular cases for specific values of the parameters.

An inventory model for random replenishment interval and imperfect quality items under demand fluctuation

Continuous review and periodic review are two extensively discussed replenishment procedures for inventory problems in the literature. But, when a supplier delivers inventories to a retailer with random inter-arrival times, it is not possible to determine the retailer's order level using these two procedures. In that case, replenishment will be periodic but replenishment intervals will be random. Considering replenishment interval as independent and identically distributed random variable an inventory model is developed in which a known percentage of received items are defective. Fluctuation in demand for perfect quality inventory, arises due to the impact of several marketing parameters, is taken into account. A portion of unmet demand for perfect quality inventory is back-ordered and the rest is lost. The mathematical model is developed. Both fluctuation and no fluctuation in demand are discussed. A numerical example is presented and sensitivity analysis of the model is carried out.

An inventory model for random replenishment interval and imperfect quality items under demand fluctuation

Continuous review and periodic review are two extensively discussed replenishment procedures for inventory problems in the literature. But, when a supplier delivers inventories to a retailer with random inter-arrival times, it is not possible to determine the retailer's order level using these two procedures. In that case, replenishment will be periodic but replenishment intervals will be random. Considering replenishment interval as independent and identically distributed random variable an inventory model is developed in which a known percentage of received items are defective. Fluctuation in demand for perfect quality inventory, arises due to the impact of several marketing parameters, is taken into account. A portion of unmet demand for perfect quality inventory is back-ordered and the rest is lost. The mathematical model is developed. Both fluctuation and no fluctuation in demand are discussed. A numerical example is presented and sensitivity analysis of the model is carried out.

Shelf Loathing: Cross Docking at an Online Retailer

Online customers expect to wait, sometimes for a delay of many days. At the fulfillment center, there might be an opportunity to fill customer orders earlier than the due date through a cross‐docking transaction: rather than picking the item from inventory, the item moves directly from the receiving to the shipping dock, saving shelving and picking transactions. While cross docking reduces shelving and picking costs, it risks changing customer expectations for how soon a product will be delivered. Given customer order arrivals random in quantity and due dates, random replenishment arrivals, and costs (or benefits) for shipping a product early, we characterize the optimal decision as to whether to cross dock a replenishment item to fulfill demand that is not immediately due or to wait to (hopefully) cross dock in later periods. With multiple demands and due dates, the cross‐docking decision depends on the number of unfulfilled demands in each period across the horizon, the number of units that have just arrived (available for cross docking), picking and shelving costs, and the delay cost (or benefit). We formulate the problem as a Markov decision process, determine the structure of the optimal policy, and propose a well‐performing heuristic.

A dynamic inventory rationing problem with uncertain demand and production rates

We investigate the structural properties of a finite horizon, discrete time single product inventory rationing problem, where we allow random replenishment (production) opportunities. In contrast to the standard models of dynamic capacity control in revenue management or production/inventory systems, we assume that the demand/production rates are not known with certainty but lie in some interval. To address this uncertainty, we formulate a robust stochastic dynamic program and show how the structural properties of the optimal policy propagate to the robust counterpart of the problem. Further, we explore how the optimal policy changes with respect to the uncertainty set. We also show that our results can be extended to certain alternative robust formulations.

A multi-level inventory system with a make-to-order supplier

We study a supply network comprising a factory, a central warehouse using a discrete-time reorder point–reorder quantity policy and multiple regional distribution centres applying discrete-time base-stock policies under consideration of a fill rate constraint. The warehouse is supplied from the factory, which has a limited capacity and which follows a make-to-order strategy. The complete system is analysed by decomposition into three layers that are linked through layer-specific random replenishment lead times. An overall optimisation model including as decision variables the processing time in the factory and the parameters of the inventory policies applied in the warehouse and the distribution centres is formulated and solved.

Inventory rationing decision models during replenishment lead time

Abstract This study considers an inventory rationing problem in which a warehouse maintains inventory to meet various future requests that are classified into a discrete number of priorities. When there is limited inventory quantity in the warehouse, we prefer to fulfill higher priority requests over lower priority requests. When a low priority request does arrive, the warehouse may need to reject the request and reserve the inventory for later higher priority requests. However, we would rather satisfy lower priority requests than have inventory leftover when the replenishment arrives. To face uncertain request arrivals during an uncertain replenishment lead time, we develop two rationing approaches, dynamic stochastic inventory rationing decision procedure (DSIR) and risk level inventory rationing decision procedure (RLIR), to determine whether to fulfill or reject an arrival request. The simulation experiments show that RLIR provides the highest fill rate for the first priority requests among all simulated approaches, whereas DSIR provides the best overall fill rate while still maintaining a good fill rate for first priority requests. Furthermore, unlike previous studies, the proposed approaches can handle inventory systems with not only random request quantity, but also random replenishment lead time. In addition, most previous studies can only deal with two priority classes, whereas this study can handle a problem of more than two classes.

