Facility Location: A Robust Optimization Approach

In this research, we apply robust optimization (RO) to the problem of locating facilities in a network facing uncertain demand over multiple periods. We consider a multi‐period fixed‐charge network location problem for which we find (1) the number of facilities, their location and capacities, (2) the production in each period, and (3) allocation of demand to facilities. Using the RO approach we formulate the problem to include alternate levels of uncertainty over the periods. We consider two models of demand uncertainty: demand within a bounded and symmetric multi‐dimensional box, and demand within a multi‐dimensional ellipsoid. We evaluate the potential benefits of applying the RO approach in our setting using an extensive numerical study. We show that the alternate models of uncertainty lead to very different solution network topologies, with the model with box uncertainty set opening fewer, larger facilities. Through sample path testing, we show that both the box and ellipsoidal uncertainty cases can provide small but significant improvements over the solution to the problem when demand is deterministic and set at its nominal value. For changes in several environmental parameters, we explore the effects on the solution performance.     

Stabilized‐Cycle Strategy for Capacitated Lot Sizing with Multiple Products: Fill‐Rate Constraints in Rolling Schedules

In practice, deterministic, multi‐period lot‐sizing models are implemented in rolling schedules since this allows the revision of decisions beyond the frozen horizon. Thus, rolling schedules are able to take realizations and updated forecasts of uncertain data (e.g., customer demands) into account. Furthermore, it is common to hold safety stocks to ensure given service levels (e.g., fill rate). As we will show, this approach, implemented in rolling schedules, often results in increased setup and holding costs while (over‐)accomplishing given fill rates. A well‐known alternative to deterministic planning models are stochastic, static, multi‐period planning models used in the static uncertainty strategy, which results in stable plans. However, these models have a lack of flexibility to react to the realization of uncertain data. As a result, actual costs may differ widely from planned costs, and downside deviations of actual fill rates from those given are very high. We propose a new strategy, namely the stabilized cycle. This combines and expands upon ideas from the literature for minimizing setup and holding costs in rolling schedules, while controlling actual product‐specific fill rates for a finite reporting period. A computational study with a multi‐item capacitated medium‐term production planning model has been executed in rolling schedules. On the one hand, it demonstrates that the stabilized‐cycle strategy yields a good compromise between costs and downside deviations. Furthermore, the stabilized‐cycle strategy weakly dominates the order‐based strategy for both constant and seasonal demands.     

Simulation-based performance assessment of master planning approaches in semiconductor manufacturing

Semiconductor manufacturing is confronted with a large number of products whose mix is changing over time, heterogeneous fabrication processes, re-entrant flows of material, and different sources of environmental and system uncertainty. In this context, the mid-term production planning approach, i.e., master planning, typically does not capture the entire complexity of the shop-floor. It deals with an aggregated representation of the production system. There is a need for evaluating the planning algorithm in use while taking the execution level into account. Therefore, we introduce in this paper a simulation-based framework that allows for modeling the behavior of the market demand and the production system. An appropriate performance assessment methodology is proposed. The performance of two heuristic approaches for master planning in semiconductor manufacturing, a genetic algorithm and a rule-based assignment procedure, is evaluated within a rolling horizon setting while considering demand and execution uncertainty. A reduced discrete-event simulation model is used to mimic a one-stage network of wafer fabrication facilities. The results of simulation experiments are discussed.     

有可再生能源和电力存储设施并网的智能电网优化用电策略

大量可再生能源和存储设施集中或分布接入电网,缓解了电网的供给压力,但同时也对电力系统安全造成新的威胁。合理使用新能源和可存储设施使之更好为电网服务,是现代电网亟待解决的一个问题。本文对有可存储设备和可再生能源并网的电力系统进行研究,根据可再生能源在实际生活中的情形,将其划分为两类：私人新能源发电和公共新能源发电,其中私人新能源发电可供自身直接使用,多余部分并入电网,而公共新能源发电直接并入电网,然后针对上述复杂情形,结合用户实际需求,以所有用户效用最大化、成本最小化为目标函数,建立优化模型,给出了一种既有可存储设备又有可再生能源复杂并网情况下用户优化用电策略——包括家用电器、新能源、以及存储设备充放电策略。对模型的性质进行研究,考虑到模型是凸规划,强对偶成立,用拉格朗日对偶算法给出了模型的解。求解过程中,由于目标函数是非光滑的,采用光滑化的技术将目标函数光滑化,将非光滑问题转化为光滑问题,进一步利用拟牛顿下降法求解。该策略能确保新能源得到优先、充分利用,体现用户效用最大化、成本最小化,同时可以避免由于新能源并网可能会造成电网不稳定情况的出现;光滑化的方法不但适用于本文,经过适当改进后也可适用于其他目标函数为非光滑的情况。仿真结果验证了模型的合理性和算法的可行性。     

