经济批量排产问题的一种排产方法

针对经济批量排产问题假定生产可以在库存降为0之前开始,并且提出新的算法求产品的生产顺序。结果表明,该排产方法成本要低于其他2种常用的经济批量排产问题的方法,并且给出了算法的时间复杂性。     

Multi-product lot scheduling with backordering and shelf-life constraints

In this paper, we revisit the economic lot scheduling problem (ELSP), where a family of products is produced on a single machine, or facility, on a continual basis. Our focus is on the determination of a feasible production schedule, including the manufacturing batch size of each item. We assume that total backordering is permissible and that each of the products has a limited post-production shelf life. Several studies examining this problem have suggested a rotational common cycle approach, where each item is produced exactly once every cycle. To ensure schedule feasibility, we resort to the technique of reducing individual production rates and allow the flexibility of producing any item more than once in every cycle, in conjunction with appropriate timing adjustments. In order to solve this more generalized model, which is NP hard, we suggest a two-stage heuristic algorithm. A numerical example demonstrates our solution approach.     

GLOBAL JOB SHOP SCHEDULING WITH A GENETIC ALGORITHM

This paper describes a global job shop scheduling procedure that uses a genetic algorithm to find a good schedule. Unlike previously considered algorithms, this procedure has been implemented in the scheduling system for a manufacturing facility and has led to improved scheduling. This facility is a semiconductor test area. The test area is a job shop and has sequence-dependent setup times at some operations. The concern of management is to meet their customer due dates and to increase throughput. This requires the coordination of many resources, a task beyond the ability of simple dispatching rules. We discuss a centralized procedure that can find a good schedule through the use of a detailed scheduling model and a genetic algorithm that searches over combinations of dispatching rules. We discuss our effort in developing a system that models the shop, creates schedules for the test area personnel, and makes a number of contributions to test area management.     

COMBINED PRODUCTION AND MAINTENANCE SCHEDULING FOR A MULTIPLE‐PRODUCT,SINGLE‐ MACHINE PRODUCTION SYSTEM

Traditionally, the problems of equipment maintenance scheduling and production scheduling in a multi‐product environment have been treated independently. In this paper, we develop a Markov decision process model that simultaneously determines maintenance and production schedules for a multiple‐product, single‐machine production system, accounting for the fact that equipment condition can affect the yield of different product types differently. The problem was motivated by an application in semiconductor manufacturing. After examining structural properties of the optimal policy, we compare the combined method to an approach often used in practice. In the nearly 6,000 test problems studied, the reward from the combined method was an average of more than 25 percent greater than the reward from the traditional method.     

带工期指派的产品服务系统订单随机调度问题研究

针对由一个制造工厂和多个区域服务中心组成的服务型制造企业，研究了考虑生产时间和服务时间均具有随机性且工期可指派的产品服务系统（PSS）订单调度问题。首先以最小化订单提前、误工和工期指派费用的期望总额为目标构建问题的优化模型，然后分析目标函数近似值的最优性条件，据此提出加权最短平均生产时间排序规则，并结合该规则与插入邻域局部搜索设计了启发式算法对问题进行求解，最后通过数值仿真验证算法的可行性和有效性。研究表明，提前费用偏差对PSS订单调度与工期指派决策的影响很小，因此企业管理者无需准确估计库存费用也能制定出比较有效的PSS订单调度策略；而工期指派费用偏差对决策结果的影响非常大，因此企业管理者在决策时必须谨慎估计该项费用。     

Minimizing tardiness on a single processor with sequence-dependent setup times: a simulated annealing approach

In today's fast-paced Just-In-Time and mass customization manufacturing in a sequence-dependent setup environment, the challenge of making production schedules to meet due-date requirements is becoming a more complex problem. Unfortunately, much of the research on operations scheduling problems has either ignored setup times or assumed that setup times on each machine are independent of the job sequence. This paper considers the problem of minimizing tardiness, a common measure of due-date performance, in a sequence-dependent setup environment. Simulated annealing was used to solve the sequencing problem, and its performance was compared with random search. Our experimental results show that the algorithm can find a good solution fairly quickly, and thus can rework schedules frequently to react to variations in the schedule. The algorithm is invaluable for ‘on-line’ production scheduling and ‘last-minute’ changes to production schedule. The results of this research also suggest ways in which more complex and realistic job shop environments, such as multiple machines with a higher number of jobs in the sequence, and other scheduling objectives can be modeled. This research also investigates computational aspects of simulated annealing in solving complex scheduling problems.     

