A flexibly structured lot sizing heuristic for a static remanufacturing system

An effective planning of lot sizes is a key strategy to efficiently manage a combined manufacturing/remanufacturing system in the presence of substantial setup costs. Due to its complex interdependencies, optimal policies and solutions have not been identified so far, but several heuristic approaches have been analyzed in recent contributions. The main heuristic shortcuts are forcing equally sized lot sizes over the planning horizon as well as imposing a specific cycle structure, i.e., a sequence of manufacturing batches is followed by a sequence of remanufacturing batches. We are instead proposing a flexibly structured heuristic that allows for differently sized remanufacturing batches. We show in a comprehensive numerical study that our approach outperforms other existing approaches in more than half of all instances by up to 17%.     

Integrative Cycle Scheduling Approach for a Capacitated Flexible Assembly System*

This study revisits the traditional single stage, multi-item, capacitated lot-sizing problem (CLSP) with a new integrative focus on problem structuring. Unlike past research, we develop integrative cycle scheduling approaches which simultaneously address lot-sizing, capacity, and sequencing issues. Our purposes are to (1) explore the effect of sequencing on inventory levels, (2) examine the problem of infeasibility in the economic lot scheduling problem (ELSP), and (3) provide a simple methodology of generating low-cost cycle schedules in an environment with discrete shipping, dynamic demands, limited capacity, zero setup cost, and sequence-independent setup times. Our procedures are compared to benchmark cycle scheduling approaches in terms of both inventory cost and computation time under different demand scenarios, using the operating data from a flexible assembly system (FAS) at the Ford Motor Company's Sandusky, Ohio plant.     

The benefit of receding horizon control: Near-optimal policies for stochastic inventory control

In this paper we address the single-item, single-stocking point, non-stationary stochastic lot-sizing problem under backorder costs. It is well known that the (s, S) policy provides the optimal control for such inventory systems. However the computational difficulties and the nervousness inherent in (s, S) paved the way for the development of various near-optimal inventory control policies. We provide a systematic comparison of these policies and present their expected cost performances. We further show that when these policies are used in a receding horizon framework the cost performances improve considerably and differences among policies become insignificant.     

Optimal production,replenishment, delivery,routing and inventory management policies for products with perishable inventory

This paper presents a generalized production-inventory-routing model with perishable inventory. We analyze the optimal integrated decisions of when and how much to deliver and sell products with varying manufacturing periods. We discuss main inventory management policies to demonstrate the applicability of the model in real-world applications for production routing problems (PRPs) with perishable inventory. Furthermore, an exact branch-and-cut algorithm is developed and discussed. We introduce new families of logical, strengthened lot-sizing and lifted Miller–Tucker–Zemlin subtour elimination constraints for the PRP with perishable inventory. Finally, we test the performance of the algorithm. We also implement and compare 8 suboptimal delivery and selling priority policies with an optimized policy to develop managerial implications.     

Discrete time-varying demand lot-sizing models with learning and forgetting effects

This paper deals with the problem of incorporating both learning and forgetting effects into discrete timevarying demand lot-sizing models to determine lot sizes. Forgetting is retrogression in learning which causes a loss of labour productivity due to breaks between intermittent production runs. Formulae are derived for calculating the production cost required to produce the first unit of each successive lot over a finite planning horizon. An optimal lotsizing model and three heuristic models are developed by extending the existing models without learning and forgetting considerations. Numerical examples and computational experience indicate that larger lot sizes are needed when the phenomenon of learning and forgetting exists. Several important conclusions are drawn from a comparison of the three heuristic solutions with the optimal solution, and suggestions for future research and for lot-size users to choose an appropriate lot-sizing technique are made.     