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%.     

Route‐Independent Analysis of Available Capacity in Flexible Manufacturing Systems

In a job shop, because of large setup times, each operation is assigned to only one machine. There is no alternative routing. In a flexible manufacturing system, each manufacturing operation can often be performed on several machines. Therefore, with automated equipment, the capacity of a machine to perform certain operations is not independent of the capacity of other machines. Often, however, operations managers can use a route‐independent answer to production planning questions. For example, how much can be produced of a certain part type and when are important capacity questions in business negotiations, when the detailed routing and scheduling are not yet of interest or cannot be known. This paper provides a mathematical model for the route‐independent analysis of the capacity of flexible manufacturing systems based on a concept of operation types. An example is provided both to illustrate the use of operation types and to highlight the differences between the traditional route‐dependent and the proposed route‐independent formulations of capacity constraints. Some computational results are also given. Finally, a sensitivity analysis is developed to analyze the feasibility of production plans when production requirements and machine capacities can change.     

Design of Stockless Production Systems

In make‐to‐stock production systems finished goods are produced in anticipation of demand. By contrast, in stockless production systems finished goods are not produced until demand is observed. In this study we investigate the problem of designing a multi‐item manufacturing system, where there is both demand‐ and production‐related uncertainty, so that stockless operation will be optimal for all items. For the problem of interest, we focus on gaining an understanding of the effect of two design variables: (i) manufacturing speed—measured by the average manufacturing rate or, equivalently, the average unit manufacturing time, and (ii) manufacturing consistency—measured by the variation in unit manufacturing times. We establish conditions on these two variables that decision makers can use to design stockless production systems. Managerial implications of the conditions are also discussed.     

LOT‐SIZING RULE AND FREEZING THE MASTER PRODUCTION SCHEDULE UNDER CAPACITY CONSTRAINT AND DETERMINISTIC DEMAND

This paper investigates the performance impact of lot‐sizing rule (LSR) selection and freezing of the master production schedule (MPS) in multi‐item single‐level systems with a single resource constraint under deterministic demand. The results of the study show that the selection of LSRS and the parameters for freezing the MPS have a significant impact on total cost, schedule instability, and the service level of the system. However, the selection of LSRS does not significantly influence the selection of the MPS freezing parameters. The basic conclusions concerning the performance of the freezing parameters under a capacity constraint agreed with previous research findings without consideration of capacity constraints.     

A strategic and global manufacturing capacity management optimisation model: A Scenario-based multi-stage stochastic programming approach

Large-scale multinational manufacturing firms often require a significant investment in production capacity and extensive management efforts in strategic planning in an uncertain business environment. In this research we first discuss what decision terms and boundary conditions a holistic capacity management model for the manufacturing industry must contain. To better understand how these decision terms and constraints have been employed by the recent model developers in the area of capacity and resource management modelling for manufacturing, 69 optimisation-based (deterministic and stochastic) models have been carefully selected from 2000 to 2018 for a brief comparative analysis. The results of this comparison shows although applying uncertainty into capacity modelling (in stochastic form) has received a greater deal of attention most recently (since 2010), the existing stochastic models are yet very simplistic, and not all the strategic terms have been employed in the current model developments in the field. This lack of a holistic approach although is evident in deterministic models too, the existing stochastic counterparts proved to include much less decision terms and inclusive constraints, which limits them to a limited applications and may cause sub-optimal solutions. Employing this set of holistic decision terms and boundary conditions, this work develops a scenario-based multi-stage stochastic capacity management model, which is capable of modelling different strategic terms such as capacity level management (slight, medium and large capacity volume adjustment to increase/decrease capacity), location/relocation decisions, merge/decomposition options, and product management (R&D, new product launch, product-to-plant and product-to-market allocation, and product phase-out management). Possibility matrix, production rates, different financial terms and international taxes, inflation rates, machinery depreciation, investment lead-time and product cycle-time are also embedded in the model in order to make it more practical, realistic and sensitive to strategic decisions and scenarios. A step-by-step open-box validation has been followed while designing the model and a holistic black-box validation plan has been designed and employed to widely validate the model. The model then has been verified by deploying a real-scaled case of Toyota Motors UK (TMUK) decision of mothballing one of their production lines in the UK after the global recession in 2010.     

