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OR/MS Models for Supply Chain Disruptions: A Review

ABSTRACT We review the Operations Research/Management Science (OR/MS) literature on supply chain disruptions in order to take stock of the research to date and to provide an overview of the research questions that have been addressed. We first place disruptions in the context of other forms of supply uncertainty and discuss common modeling approaches. We then discuss 180 scholarly works on the topic, organized into six categories: evaluating supply disruptions; strategic decisions; sourcing decisions; contracts and incentives; inventory; and facility location. We conclude with a discussion of future research directions.

Inventory Strategies to Manage Supply Disruptions

Disruptions in supply chains occur routinely—both large ones, due to natural disasters, labor strikes, or terrorist attacks, and small ones, due to machine breakdowns, supplier stockouts, or quality problems (to name a few examples). Companies whose supply processes are affected by disruptions may experience delays in transportation and dysfunction in some of their facilities, which may result in inventory shortages. Although firms can take measures to prevent them, some disruptions are inevitable. Hence, in order to avoid the drastic impact of these disruptions, firms need to protect against them. There are multiple tactics that companies can choose from for managing the risk of disruptions. One of the most common tactics is to use inventory to buffer against the additional uncertainty. The main concern in inventory management problems is to find the optimal replenishment policy that tells when, from whom and how much to order.

Disruptions in One-Warehouse Multiple-Retailer Systems

We study two-echelon distribution systems (also known as one-warehouse, multiple-retailer (OWMR) systems) subject to supply disruptions. We propose algorithms to find the optimal or near-optimal stocking levels of all the locations in the system by assuming periodic review base-stock policies, deterministic demands at the retailers and non-overlapping disruptions at the supply processes of the warehouse and the retailer. This is the first paper to consider OWMR systems with all locations keeping inventory and all locations subject to supply disruptions. We show how supply disruptions at different parts of the network affect inventory decisions and we quantify the effects of ignoring the disruptions at different parts of the supply chain. Our results suggest that companies should work on reducing the duration of supply disruptions instead of trying to prevent them. In addition, if they choose to do nothing to prevent the consequences of some of the disruptions, these should not be the ones happening close to the customers.

Setting planned leadtimes in customer-order-driven assembly systems

We study an assembly system with a number of parallel multistage processes feeding a multistage final assembly process. Each stage has a stochastic throughput time. We assume that the system is controlled by planned leadtimes at each stage. From these planned leadtimes the start and due times of all stages can be derived. If a job finishes at a particular stage and has to wait before the start of the next job(s), a holding cost proportional to the waiting time is incurred. A penalty cost proportional to the lateness is incurred when the last stage of the final assembly process finishes after its due time. The objective is to determine planned leadtimes for each individual stage, such that the expected cost of a customer order is minimized.We derive the recursive equations for the tardiness and earliness at all stages and an exact expression for the expected cost. We discuss the similarity between these expressions and those for serial inventory systems. Based on this observation and a conjecture related to the generalized Newsvendor equations, we develop an iterative heuristic procedure. Comparison with a numerical optimization method confirms the accuracy of the heuristic. Finally, we discuss an application of the model to a real-life case, showing the added value of a system-wide optimization of planned leadtimes compared to current practice.

EOQ models with supply disruptions

Most of the early research in inventory theory concentrates purely on demand uncertainty. However, models which aim to capture the dynamics of real-world systems must also take uncertainties in the supply side into consideration. One type of supply uncertainty that has attracted considerable attention during the past decade is supply disruptions, such as those that arise as a result of customs delays, labor strikes, and natural disasters. Over the past several years, companies have developed many strategies to mitigate the effects of such disruptions. One strategy is to hold more inventory with the additional amount serving as a buffer against disruptions. Since it is among the most basic inventory models, the EOQ model features prominently in the earliest work on disruptions, as well as many subsequent models. This chapter summarizes the studies on EOQ models with supply disruptions.

Optimal and heuristic policies for assemble-to-order systems with different review periods

We study an assemble-to-order (ATO) system with a single end product assembled from two components. The inventory levels of the components are reviewed periodically. One component is expensive and has a long lead time and short review period, whereas the other component is relatively cheap with a shorter lead time and longer review period. The lead times are deterministic and review periods are determined exogenously. Stochastic customer demand occurs for the end product only and unsatisfied customer demands are backordered. The system incurs holding costs for component inventories and penalty costs for backorders. Assuming an infinite planning horizon, our objective is to identify the optimal component ordering policy to minimize the long-run average cost. Under specific demand distributions we identify the properties of the optimal component ordering policy and observe that the optimal policy has a complex state-dependent structure. Motivated by the complexity of the optimal policy, we introduce a heuristic component ordering policy for more general demand distributions. Given that the heuristic performs well, we use it to measure the effects of various system parameters on the total cost.

Setting optimal planned leadtimes in configure-to-order assembly systems

Abstract We study a configure-to-order assembly system consisting of multiple parallel subassembly stages and one final assembly stage. Each stage has a stochastic leadtime. The system is controlled by planned leadtimes at each stage. Planned leadtimes are used to plan start and finish times at all stages. The system incurs holding cost for each stage from the planned start time of the stage until the final product is delivered to the customer. In addition, a penalty cost is incurred if the final assembly stage is late. The objective is to set the planned leadtimes for each stage such that the total expected cost is minimized. We prove that the optimal planned leadtimes satisfy a set of Newsvendor equations and show that the probability that a stage is “blamed” for the lateness of the system equals a Newsvendor fractile. We derive structural properties of the optimal solution and compare it with the optimal solution under an alternative holding cost regime.

Lateral Transshipment and Rationing Policies for Multi-Retailer Systems

Many retailers discriminate among their customers based on their value to the firm. Instead of losing a customer due to this discrimination or lack of inventory, a retailer might prefer to request that other retailers satisfy the customers demand. The system as a whole can benefit from this types of transshipments. In this paper, we study a multi-retailer system with each retailer serving two types of customers: high and low priority. Each retailer employs a rationing, critical-level policy in the context of a continuous-review (r,Q) inventory model with lost sales. Retailers can transship items from either other retailers or a central depot. Therefore, no demand is lost; all demand is satisfied by the system. We propose an approximate iterative procedure to find the cost-minimizing policy parameters for individual retailers and propose an iterative heuristic, which relies on adjusting the demand arrival rates and the transshipment costs for both types of customers at all retailers, to solve the overall rationing and transshipment problem. Via numerical analysis, we identify the conditions under which a retailer can benefit from transshipments by changing its rationing policy. In addition, we study the sensitivity of the cost benefit resulting from transshipments with regard to different system parameters.