A Base Stock Inventory Model for a Remanufacturable Product

We report on an industrial project in which we developed an inventory model to provide decision support for the design and deployment of the field service support system for a remanufacturable product. The product was a dialysis unit for home use. Each unit that was installed in a home would eventually be removed due to failure, or the need for preventative maintenance, or the termination of the service. Upon removal, each unit was shipped to a central depot for re-manufacturing so that it could be returned to service. We develop a model to determine the inventory requirements at each regional depot, and then describe how to use the model to determine the inventory requirements in the two-echelon system consisting of the central facility and the regional depots.Singapore-MIT Alliance (SMA

Performance Analysis of Order Fulfillment for Low Demand Items in E-tailing

We study inventory allocation and order fulfillment policies among warehouses for low-demand SKUs at an online retailer. 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. Thus, given the global demand and an order fulfillment policy, there are trade-offs involving inventory holding costs, transshipment costs, and backordering costs in determining the optimal system inventory level and allocation of inventory to warehouses. For the case of Poisson demand and constant lead time, we develop methods to approximate the key system performance metrics like transshipment, backorders and average system inventory. We then use these results to develop guidelines for inventory stocking and order fulfillment policies for online retailers.Singapore-MIT Alliance (SMA

The Travelling Salesman Problem and Related Problems

New formulations are presented for the Travelling Salesman problem, and their relationship to previous formulations is investigated. The new formulations are extended to include a variety of transportation scheduling problems, such as the Multi-Travelling Salesman problem, the Delivery problem, the School Bus problem and the Dial-a-Bus problem. A Benders decomposition procedure is applied on the new formulations and the resulting computational rocedure is seen to be identical to previous methods for solving the Travelling Salesman problem. Based on the Lagrangean Relaxation method, a new procedure is suggested for generating lagrange multipliers for a subgradient optimization procedure. The effectiveness of the bounds obtained is demonstrated by computational test results.Research supported, in part, by the Office of Naval Research under Contract N00014-75-C-0556

Tactical Shipping and Scheduling at Polaroid with Dual Lead-Times

We report on a project with Polaroid Corporation in which we developed a supply chain model to provide decision support for planning production and transportation. Production occurs in Asia to serve world-wide demand. Production planners must determine both the production quantities as well as whether to ship by sea or by air. We develop a model to optimize a static version of this problem and then show how to use this static model in a dynamic setting. We test the model with data from Polaroid and show its effectiveness.Singapore-MIT Alliance (SMA

The Compensation Method Applied to a One-Product Production Inventory Problem

This paper considers a one-product, one-machine production/inventory probelm. Demand requests for the product are governed by a Poisson process with demand size being an exponential random variable. The production facility may be in production or idle; while in production, the facility produces continuously at a constant rate. The objective is to minimize system costs consisting of setup costs, inventory holding costs, and backorder costs. Given a two-critical-number policy, the problem is analyzed as a constrained Markov process using the compensation method. The policy space may then be searched to find the optimal policy.Research supported, in part, by the Office of Naval Research under Contract N00014-75-C-0556

Setting optimal production lot sizes and planned lead times in a job shop

In this research, we model a job shop that produces a set of discrete parts in a make-to-stock setting. The intent of the research is to develop a planning model to determine the optimal tactical policies that minimise the relevant manufacturing costs subject to workload variability and capacity limits. We consider two tactical decisions, namely the production lot size for each part and the planned lead time for each work station. We model the relevant manufacturing costs, entailing production overtime costs and inventory-related costs, as functions of these tactical decisions. We formulate a non-linear optimisation model and implement it in the Excel spreadsheet. We test the model with actual factory data from our research sponsor. The results are consistent with our intuition and demonstrate the potential value from jointly optimising over these tactical policies

A forecast-driven tactical planning model for a serial manufacturing system

We examine tactical planning for a serial manufacturing system that produces a product family with many process steps and low volumes. The system is subject to uncertainty in demand, in the supply of raw materials, and in yield at specific process steps. A multi-period forecast gets updated each period, and demand uncertainty is realised in terms of forecast errors. The objective of the system is to satisfy demand at a high service level with minimal operating costs. The primary means for handling the system uncertainty are inventory and production flexibility: each process step can work overtime. We model the trade-offs associated with these tactics, by building a dynamic programming model that allows us to optimise the placement of decoupling buffers across the line, as well as to determine the optimal policies for production smoothing and inventory replenishment. We test the model using both data from a real factory as well as hypothetical data. We find that the model results confirm our intuition as to how these tactics address the trade-offs; based on these tests, we develop a set of managerial insights on the application of these operating tactics. Moreover, we validate the model by comparing its outputs to that from a detailed factory simulation

Optimizing Safety Stock Placement in General Network Supply Chains

In the paper, we minimize the holding cost of the safety stock held in a supply chain modeled as a general network. By our assumption, the demand is bounded by a concave function. This fact allows us to formulate the problem as a deterministic optimization. We minimize a concave function over a discrete polyhedron. The main goal of the paper is to describe an algorithm to solve the problem without assuming any particular structure of the underlying supply chain. The algorithm is a branch and bound algorithm.Singapore-MIT Alliance (SMA

Velocity-based Storage Assignment in Semi-automated Storage Systems

Our research focuses on the storage decision in a semi-automated storage system, where the inventory is stored on mobile storage pods. In a typical system, each storage pod carries a mixture of items, and the inventory of each item is spread over multiple storage pods. These pods are transported by robotic drives to stationary stations on the boundary of the storage zone where associates conduct pick or stow operations. The storage decision is to decide to which storage location within the storage zone to return a pod upon the completion of a pick or stow operation. The storage decision has a direct impact on the total travel time, and hence the workload of the robotic drives. We develop a fluid model to analyze the performance of velocity-based storage policies. We characterize the maximum possible improvement from applying a velocity-based storage policy in comparison to the random storage policy. We show that class-based storage with two or three classes can achieve most of the potential benefits and that these benefits increase with greater variation in the pod velocities. To validate the findings, we build a discrete-time simulator with real industry data. We observe an 8% to 10% reduction in the travel distance with a 2-class or 3-class storage policy, depending on the parameter settings. From a sensitivity analysis we establish the robustness of the class-based storage policies as they continue to perform well under a broad range of warehouse settings including different zoning strategies, resource utilization and space utilization levels

The Complexity of Safety Stock Placement in General-Network Supply Chains

We consider the optimization problem of safety stock placement in a supply chain, as formulated in [1]. We prove that this problem is NP-Hard for supply chains modeled as general acyclic networks. Thus, we do not expect to find a polynomial-time algorithm for safety stock placement for a general-network supply chain.Singapore-MIT Alliance (SMA