Experimental earliness/tardiness production planning with the due window system

In order to use the philosophy of JIT to improve the production planning method of MRP-II, we propose the experimental software system of the earliness/tardiness produc tion planning problem with due window. By means of the approaches and model reported in this paper, the optimal production planning can be achieved. The recommended model extends the problem of due window from the shop scheduling level into the aggregated planning level of mass manufacturing systems. Simulation results have demonstrated that the experimental software is a useful tool for the production management of repetitive manufacturing enterprises.     

A DISCRETE PRODUCTION SWITCHING RULE FOR AGGREGATE PLANNING

Aggregate planning (AP) is a necessary activity for manufacturing and services alike. A shift toward high-volume batch and continuous flow processes within American manufacturing has given rise to increasing numbers of crew-loaded facilities. A majority of AP approaches incorporate continuous decision variables and require frequent adjustments to both production and work-force settings. Despite the availability and diversity of these approaches, few significant applications have been reported. This paper presents the detailed development of a discrete AP switching rule that can be applied to a variety of cost environments. Inventory costs are estimated using an interval approach rather than traditional point estimates. The model allows incorporation of overtime options and is interactive in nature. Decision variables from the model can be disaggregated and linked directly to lower-level planning activities. Actual results of model implementation are reported. An overview of the model's incorporation into the larger context of hierarchical production planning is found in [21].     

分布决策环境下生产-分销协同计划研究

针对分布决策环境下因信息不对称使得供应链协同计划求解困难及难以达到全局最优的问题,本文利用多层规划理论和方法构建一个供应链生产-分销协同计划模型,采用模糊交互式协商和遗传算法的优化求解方法对协同计划模型进行求解。该方法求解的结果是一组满足约束条件的满意解,各节点企业根据自身偏好和约束信息决定是否接受该满意解,或者修正各自目标满意度隶属函数重新求解。决策过程具有一定的柔性。最后通过算例给出供应链生产-分销协同计划满意解的求解过程,对文中所建立的模型和算法进行了有效地说明和验证。求解结果说明该模型和协商方法能够有效地解决非对称信息条件下供应链生产-分销协同计划的求解和冲突问题。     

Multi-site aggregate production planning with multiple objectives: A goal programming approach

This paper addresses the problem of aggregate production planning (APP) for a multinational lingerie company in Hong Kong. The multi-site production planning problem considers the production loading plans among manufacturing factories subject to certain restrictions, such as production import/export quotas imposed by regulatory requirements of different nations, the use of manufacturing factories/locations with regard to customers' preferences, as well as production capacity, workforce level, storage space and resource conditions of the factories. In this paper, a multi-objective model is developed to solve the production planning problems, in which the profit is maximized but production penalties resulting from going over/under quotas and the change in workforce level are minimized. To enhance the practical implications of the proposed model, different managerial production loading plans are evaluated according to changes in future policy and situation. Numerical results demonstrate the robustness and effectiveness of the developed model.     

A goal programming approach to production planning for flexible manufacturing systems

The increased use of flexible manufacturing systems (FMS) reduces production time variability as the fixed processing time of automated systems replaces the variable processing time of human resources in production systems. This reduction in the variability permits the application of deterministic, constrained optimization models that recognize the conflicting multi-objective nature of resource utilization in an FMS environment. One such multi-objective optimization model is linear goal programming. Unlike most linear programming models, linear goal programming is designed to handle conflicting multi-objective problems. A goal programming model is developed a and presented in this paper as an aid in FMS planning. An application is also presented to illustrate the informational benefits of using the proposed model.     

