General Demand Process Research Articles

Truncated Balancing Policy for Perishable Inventory Management: Combating High Shortage Penalties

Problem definition: Motivated by a platelet inventory management problem, we study a fixed lifetime perishable inventory management problem under a general demand process. Determining an optimal ordering policy for perishable inventory systems is particularly challenging because of the well-known “curse of dimensionality.” Approximation policies with worst-case performance bounds have been developed in the literature for perishable inventory systems. However, using real data, we observe that the existing policies tend to underorder when the unit shortage penalty is high, which is an important concern for critical perishable products, such as lifesaving blood products. We seek to address this problem in this paper. Methodology/results: We present a new approximation policy for perishable inventory systems, which we call a truncated balancing (TB) policy. In particular, we first define a new balancing ordering quantity and prove a novel lower bound on the optimal ordering quantity. We then define our TB policy such that the maximum between the balancing ordering quantity and the lower bound is ordered at each period. We prove that when first in, first out is an optimal issuing policy, (1) our proposed TB policy admits a worst-case performance bound of two, and (2) it is asymptotically optimal when the unit shortage penalty goes to infinity. Finally, we present a calibrated numerical study based on real data from our partner hospital and show that our proposed policy performs significantly better than the existing policies in practical scenarios with reasonably high shortage penalties. Managerial implications: Our analysis offers managerial insights for perishable inventory management, especially for systems with an imbalance in underage and overage cost parameters. When the unit shortage penalty is high, simply balancing the underage and overage costs can lead to underordering, whereas our proposed policy effectively addresses this drawback. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0644 .

The impact of cost structure on supply chain cash flow risk

Managing supply chain cash flow risk has become a crucial task for many cash-stressed businesses. Cash flows usually lag behind operating earnings and exhibit higher volatility than earnings, making them less predictable. Through the three components of the cash conversion cycle – days in inventory, receivables, and payables, this study investigates the impact of cost structure – cost ratios and cost compositions – on cash flow risk (standard deviation) and explains why and how management philosophies, such as Just-In-Time, and new production technologies, such as 3D printing, can lower cash flow risk by shortening days in inventory and shifting cost structure. An analytical model built on a simple demand process examines the basic relationship between cost structure and cash flow risk while a simulation approach studies the same relationship under a more general demand process with additional modelling considerations and a benchmark test. The simulation approach is applied on a publicly traded company’s financial data to demonstrate how supply chain process improvement can reduce the cash flow risk.

On the benefits of delayed ordering

Practical experience and scientific research show that there is scope for improving the performance of inventory control systems by delaying a replenishment order that is otherwise triggered by generalised and all too often inappropriate assumptions. This paper presents the first analysis of the most commonly used continuous (s, S) policies with delayed ordering for inventory systems with compound demand. We analyse policies with a constant delay for all orders as well as more flexible policies where the delay depends on the order size. For both classes of policies and general demand processes, we derive optimality conditions for the corresponding delays. In a numerical study with Erlang distributed customer inter-arrival times, we compare the cost performance of the optimal policies with no delay, a constant delay and flexible delays. Sensitivity results provide insights into when the benefit of delaying orders is most pronounced, and when applying flexible delays is essential.

Periodic review and continuous ordering

Abstract Many inventory control studies consider either continuous review and continuous ordering, or periodic review and periodic ordering. Mixtures of the two are hardly ever studied. However, the model with periodic review and continuous ordering is highly relevant in practice, as information on the actual inventory level is not always up to date while making ordering decisions. This paper will therefore treat this model. Assuming zero fixed ordering costs, and allowing for a non-negative lead time and a general demand process, we first consider a one-period decision problem without salvage cost for inventory remaining at the end of the period. In this setting we derive a base-line optimal order path, described by a simple newsvendor solution with safety stocks increasing towards the end of a review period. We then show that for the general, multi-period problem, the optimal policy in a period is to first arrive at this path by not ordering until the excess buffer stock from the previous review period is depleted, then follow the path by continuous ordering, and stop ordering towards the end to limit excess stocks for the next review period. An important managerial insight is that, typically, no order should be placed at a review moment, although this may seem intuitive and is also the standard assumption in periodic review models. We illustrate that adhering to the optimal ordering path instead can lead to cost reductions of 30–60 percent compared to pure periodic ordering.

Dynamic inventory rationing for systems with multiple demand classes and general demand processes

We consider the dynamic rationing problem for inventory systems with multiple demand classes and general demand processes. We assume that backorders are allowed. Our aim is to find the threshold values for this dynamic rationing policy. For single period systems, dynamic critical level policy is developed and the detailed cost approximation subject to this policy is derived. For multiperiod systems, a dynamic rationing policy with periodic review is proposed. The numerical study shows that our dynamic critical level policies are close to being optimal for various parameter settings.

Performance analysis of single stage kanban controlled production systems using parametric decomposition

We present a new approach that permits efficient performance analysis of kanban systems with general demand processes, material arrival processes, and service times. The approach is based on parametric characterization of the traffic processes (arrival and departure) in the network and uses two-moment approximations to estimate performance measures at individual stations. We derive traffic flow constraints that are particular to closed queuing networks with synchronization stations and use these to establish relationships between the parameters characterizing arrival and departure processes at the stations in the network. The resultant set of non-linear equations is solved to estimate network performance measures. Numerical studies show that the approach is not only fast but also reasonably accurate when compared to simulation. These studies also provide insights with respect to the impact of different types of variability on the performance of a kanban system. This work also provides a fundamental building block that can be used in the analysis of multi-stage kanban systems.

Optimal Policy for a Multi-Product, Dynamic, Nonstationary Inventory Problem

This paper is concerned with a multi-product dynamic nonstationary inventory problem in which the system is reviewed at the beginning of each of a sequence of periods of equal length. The model has the following features. There is a general demand process with no stationarity or independence assumptions, partial or complete backlogging of unfilled demand, a fixed non-negative delivery lag (which may be positive only under complete backlogging), a nonstationary linear ordering cost, a nonstationary holding and shortage cost function, discounting of future costs, and nonstationary restrictions like budget and storage limitations. The objective is to choose an ordering policy that minimizes the expected discounted costs over an infinite time horizon. Conditions are given that ensure that the base stock ordering policy is optimal and that the base stock levels in each period are easy to calculate.