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。     

A Comparison of Due Date Setting,Resource Assignment,and Job Preemption Heuristics for the Multiproject Scheduling Problem*

This research examines a heuristic, rule-based approach for setting due dates in a multiproject, multijob, or assembly shop. Due date estimation is a challenging problem because the operating environment is capacitated, involves the allocation of multiple resources, and allows for the preemption of resources from one project or job to another. The dynamic, continuous arrival of new jobs or orders frequently results in the preemption of resources through the application of managerially determined priority policies. These preemption policies have a significant impact on the ultimate completion time of a job or a project. A three-factor, full-factorial computer simulation experiment is used to assess the relative effectiveness of combinations of four due date setting heuristics, five resource assignment heuristics, and three resource preemption heuristics. Recommendations are made for the selection of due date and resource assignment heuristic combinations under the three preemption policies examined.     

Integrated Order Scheduling and Packing

We consider an integrated production–distribution scheduling model in a make‐to‐order supply chain consisting of one supplier and one customer. The supplier receives a set of orders from the customer at the beginning of a planning horizon. The supplier needs to process all the orders at a single production line, pack the completed orders to form delivery batches, and deliver the batches to the customer. Each order has a weight, and the total weight of the orders packed in a batch must not exceed the capacity of the delivery batch. Each delivery batch incurs a fixed distribution cost. The problem is to find jointly a schedule for order processing and a way of packing completed orders to form delivery batches such that the total distribution cost (or equivalently, the number of delivery batches) is minimized subject to the constraint that a given customer service level is guaranteed. We consider two customer service constraints—meeting the given deadlines of the orders; or requiring the average delivery lead time of the orders to be within a given threshold. Several problems of the model with each of those constraints are considered. We clarify the complexity of each problem and develop fast heuristics for the NP‐hard problems and analyze their worst‐case performance bounds. Our computational results indicate that all the heuristics are capable of generating near optimal solutions quickly for the respective problems.     

On-line machine scheduling with batch setups

We study a class of scheduling problems with batch setups for the online-list and online-time paradigms. Jobs are to be scheduled in batches for processing. All jobs in a batch start and complete together, and a constant setup is prior to each batch. The objective is to minimize the total completion time of all jobs. We primarily consider the special cases of these problems with identical processing times, for which efficient on-line heuristics are proposed and their competitive performance is evaluated.     

Replanning the Master Production Schedule for a Capacity-Constrained Job Shop

This research examines the use of both frozen and replanning intervals for planning the master production schedule (MPS) for a capacity-constrained job shop. The results show that forecast error, demand lumpiness, setup time, planned lead time, and order size have a greater impact on the mean total backlog, total inventory, and number of setups than the frozen and replanning intervals. The study also shows that a repetitive lot dispatching rule reduces the importance of lot sizing, and a combination of repetitive lot dispatching rule and single-period order size consistently produces the lowest mean total backlog and total inventory. The results also indicate that rescheduling the open orders every period produces a lower mean total backlog and total inventory when the forecast errors are large relative to the order sizes. This result suggests that the due date of an open order should be updated only when a significant portion of the order is actually needed on the new due date.     

考虑交货因素的热轧无缝钢管订单排程模型与算法

无缝钢管的市场需求具有多品种、小批量的特点，为了在满足客户需求的同时保证高效连续化生产，文章在满足生产工艺特征的基础上将配送地址和交货期等合同因素引入热轧无缝钢管订单排程问题中，建立了以适期交货、订单集中生产配送和最小化机器设备调整为优化目标的订单排程优化模型，并设计了两阶段求解算法：首先，以订单交货期与配送地址差异最小为目标，基于凝聚策略设计了订单聚类算法，将具有相同工艺约束、相似合同要求的订单进行聚类，并形成初始轧制计划；然后，以设备调整和提前/拖期最小为目标，设计混合变邻域搜索算法，对初始轧制批次进行排程优化。基于实际订单数据的实验结果表明，模型和算法对问题的描述和求解是可行有效的。     

Reducing the number of setups for CNC punch presses

Large computer numerical control (CNC) punch presses are widely used for punching holes in heavy gage sheet metals. The turret of such presses has limited tool capacity, and any tool changes require dismantling the turret. Dismantling and reloading the turret generally takes several hours and is the dominant element of the total flow time for a batch of sheet metals. Reducing the turret setup time requires judicious grouping of the required tool set. We formulated an integer program to obtain the minimum number of setups. However, since the problem is nondeterministic polynomial-time hard (NP-hard), we offer three heuristics to solve the problem. We compare solutions obtained from the three heuristics with their respective optimal solutions using three simulated data sets and an industrial data set.     

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.     

Constructing Near Optimal Schedules for the Flow-Shop Lot Streaming Problem with Sublot-Attached Setups

Lot streaming—the process of splitting a production lot into sublots—has been a common practice in flow-shop systems during the past decade. Nevertheless, a major limiting assumption has been made in the analysis of these systems in that the setup time is, at most, lot-attached but not sublot-attached. In this paper, we consider the single and multiple batch flow-shop lot-streaming problems with sublot-attached setup times. A fast, optimal solution algorithm for the single batch problem is presented. For the multiple batch problem, we propose a near optimal solution procedure which is optimal in two-machine flow-shops. Computational results are also presented for the multiple batch problem which indicate both the efficiency and effectiveness of this procedure.     