多品种集约生产计划问题的模糊方法

提出具有模糊需求量和模糊能力约束以及资本水平约束的多品种类集约生产计划问题 的模糊优化模型及模糊解方法. 通过对模糊需求量和模糊等式的描述,提出了模糊需求环境下 生产- 库存平衡方程的两种等价的描述方法, 并给出了模糊等式的实用解释. 建立了具有模 糊需求量和模糊能力约束集约生产计划问题的优化模型FMAPP ,并给出了求解模型的参数规 划方法.     

多阶段资产投资的动态规划决策模型

本文针对多阶段资产投资问题,给出了在满足一定的风险承受能力情况下的、以最终的总收益尽可能大为决策目标的资产投资组合问题的一个多阶段动态规划决策模型,从中可以求得多阶段投资的整休最优投资组合。继而讨论了其与单阶段投资模型的关系。最后把模型转化为线性动态规划模型。     

A Capacitated Multi‐echelon Inventory Placement Model under Lead Time Constraints

We develop an inventory placement model in the context of general multi‐echelon supply chains where the delivery lead time promised to the customer must be respected. The delivery lead time is calculated based on the available stocks of the different input and output products in the different facilities and takes into account the purchasing lead times, the manufacturing lead times, and the transportation lead times. We assume finite manufacturing capacities and consider the interactions of manufacturing orders between time periods. Each facility manages the stocks of its input and output products. The size of customer orders and their arrival dates and due dates are assumed to be known as in many B2B situations. We perform extensive computational experiments to derive managerial insights. We also derive analytical insights regarding the manufacturing capacities to be installed and the impacts of the frequency of orders on the system cost.     

面向并行制造的多生产单元协同调度研究

为提升多生产单元制造系统整体效率,在其系统内开展面向并行制造的协同调度研究,在考虑运输、换线等时间的基础上,构建多生产单元并行协同调度模型,采用并行分段协同遗传算法求解;在此基础上,将所研究协同调度方法应用于某复杂机电产品多生产单元制造车间,并与变批量调度与等批量调度比较。研究表明,所提的并行协同调度方法可以显著提升生产单元效率,提高生产单元设备和人员利用率。     

A Production–Inventory Model for a Push–Pull Manufacturing System with Capacity and Service Level Constraints

We study a hybrid push–pull production system with a two‐stage manufacturing process, which builds and stocks tested components for just‐in‐time configuration of the final product when a specific customer order is received. The first production stage (fabrication) is a push process where parts are replenished, tested, and assembled into components according to product‐level build plans. The component inventory is kept in stock ready for the final assembly of the end products. The second production stage (fulfillment) is a pull‐based assemble‐to‐order process where the final assembly process is initiated when a customer order is received and no finished goods inventory is kept for end products. One important planning issue is to find the right trade‐off between capacity utilization and inventory cost reduction that strives to meet the quarter‐end peak demand. We present a nonlinear optimization model to minimize the total inventory cost subject to the service level constraints and the production capacity constraints. This results in a convex program with linear constraints. An efficient algorithm using decomposition is developed for solving the nonlinear optimization problem. Numerical results are presented to show the performance improvements achieved by the optimized solutions along with managerial insights provided.     

Production planning in practice

The changes and pressures facing the manufacturing and engineering industries today are increasing the importance of effective aggregate manpower and production planning. Several different theoretical optimisation models to tackle this problem have been described in detail in the literature but there have been few applications of them in practice.The reasons for this are many but include: the difficulty in expressing managements' conflicting and mixed objectives in an objective function; the necessity to oversimplify real life systems to enable these methods to be used; the simplistic approach to manpower planning used in these models; the difficulty in gaining managements' acceptance and finally the fact that what management actually wants is a tool to assist them in planning and decision making.What is being used by many managements is a case-study deterministic simulation model. Many companies are adopting this type of model for all types of planning and twelve out of twenty-seven companies visited in a research project described in this paper were using this type of model for aggregate manpower and production planning. It is proving to be an effective management tool and is being readily accepted principally because modern specialised financial modelling languages are enabling these models to be built, understood and used by non-specialist managers.