Analysis of an assemble-to-order system with different review periods

We consider a single item assembled from two components. One of the components has a long leadtime, high holding cost and short review period as compared to the other one. We assume that net stocks are reviewed periodically, customer demand is stochastic and unsatisfied demand is back ordered. We analyze the system under two different policies and show how to determine the policy parameters minimizing average holding and backorder costs. First, we consider a pure base stock policy, where orders for each component are placed such that the inventory position is raised up to a given base stock level. In contrast to this, only the orders for one component follow this logic while the other orders are synchronized in case of a balanced base stock policy. Through mathematical analysis, we come up with the exact long-run average cost function and we show the optimality conditions for both policies. In a numerical study the policies are compared and the results suggest that the balanced base stock policy works better than the pure base stock policy under low service levels and when there is a big difference in the holding costs of the components

Push verse pull:Inventory-leadtime tradeoff for managing system variability

We study a two-stage push–pull system in an assemble-to-order manufacturing environment. Modelling the system as an inventory-queue model, we construct a decision model to determine the optimal stock level of the semifinished base product and the optimal leadtime of the finished products that will minimize the total operational cost. We analytically characterize the structure of the optimal policy. For systems with moderate demand and upstream processing time variabilities, there exists a threshold determined purely by the tradeoff of operational costs so that when the upstream utilization is above the threshold, the push–pull strategy is optimal; otherwise the pure-pull strategy is optimal. When the inter-arrival time or the upstream service time follows a general probability distribution, the optimal policy depends on the demand or process variability at the upstream stage. Our results can be used to guide managers in selecting the right inventory and leadtime strategy to cope with system variability. We find that in comparison of the downstream variability, under some mild condition, the upstream variability has a more significant impact on the choice of the optimal policy, the corresponding inventory, and lead time. Further, the guaranteed/constant downstream processing time does not always benefit the supply chain performance

Spare parts inventory control for an aircraft component repair shop

We study spare parts inventory control for a repair shop for aircraft components. Defect components that are removed from the aircraft are sent to such a shop for repair. Only after inspection of the component, it becomes clear which specific spare parts are needed to repair it, and in what quantity they are needed. Market requirements on shop performance are reflected in fill rate requirements on the turn around times of the repairs for each component type. The inventory for spare parts is controlled by independent min-max policies. Because parts may be used in the repair of different component types, the resulting optimization problem has a combinatorial nature. Practical instances may consist of 500 component types and 4000 parts, and thus pose a significant computational challenge. We propose a solution algorithm based on column generation. We study the pricing problem, and develop a method that is very efficient in (repeatedly) solving this pricing problem. With this method, it becomes feasible to solve practical instances of the problem in minutes

Periodic review base-stock replenishment policy with endogenous lead times.

In this paper, we consider a two stage supply chain where the retailer's inventory is controlled by the periodic review, base-stock level (R,S) replenishment policy and the replenishment lead times are endogenously generated by the manufacturer's production system with finite capacity. We extend the work of Benjaafar and Kim (2004) who study the effect of demand variability in a continuously reviewed base-stock policy with single unit demands. In our analysis, we allow for demand in batches of variable size, which is a common setting in supply chains. A procedure is developed using matrix analytic methods to provide an exact calculation of the lead time distribution, which enables the computation of the distribution of lead time demand and consequently the safety stock in an exact way instead of using approximations. Treating the lead time as an endogenous stochastic variable has a substantial impact on safety stock. We numerically show that the exogenous lead time assumption may dramatically degrade customer service.Production/inventory systems; Base-stock replenishment policy; endogenous lead times; Safety stock; Phase-type distribution; Matrix-analytical methods;

Order fulfillment in online retailing : what goes where

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2005.Includes bibliographical references (p. 139-146).We present three problems motivated by order fulfillment in online retailing. First, we focus on one warehouse or fulfillment center. To optimize the storage space and labor, an e-tailer splits the warehouse into two regions with different storage densities. One is for picking customer orders and the other to hold a reserve stock that replenishes the picking area. Consequently, the warehouse is a two-stage serial system. We investigate an inventory system where demand is stochastic by minimizing the total expected inventory- related costs subject to a space constraint. We develop an approximate model for a periodic review, nested ordering policy. Furthermore, we extend the formulation to account for shipping delays and advance order information. We report on tests of the model with data from a major e-tailer. Second, we focus on the entire network of warehouses and customers. When a customer order occurs, the e-tailer assigns the order to one or more of its warehouses and/or drop- shippers, so as to minimize procurement and transportation costs, based on the available current information. However, this assignment is necessarily myopic as it cannot account for any subsequent customer orders or future inventory replenishments.(cont.) We examine the benefits from periodically re-evaluating these real-time assignments. We construct near- optimal heuristics for the re-assignment for a large set of customer orders by minimizing the total number of shipments. Finally, we present saving opportunities by testing the heuristics on order data from a major e-tailer. Third, we focus on the inventory allocation among warehouses for low-demand SKUs. A large e-tailer strategically stocks inventory for SKUs with low demand. The motivations are to provide a wide range of selections and faster customer fulfillment service. We assume the e-tailer has the technological capability to manage and control the inventory globally: all warehouses act as one to serve the global demand simultaneously. The e-tailer will utilize its entire inventory, regardless of location, to serve demand. Given we stock certain units of system inventory, we allocate inventory to warehouses by minimizing outbound transportation costs. We analyze a few simple cases and present a methodology for more general problems.by Ping Josephine Xu.Ph.D

Integrated service engineers and spare parts planning in the maintenance logistics

We analyze the integrated tactical capacity planning of spare parts supply and workforce allocation in maintenance logistics of advanced equipment. The equipment time-to-failure, spare parts replenishment time, and equipment repair time are random and independent of each other

Traditional Inventory Models in an E-Retailing Setting: A Two-Stage Serial System with Space Constraints

In an e-retailing setting, the efficient utilization of inventory, storage space, and labor is paramount to achieving high levels of customer service and company profits. To optimize the storage space and labor, a retailer will split the warehouse into two storage regions with different densities. One region is for picking customer orders and the other to hold reserve stock. As a consequence, the inventory system for the warehouse is a multi-item two-stage, serial system. We investigate the problem when demand is stochastic and the objective is to minimize the total expected average cost under some space constraints. We generate an approximate formulation and solution procedure for a periodic review, nested ordering policy, and provide managerial insights on the trade-offs. In addition, we extend the formulation to account for shipping delays and advanced order information.Singapore-MIT Alliance (SMA

Maintenance Centered Service Parts Inventory Control

High-tech capital goods enable the production of many services and articles that have become a part of our daily lives. Examples include the refineries that produce the gasoline we put in our cars, the photolithography systems that enable the production of the chips in our cell phones and laptops, the trains and railway infrastructure that facilitate public transport and the aircraft that permit us to travel long distances. To prevent costly production disruptions of such systems when failures occur, it is crucial that service parts are readily available to replace any failed parts. However, service parts represent significant investments and failures are unpredictable, so it is unclear which parts should be stocked and in what quantity. In this thesis, analytical models and solution methods are developed to aid companies in making this decision. Amongst other things, we analyze systems in which multiple parts need replacement after a failure, a situation that is frequently encountered in practice. This affects the ability to complete repairs in a timely fashion. We develop new modeling techniques in order to successfully apply scalable deterministic approaches, such as column generation techniques and sample average approximation methods, to this stochastic problem. This leads to solution techniques that, unlike traditional methods, can ensure that all parts needed to complete maintenance are readily available. The approach is capable of meeting the challenging requirements of a real-life repair shop