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.     

Solving the Economic Lot-Scheduling Problem Using the Method of Prime Subperiods

In recent years the reported successes of Japanese production systems, particularly the just-in-time approach to inventory control, has caused managers to focus more of their attention on efficient decision-making procedures for determining production schedules that minimize inventory costs. One such potential area of attention is the economic lot-scheduling problem (ELSP), which occurs in a variety of manufacturing environments where machining operations are prevalent. The economic lot-scheduling problem addresses the determination of lot sizes for N products with constant demand (and cycled through one machine with a given production rate) to minimize setup and inventory costs. The most successful solution approaches to the ELSP have been based on the concept of a basic period that is of sufficient length for the production of all items, even though each item might not be produced during each repetition of the basic period. This paper proposes a heuristic approach to the solution of the ELSP (referred to as the method of prime subperiods), which is an extension of the basic period approaches. The procedure is described and demonstrated via an example and then tested using a set of six example problems previously employed in the literature related to the ELSP. The results indicate as good or superior performance by the proposed method of prime subperiods.     

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.     

USING SHORT-TERM DEDICATION FOR SCHEDULING MULTIPLE PRODUCTS ON PARALLEL MACHINES

In a multiproduct, parallel machine environment, it may be beneficial to dedicate one or more of the machines to a single product for consecutive time periods. However, previous lot-sizing and scheduling models usually do not allow for such short-term dedication. This paper presents a mixed-integer programming model that allows for short-term dedication in scheduling parallel machines serving multiple products with dynamic demands. It also describes a Lagrangian-based algorithm for solving such scheduling problems. An experiment verifies the effectiveness of the algorithm and demonstrates the importance of allowing for short-term dedication. Capacity utilization, one of six factors investigated, greatly affects the use of dedication. A strong interaction effect between the number of machines and the number of products is also seen with respect to the usefulness of short-term dedication. A measure of estimated production frequency incorporates these two factors along with magnitudes of periodic demands. This measure has a strong relationship with the amount of short-term dedication used in solutions. Operations managers employing parallel machines could use the experimental results in deciding whether to use short-term dedication to reduce costs.     

A COMPARISON OF ORDER-RELEASE AND DISPATCH RULES FOR THE DYNAMIC WEIGHTED EARLY/TARDY PROBLEM

The early/tardy problem is one of the most vexing pieces of the complex production scheduling decision process. So far most of the research has been on single-machine environments. Hence, we considered the weighted early/tardy scheduling problem in a simulated dynamic multimachine job shop. We analyzed controlled job-release and dispatch rules using time and cost information at a variety of stationary and nonstationary utilization rates, due-date allowances, and early/tardy cost levels. We found a newly developed method for controlling the release for all job operations using early/tardy cost information, superior to other release mechanisms overall in both our stationary and nonstationary analyses. We found immediate release useful at many high utilization conditions and a gateway-only release method best in many low utilization conditions. A modified version of a single-machine early/tardy dispatch method was clearly superior to the dispatch rules for almost all the simulated shop conditions.     

SCHEDULING PARALLEL PROCESSORS WITH SETUP COSTS AND RESOURCE LIMITATIONS

An integer linear programming model is presented for the scheduling of n products on m identical machines. The particular problem studied is one that occurs frequently in the fiberglass and textile industries. The model incorporates setup costs, lost production costs, and overtime costs. Due to the structure of the model, integer solutions can be obtained by explicitly restricting only a small number of the integer variables. This allows those responsible for scheduling to solve realistically sized problems in an efficient manner. Computational results are provided for a set of generated test problems.     

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.     

Inventory Control and Scheduling of Multiple Products in a Common Facility*

Consider a set of chemical products to be produced in a single facility. Each product has its own unique reaction time (which is assumed to be independent of its batch size), as well as other cost and demand values. In this paper, we address the problem of determining the optimal number of batches, batch sizes, and an accompanying production schedule for these products in the single facility that will minimize the total cost. Two different algorithms have been developed for this problem, the performances of which are contrasted with classical cyclic production schedules. Finally, some guidelines for the application of these methods to real-life problems are outlined.     

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 MODEL-BASED DECISION SUPPORT SYSTEM FOR SCHEDULING LUMBER DRYING OPERATIONS

Raw lumber must be dried to a specified level of moisture content before it can be used to make furniture. This paper deals with a model-based decision support system (DSS) for a local furniture manufacturing company to assist its management in scheduling lumber drying operations. In addition to buying ready-to-use dried lumber from vendors at a premium, the company processes raw lumber in house using two production process that require various lengths of processing time in predryers and dry-kilns. Given the demand for various types of dried lumber over a specified planning horizon, the processing times and costs for each production process, technological restrictions, and management policies, the problem of interest is to satisfy the demand at a minimum cost. The DSS incorporates the mathematical formulation of this problem, is user friendly, maintains model and data independence, and generates the necessary reports, including loading and unloading schedules for the equipment.     

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.     

Joint Lot Sizing and Scheduling of Multiple Items with Sequence-Dependent Setup Costs

The objective of this research is to investigate the effects of setup-cost estimating methods on the lot sizing and scheduling of multiple products in multiple periods. These initial setup cost estimators (ISCEs) are used to estimate sequence-independent initial setup costs from sequence-dependent setup costs. A search of the literature reveals that, although sequence-dependent setup costs are frequently found in practice and ISCEs are frequently used, there is a dearth of research concerning the effect of using ISCEs. After a review of the literature, a mixed integer formulation of the joint problem of lot sizing and scheduling is presented, followed by a discussion of the difficulty in solving the formulation. Next, the six ISCEs evaluated are presented. These ISCEs range from simple (select the minimum setup cost) to complex (use the branch-and-bound solution to a traveling salesman-type problem). Each ISCE is evaluated using a full factorial design with five independent variables: demand distribution (three levels), demand trend (three levels), setup to inventory level (six levels), setup distribution (three levels), and setup variability (two levels). Two hypotheses are researched. Do the more computationally complex ISCEs produce lower overall costs than do the simpler ISCEs? Does the reduction in total cost justify the additional computation cost? The results of this study demonstrate that it may be incorrect to use “conventional wisdom'’when selecting an ISCE.     

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。     

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.