The Impact of Product Lifecycle on Capacity Planning of Closed‐Loop Supply Chains with Remanufacturing

Product recovery operations in reverse supply chains face rapidly changing demand due to the increasing number of product offerings with reduced lifecycles. Therefore, capacity planning becomes a strategic issue of major importance for the profitability of closed‐loop supply chains. This work studies a closed‐loop supply chain with remanufacturing and presents dynamic capacity planning policies developed through the methodology of System Dynamics. The key issue of the paper is how the lifecycles and return patterns of various products affect the optimal policies regarding expansion and contraction of collection and remanufacturing capacities. The model can be used to identify effective policies, to conduct various “what‐if” analyses, and to answer questions about the long‐term profitability of reverse supply chains with remanufacturing. The results of numerical examples with quite different lifecycle and return patterns show how the optimal collection expansion/contraction and remanufacturing contraction policies depend on the lifecycle type and the average usage time of the product, while the remanufacturing capacity expansion policy is not significantly affected by these factors. The results also show that the collection and remanufacturing capacity policies are insensitive to the total product demand. The insensitivity of the optimal policies to total demand is a particularly appealing feature of the proposed model, given the difficulty in obtaining accurate demand forecasts.     

WIP inventories in the simultaneous determination of optimal production and purchase lot sizes

This paper studies an integrated production and purchasing lot sizing model with work-in-process WIP inventory. In this model, the single product is made in a multiprocess manufacturing system. The raw materials are procured from outside sources and are converted gradually into the product. A solution procedure is developed to simultaneously find the optimal lot sizes for the product and its raw materials and the corresponding total relevant cost. It is shown that if the cost of WIP inventory is considered in the production lot size computation, the optimal lot sizes of the product as well as those of the raw materials could be altered significantly.     

Economic Lot Scheduling Problem with Returns

Motivated by a case study of a company that produces car parts, we study the multi‐product economic lot scheduling problem for a hybrid production line with manufacturing of new products and remanufacturing of returned products. For this economic lot scheduling problem with returns (ELSPR), we consider policies with a common cycle time for all products, and with one manufacturing lot and one remanufacturing lot for each product during a cycle. For a given cycle time, the problem is formulated as a mixed integer linear programming (MIP) problem, which provides the basis for an exact solution. The application of this model for one of the core products of the case study company indicates a 16% reduction in cost compared to the current lot scheduling policy.     

The Value of Quality Grading in Remanufacturing

In this paper we consider a tactical production‐planning problem for remanufacturing when returns have different quality levels. Remanufacturing cost increases as the quality level decreases, and any unused returns may be salvaged at a value that increases with their quality level. Decision variables include the amount to remanufacture each period for each return quality level and the amount of inventory to carry over for future periods for both returns (unremanufactured), and finished remanufactured products. Our model is grounded with data collected at Pitney‐Bowes from their mailing systems remanufacturing operations. We derive some analytic properties for the optimal solution in the general case, and provide a simple greedy heuristic to computing the optimal solution in the case of deterministic returns and demand. Under mild assumptions, we find that the firm always remanufactures the exact demand in each period. We also study the value of a nominal quality‐grading system in planning production. Based on common industry parameters, we analyze, via a numerical study, the increase in profits observed by the firm if it maintains separate inventories for each quality grade. The results show that a grading system increases profit by an average of 4% over a wide range of parameter values commonly found in the remanufacturing industry; this number increases as the returns volume increases. We also numerically explore the case where there are capacity constraints and find the average improvement of a grading system remains around 4%.     

有限分布信息条件下MTO再制造系统提前期优化

在只知道零部件再制造时间有限分布信息（即一阶矩、二阶矩）条件下,基于MTO再制造策略研究由再制件和采购件组成的再制品的提前期问题,该问题被描述为一个矩问题。以最小化库存持有成本和缺货成本为目标建立min-max优化模型,在具有相同一阶矩、二阶矩的分布集合中寻找使最坏分布下的目标函数值最小的最优再制造提前期。最后通过算例进行了验证,求解结果与传统假设再制造时间服从正态分布、均匀分布得到的结果吻合较好,但本文的方法更符合生产实际,能保证在具有同样一阶矩和二阶矩的所有分布情况下的解的鲁棒性,对企业制定再制造计划、采购计划等具有现实的指导意义。     