Optimal MRP parameters for a single item inventory with random replenishment lead time, POQ policy and service level constraint

This study deals with Material Requirement Planning (MRP) software parameterization under uncertainties. The actual lead time has random deviations; so it can be considered as a random variable. MRP approach with Periodic Order Quantity (POQ) policy is considered. The aim is to find the optimal MRP time phasing corresponding to each periodicity of the POQ policy. This is a crucial issue in supply planning with MRP approach because inappropriate planned lead times under lead time uncertainties invariably lead to large and costly inventories or insufficient customer service levels. The proposed model and algorithms minimize the sum of the setup and holding costs while satisfying a constraint on the service level. Our approach does not need to employ the commonly used normal probability distributions. Instead, its originality is in finding a closed form of the objective function, valid for any probability distribution of the actual lead times.

Replenish-up-to inventory control policy with random replenishment intervals

The multi period inventory problems have been studied under two main assumptions. Continuous review assumption where an order can be made at any time depending on inventory position and periodic review assumption where an order can be initiated only at discrete time epochs. In this study, we analyze a multi period inventory problem that falls under neither of these two assumptions. In the case we consider, there are periodic replenishments but the replenishment intervals are taken to be i.i.d. random variables. This setting represents the real life cases where a supplier visits a retailer with random inter arrival times and the retailer replenishes his inventories based on a replenish-up-to-level inventory control policy. We also assume that only a certain fraction of unmet demand is backordered and the rest of it is lost.In this setting under general distribution between replenishment epochs, we show the concavity of the expected profit function and give the condition that must hold for the optimal replenish-up-to-level. We also present the specific solutions and analysis under two different distributions, namely, uniform and exponential distributions, together with some numerical examples.

The effectiveness of investment in lead time reduction for a make-to-stock product

This paper focuses on a firm selling a make-to-stock product with a constant customer demand rate. The firm follows an exact (Q, r) policy for raw material inventory control and faces a random replenishment lead time. Through this research, we wish to gain a better understanding of the impact of investing in reducing supply lead time when the investment costs have to be borne, partly or fully, by the firm. This work is motivated by the recognition that lead time reduction is now of strategic importance in the successful operation of a firm. We examine different types of investment schemes in replenishment lead time reduction and the different cost models they generate. We present analytical and numerical results and insights for each type of model, compute the optimal (Q, r) policy and the associated investment levels. The work presents new results, and sheds light on some apparently counter-intuitive observations.

A dynamic inventory model with random replenishment quantities

A periodic-review, random-demand inventory model is analyzed under the assumption that replenishment quantities are random fractions of the amounts ordered. Results of a previous study of a single-period model are generalized to form an easily computed heuristic adaptation of the ( s, S) policy for use in this environment. The heuristic is based on the simple practice of scaling down pipeline inventories to estimate the inventory position, and scaling up the order quantity in anticipation of an average replenishment yield. Simulation experiments are used to estimate the most cost-efficient ( s, S) policies and to estimate the performance of heuristic policies in environments where replenishment randomness ranges from mild (0–20% defectives) to moderate (0–50% defectives). The heuristic is shown to perform quite well, with expected total costs typically within a few percent of the best ( s, S) costs. The results tend to support common practice in industry which is similar to the approach studied here. Although the heuristic is naive in the sense that it ignores the degree of randomness in the replenishment quantity, the simulation results support the speculation that unless the target service level is extremely high, the replenishment process must be extremely random for its variability to be a significant explicit factor in the selection of a practical, cost-effective policy.

The newsboy with known demand and uncertain replenishment: Applications to quality control and container fill

Consider a newsboy problem with known demand and random replenishment. The distribution of the replenishment quantity is determined by a location-scale parameter, (μ, δ), which can be controlled. The usual expected cost function includes a separate term associated with the choice of δ. The asymptotic behavior of the optimal parameter values, as functions of the holding and shortage costs, is examined.