FREQUENCY OF REPLANNING IN A ROLLING HORIZON MASTER PRODUCTION SCHEDULE FOR A PROCESS INDUSTRY ENVIRONMENT: A CASE STUDY

This study addresses the problem of replanning frequency for a rolling horizon master production schedule (MPS) in a process industry environment under demand certainty. The major contribution of this paper is the demonstration of how the appropriate replanning frequency for a MPS can be determined under the conditions of minimum batch-size production restrictions in a rolling planning horizon setting. In addition, the problem environment for this study is an actual MPS operation that includes features such as multiple production lines, multiple products, capacity constraints, minimum inventory requirements, and multiple goals. Actual data from a paint company are used to determine the appropriate replanning frequency for a rolling horizon MPS. Results indicate that a 2-month replanning frequency was the best at this firm because of the significant cost savings it provided when compared to actual company performance and the other replanning intervals.     

Coordinated scheduling of production and delivery stages with stage-dependent inventory holding costs

This paper considers a problem of integrated decision-making for job scheduling and delivery batching wherein different inventory holding costs between production and delivery stages are allowed. In the problem, jobs are processed on a facility at a production stage and then delivered at the subsequent delivery stage by a capacitated vehicle. The objective is to find the coordinated schedule of production and delivery that minimizes the total cost of the associated WIP inventory, finished product inventory and delivery, where both the inventory costs are characterized in terms of the weighted flow-time and the delivery cost is proportional to the required number of delivery batches. It is proved that the problem is NP-hard in the strong sense. Thereupon, three heuristic algorithms are derived. Some restricted cases are also characterized as being solvable in polynomial time. Numerical experiments are conducted to evaluate the performance of the derived heuristic algorithms.     

A MARKET UTILITY‐BASED MODEL FOR CAPACITY SCHEDULING IN MASS SERVICES

Only a small set of employee scheduling articles have considered an objective of profit or contribution maximization, as opposed to the traditional objective of cost (including opportunity costs) minimization. In this article, we present one such formulation that is a market utility‐based model for planning and scheduling in mass services (MUMS). MUMS is a holistic approach to market‐based service capacity scheduling. The MUMS framework provides the structure for modeling the consequences of aligning competitive priorities and service attributes with an element of the firm's service infrastructure. We developed a new linear programming formulation for the shift‐scheduling problem that uses market share information generated by customer preferences for service attributes. The shift‐scheduling formulation within the framework of MUMS provides a business‐level model that predicts the economic impact of the employee schedule. We illustrated the shift‐scheduling model with empirical data, and then compared its results with models using service standard and productivity standard approaches. The result of the empirical analysis provides further justification for the development of the market‐based approach. Last, we discuss implications of this methodology for future research.     

OPTIMAL AND NEAR OPTIMAL CONTROL OF A TWO-PART-TYPE STOCHASTIC MANUFACTURING SYSTEM WITH DYNAMIC SETUPS

This paper deals with a manufacturing system consisting of a single machine subject to random failures and repairs. The machine can produce two types of parts. When the production is switched from one part type to the other, a random setup time is incurred at a constant cost rate. The objective is to track the demand, while keeping the work-in-process as close as possible to zero for both products. The problem is formulated as an optimal stochastic control problem. The optimal policy is obtained numerically by discretizing the continuous time continuous state opti-mality conditions using a Markov chain approximation technique. The discretized optimality conditions are shown to correspond to an infinite horizon, discrete time, discrete state dynamic programming problem. The optimal setup policy is shown to have two different structures depending on the parameters of the system. A heuristic policy is proposed to approximate the optimal setup policy. Simulation results show that the heuristic policy is a very good approximation for sufficiently reliable systems.     