Dynamic performance of a hybrid inventory system with a Kanban policy in remanufacturing process

In this paper we study a hybrid system with both manufacturing and remanufacturing. The inventory control strategy we use in the manufacturing loop is an automatic pipeline, inventory and order based production control system (APIOBPCS). In the remanufacturing loop we employ a Kanban policy to represent a typical pull system. The methodology adopted uses control theory and simulation. The aim of the research is to analyse the dynamic (as distinct from the static) performance of the specified hybrid system. Dynamics have implications on total costs in terms of inventory holding, capacity utilisation and customer service failures. We analyse the parameter settings to find preferred “nominal”, “fast” and “slow” values in terms of system dynamics performance criteria such as rise time, settling time and overshoot. Based on these parameter settings, we investigate the robustness of the system to changes in return yield and the manufacturing/remanufacturing lead time. Our results clearly show that the system is robust with respect to the system dynamics performance and the remanufacturing process can help to improve system dynamics performance. Thus, the perceived benefits of remanufacturing of products, both environmentally and economically, as quoted in the literature are found not to be detrimental to system dynamics performance when a Kanban policy is used to control the remanufacturing process.     

基于改进策略的混合型制造/再制造系统分析

在制造和再制造并存的混合型系统中,制造商需要同时协调新产品生产过程和旧产品再制造过程,这种双向物流的集成运作使得传统的生产规划和库存管理方式不再适用,如何构建一种有效的控制策略来协调生产过程和再制造过程就显得十分关键。本文在优化库存信息的基础上提出了一种适用于混合系统的改进策略,同时考虑到系统复杂性,主要采用控制理论中的传递函数技术构建了系统模型。仿真结果表明,本文提出的改进策略不仅可以有效协调新产品生产过程和旧产品再制造过程,而且还可以显著改善系统性能。     

Coordination and Priority Decisions in Hybrid Manufacturing/Remanufacturing Systems

Companies are increasingly realizing the need to coordinate their manufacturing and remanufacturing operations. This can be a challenge due to the inherent variability in the condition and amount of returns, which has a direct impact on remanufacturing costs and leadtimes. In this paper, we develop a modeling framework to compare two alternative strategies that use either manufacturing or remanufacturing as the primary means of satisfying customer demand. Of course, in the event that the demand cannot be met by the prioritized process, the secondary process is used as a contingency. In our basic model, the priority decisions are made at the component level in replenishing the serviceable inventory, while the disposal and new component ordering decisions are made independently. The second model represents the coordination of remanufacturable and new component inventory control decisions. Using simulation‐based optimization on a large number of experiments, we observe that when prioritization is in the upstream echelon and there is no coordination in managing component stocks, there exists a critical return ratio, below which it is beneficial to give priority to manufacturing and above which it is beneficial to give priority to remanufacturing. We also see that coordinated control of the component inventories considerably reduces the importance of prioritization. These observations remain valid when congestion in the shop floor is also taken into account. We also study the benefits of state‐dependent dispatching policies in a realistic case.     

Integrated procurement- production system in a just-in-time environment-modelling and analysis

Classically, economic lot size models have been used separately for procurement and production subsystems. However, when the raw materials are used in production, the procurement policies are dependent on the schedule and the batch size for the product. Hence, it is necessary to unify the procurement and production policies. The just-in-time JIT environment provides an ideal setting for such a coordination between the procurement and production policies. The model proposed here is a traditional inventory model recast into a model for a JIT system for a single product, multistage batch environment aiming at the minimization of total variable cost and thereby determining the batch sizes for the product and raw material order sizes. A JIT system aims at minimizing setup time and this feature is captured in the proposed model. The computational experience reported in this paper is based on a number of simulated problem sets. The possible domain of application is also highlighted.     

A BRANCH AND BOUND PROCEDURE FOR SETUP PROBLEMS IN FLEXIBLE MANUFACTURING SYSTEMS

We address a medium- to short-term production planning problem in a flexible manufacturing environment. First we present a single-machine, mixed integer programming model for part type selection and lot-sizing problems over a T-period planning horizon. Demand for part types changes dynamically through the periods. The objective is to meet the demand for part types during the periods they are demanded. Available machine time and tool magazine capacities are the system constraints in our models. We next extend on the single- machine model to include multiple machines. In addition to part type selection and lotsizing decisions, the extended model also addresses the machine-loading decision. We present exact branch and bound procedures based on linear programming relaxations for the two models. We also report the results of our computational experiments.     

Coordinating replenishments in a supply chain with quality control considerations

We study the impact of coordinated replenishment, a popular supply chain initiative, on a quality control system. We use the (Q, S) policy to manage a two-item inventory control system. If the items are jointly replenished, the number ordered for each item varies from lot to lot. As the number varies, the sampling plan will also be changed. Companies have to determine sampling plans to minimize quality cost when the order is mixed with several items and the number of each item varies from order to order. Management's primary concern is to determine the optimal sampling sizes and acceptance numbers for all items in an order.     

Managing Retail Shelf and Backroom Inventories When Demand Depends on the Shelf‐Stock Level

Inventory displayed on the retail sales floor not only performs the classical supply function but also plays a role in affecting consumers’ buying behavior and hence the total demand. Empirical evidence from the retail industry shows that for some types of products, higher levels of on‐shelf inventory have a demand‐increasing effect (“billboard effect”) while for some other types of products, higher levels of on‐shelf inventory have a demand‐decreasing effect (“scarcity effect”). This suggests that retailers may use the amount of shelf stock on display as a tool to influence demand and operate a store backroom to hold the inventory of items not displayed on the shelves, introducing the need for efficient management of the backroom and on‐shelf inventories. The purpose of this study is to address such an issue by considering a periodic‐review inventory system in which demand in each period is stochastic and depends on the amount of inventory displayed on the shelf. We first analyze the problem in a finite‐horizon setting and show under a general demand model that the system inventory is optimally replenished by a base‐stock policy and the shelf stock is controlled by two critical points representing the target levels to raise up/drop down the on‐shelf inventory level. In the infinite‐horizon setting, we find that the optimal policies simplify to stationary base‐stock type policies. Under the billboard effect, we further show that the optimal policy is monotone in the system states. Numerical experiments illustrate the value of smart backroom management strategy and show that significant profit gains can be obtained by jointly managing the backroom and on‐shelf inventories.     

An inventory control policy for liquefied natural gas as a transportation fuel

In this paper, we study a novel stochastic inventory management problem that arises in storage and refueling facilities for Liquefied Natural Gas (LNG) as a transportation fuel. In this inventory problem, the physio-chemical properties of LNG play a key role in the design of inventory policies. These properties are: (1) LNG suffers from both quantity decay and quality deterioration and (2) the quality of on-hand LNG can be upgraded by mixing it with higher-quality LNG. Given that LNG quality can be upgraded, an inventory control policy for this problem needs to consider the removal of LNG as a decision variable. We model and solve the problem by means of a Markov Decision Process (MDP) and study the structural characteristics of the optimal policy. The insights obtained in the analysis of the optimal policy are translated into a simple, though effective, inventory control policy in which actions (i.e., replenishment and/or removal) are driven by both the quality and the quantity of the inventories. We assess the performance of our policy by means of a numerical study and show that it performs close to optimal in many numerical instances. The main conclusion of our study is that it is important to take quality into consideration when design inventory control policies for LNG, and that the most effective way to cope with quality issues in an LNG inventory system involves both the removal and the replenishment of inventories.     

回收物流库存控制研究

本文探讨了包含回收品的库存系统。回收物流库存中既有一般生产过程的新产品,也有经再制造的回收品,使其最优库存策略非常复杂,论文推导出不同控制方式下的EOQ模型,以确定最优生产和再制造批量。此外,还对求得的最优批量进行适当的调整,以确保在循环周期中的定货次数为整数。该模型形式、结构简单易于在实践中应用。