A FRAMEWORK FOR MACHINE SCHEDULING PROBLEMS WITH CONTROLLABLE PROCESSING TIMES

This is a study of single and parallel machine scheduling problems with controllable processing time for each job. The processing time for job j depends on the position of the job in the schedule and is a function of the number of resource units allocated to its processing. Processing time functions and processing cost functions are allowed to be nonlinear. The scheduling problems considered here have important applications in industry and include many of the existing scheduling models as special cases. For the single machine problem, the objective is minimization of total compression costs plus a scheduling measure. The scheduling measures include makespan, total flow time, total differences in completion times, total differences in waiting times, and total earliness and tardiness with a common due date for all jobs. Except when the total earliness and tardiness measure is involved, each case the problem is solved efficiently. Under an assumption typically satisfied in just-in-time systems, the problem with total earliness and tardiness measure is also solved efficiently. Finally, for a large class of processing time functions; parallel machine problems with total flow time and total earliness and tardiness measures are solved efficiently. In each case we reduce the problem to a transportation problem.     

A NOTE ON “COMMON DUE WINDOW SCHEDULING”

Kramer and Lee recently addressed a common due window scheduling problem with earliness and tardiness penalties, where earliness and tardiness penalty factors are constant and the common window size is given. They showed that the problem is polynomial when the location of the due window is a decision variable. For the case where the location of the due window is given, the problem is also polynomial when the latest due date is greater than or equal to the makespan, and they proposed a pseudopolynomial dynamic programming algorithm to find an optimal schedule when the latest due date is less than the makespan. In this note we address the problem for the case where the location of the due window is given. Specifically, we show that the problem is polynomial if the window location is unrestricted, and present a more efficient dynamic program algorithm to optimally solve the problem if the window location is restricted. The concepts of unrestricted and restricted window locations are defined in this note.     

冷轧生产批量计划与调度问题模型及算法

对冷轧生产系统特点进行分析,将冷轧生产批量计划与调度问题抽象为多阶段、多品种带有中间库的批量计划与调度问题。针对该问题建立了数学模型,通过对库存成本和调整成本惩罚系数的控制可以协调库存水平和调整次数的关系。对所建立的模型,提出了基于二进制粒子群优化与局部搜索的混合求解算法。最后,通过对企业实际生产数据的计算和分析,验证了模型和算法的可行性和有效性。     

Tactical production and distribution planning with dependency issues on the production process

Tactical production-distribution planning models have attracted a great deal of attention in the past decades. In these models, production and distribution decisions are considered simultaneously such that the combined plans are more advantageous than the plans resolved in a hierarchical planning process. We consider a two-stage production process, where in the first stage raw materials are transformed into continuous resources that feed the discrete production of end products in the second stage. Moreover, the setup times and costs of resources depend on the sequence in which they are processed in the first stage. The minimum scheduling unit is the product family which consists of products sharing common resources and manufacturing processes. Based on different mathematical modelling approaches to the production in the first stage, we develop a sequence-oriented formulation and a product-oriented formulation, and propose decomposition-based heuristics to solve this problem efficiently. By considering these dependencies arising in practical production processes, our model can be applied to various industrial cases, such as the beverage industry or the steel industry. Computation tests on instances from an industrial application are provided at the end of the paper.     

Managing Production and Distribution for Supply Chains in the Processed Food Industry

We develop and evaluate a modeling approach for making periodic review production and distribution decisions for a supply chain in the processed food industry. The supply chain faces several factors, including multiple products, multiple warehouses, production constraints, high transportation costs, and limited storage at the production facility. This problem is motivated by the supply chain structure at Amy's Kitchen, one of the leading producers of natural and organic foods in the United States. We develop an enhanced myopic two‐stage approach for this problem. The first stage determines the production plan and uses a heuristic, and the second stage determines the warehouse allocation plan and uses a non‐linear optimization model. This two‐stage approach is repeated every period and incorporates look‐ahead features to improve its performance in future periods. We validate our model using actual data from one factory at Amy's Kitchen and compare the performance of our model to that of the actual operation. We find that our model significantly reduces both inventory levels and stockouts relative to those of the actual operation. In addition, we identify a lower bound on the total costs for all feasible solutions to the problem and measure the effectiveness of our model against this lower bound. We perform sensitivity analysis on some key parameters and assumptions of our modeling approach.     

Appointment Scheduling with No‐Shows and Overbooking

We study an overbooking model for scheduling arrivals at a medical facility under no‐show behavior, with patients having different no‐show probabilities and different weights. The scheduler has to assign the patients to time slots in such a way that she minimizes the expected weighted sum of the patients' waiting times and the doctor's idle time and overtime. We first consider the static problem, where the set of patients to be scheduled and their characteristics are known in advance. We partially characterize the optimal schedule and introduce a new sequencing rule that schedules patients according to a single index that is a function of their characteristics. Then we apply our theoretical results and conclusions from numerical experiments to sequential scheduling procedures. We propose a heuristic solution to the sequential scheduling problem, where requests for appointments come in gradually over time and the scheduler has to assign each patient to one of the remaining slots that are available in the schedule for a given day. We find that the no‐show rate and patients' heterogeneity have a significant impact on the optimal schedule and should be taken under consideration.     

The Production of Several Items in a Single Facility with Linearly Changing Demand Rates

In this paper we extend the ELSP model to allow for linearly changing demand rates over a fixed planning horizon. This extension of the ELSP research provides a model that can be used in coordinating the production and marketing planning activities in a firm. The model allows the user to evaluate the impact of changes in product demand on production costs and customer service. We solve the model using a standard nonlinear programming package (MINOS) and show through examples based on actual production data how the model can be used to support coordinated production and marketing planning.     

A REVIEW OF FLOWSHOP SCHEDULING RESEARCH WITH SETUP TIMES

Flowshop scheduling problems with setup times arise naturally in many practical situations. This paper provides a review of static and deterministic flowshop scheduling research involving machine setup times. The literature is classified into four broad categories, namely sequence independent job setup times, sequence dependent job setup times, sequence independent family setup times, and sequence dependent family setup times. Using the suggested classification scheme, this paper organizes the flowshop scheduling literature involving setup and/or removal times and summarizes the existing research for different flowshop problem types. This review reveals that, while a considerable body of literature on this subject has been created, there still exist several potential areas worthy of further research.     

Coordinating pricing and production decisions for multiple products

We consider a dynamic problem of joint pricing and production decisions for a profit-maximizing firm that produces multiple products. We model the problem as a mixed integer nonlinear program, incorporating capacity constraints, setup costs, and dynamic demand. We assume demand functions to be convex, continuous, differentiable, and strictly decreasing in price. We present a solution approach which is more general than previous approaches that require the assumption of a specific demand function. Using real-world data from a manufacturer, we study problem instances for different demand scenarios and capacities and solve for optimal prices and production plans. We present analytical results that provide managerial insights on how the optimal prices change for different production plans and capacities. We extend some of the earlier works that consider single product problems to the case of multiple products and time variant production capacities. We also benchmark performance of proposed algorithm with a commercial solver and show that it outperforms the solver both in terms of solution quality and computational times.     

随机订单干扰下考虑合并决策的供应链网络调度研究

为满足客户个性化需求的快速响应，企业需具备柔性的外部供应链网络结构，以协同方式共同完成产品生产。本文考虑具有交互特征的多个不同类型协同供应链网络，构建生产成本、库存成本、等待成本以及订单延期交货成本最小化的目标函数，并设计合并决策判断变量构建同类订单在相同协同企业处的开始时间约束。此外，模型中考虑确定订单以及随机订单两种类型订单，并设计随机订单在区间时间段中离散时间点的到达概率。为获取协同供应链网络生产调度优化策略，基于随机订单到达与否的场景构建四个子决策模型，并进一步设计判断提前安排随机订单协同生产和不提前安排随机订单协同生产不同调度策略下成本差异的主决策模型。仿真结果表明合并决策在带来生产成本效益的同时也引起了部分订单的延期交货，且不同类型的协同供应链网络对随机订单的抗干扰能力存在一定程度的差异。