Dynamic Group Scheduling Heuristics in a Flow-through Cell Environment*

The increased use of cellular manufacturing configurations designed to grapple with increasing competitive pressures is providing manufacturing managers and engineers with a broad variety of operational challenges. Many questions concerning the best procedures and policies for the day-to-day operation of manufacturing cells are still unanswered. The primary objective of this study is to compare the performance of traditional single-stage heuristics and the two-stage group scheduling heuristics that have exhibited superior performance in previous studies in a flow-through cell environment under a rigorous set of experimental conditions. Such a comparison is of great interest since each previous study has focused on proposing new heuristics and testing them against some particular baseline heuristic, often without comprehensive comparisons to the broad variety of previously proposed heuristics. Two single-stage heuristics and four two-stage heuristics are examined under sixteen experimental conditions (four experimental factors at two levels each). The experimental factors examined are shop load, due date tightness, setup to run-time ratio, and interarrival time distribution. Results vary by experimental condition and performance criteria, but in general, two-stage heuristics outperformed single-stage heuristics under all experimental conditions, as well as being relatively insensitive to changing experimental conditions. In addition, two of the two-stage heuristics displayed superior performance on all performance measures under most experimental conditions. Finally, the results indicated that interarrival time distribution does have a major impact on the performance of scheduling heuristics.     

A joint economic lot size model for raw material ordering,manufacturing setup,and finished goods delivering

In this research we consider a single-manufacturer single-buyer supply chain problem where the manufacturer orders raw materials from its supplier, then using its manufacturing processes converts the raw materials to finished goods, and finally delivers the finished goods to its customer. The manufacturer produces the product in batches at a finite rate and periodically delivers the finished goods at a fixed lot size to its customer, who has a constant demand rate. An integrated inventory control model, making joint economic lot sizes of manufacturer's raw material ordering, production batch, and buyer's ordering, is developed to minimize the mean total cost per unit time of the raw materials ordering and holding, manufacturer's setup and finished goods holding, the buyer's ordering, and inventory holding. Numerical examples are also setup to illustrate that jointly considering the inventory costs above results in less mean total cost than that of considering them separately.     

Cost models for lot streaming in a multistage flow shop

Lot streaming is a technique used to split a processing batch into several transfer batches. In this way, overlapping operations can be performed in different manufacturing stages, and production can be accelerated. This paper proposes two cost models for solving lot streaming problems in a multistage flow shop. The purpose is to determine the optimal processing batch size and the optimal number of transfer batches that minimize the total annual cost in each model. In the first model, a more complete and accurate method is developed to compute the costs of raw materials, work-in-process, and finished-product inventories. The total cost includes the setup cost, the transfer batch movement cost, the three-type inventory holding cost, and the finished-product shipment cost. The second model contains not only the four costs in the first model, but also the imputed cost associated with the makespan time. The total annual cost functions in both models are shown to be convex, and two solution approaches are suggested. An experiment consisting of three phases was conducted to explore the effect on the optimal solution when changing the value of one parameter at a time. The results indicate that three parameters have significant effects on the optimal solution.     

MINIMIZING TOTAL WEIGHTED COMPLETION TIME ON A SINGLE BATCH PROCESSING MACHINE

We study the problem of scheduling jobs on a single batch processing machine to minimize the total weighted completion time. A batch processing machine is one that can process a number of jobs simultaneously as a batch. The processing time of a batch is given by the processing time of the longest job in the batch. We present a branch and bound algorithm to obtain optimal solutions and develop lower bounds and dominance conditions. We also develop a number of heuristics and evaluate their performance through extensive computational experiments. Results show that two of the heuristics consistently generate high-quality solutions in modest CPU times.     

Efficient Heuristics for MRP Lot Sizing with Variable Production/Purchasing Costs*

Two heuristics based on branch and bound (B&B) are developed to solve closed-loop material requirements planning (MRP) lot-sizing problems that have general product structures and variable costs. A “look ahead method'’(LAM) heuristic allows for variable production/purchasing costs and uses a single-level B&B procedure to rapidly improve lower bound values; thus, LAM efficiently uses computer-storage capacity and allows solution of larger problems. The “total average modification'’(TAM) heuristic uses B&B, applied level by level, and modified setup and carrying costs to solve the variable production/purchasing costs MRP lot-sizing problem. LAM and TAM are tested on problems and compared to heuristics in the literature. TAM may be used to solve large MRP lot-sizing problems encountered in practice.     

A queuing/management consideration on Japanese production systems

A single-stage lot/cell production under a Poisson arrival and exponential service in a batch is considered. The three economic queuing models of push and pull types are presented, an economic comparison of push versus pull types is considered, and a strategic management/design consideration to the lot production is given. First, the total expected operating cost is given for the three queuing models including the Omote-Kanban type similar to VMI. Second, the push versus pull system is discussed from a view of setup time, inventory or operating cost, and it is ascertained that the three types are alternative. Finally, a strategic management basis for economic traffic, leadtime setting is given, and discussed by the introduction of production matrix on 2-stage design.     

Inventory Rationing in a Make‐to‐Stock System with Batch Production and Lost Sales

We address an inventory rationing problem in a lost sales make‐to‐stock (MTS) production system with batch ordering and multiple demand classes. Each production order contains a single batch of a fixed lot size and the processing time of each batch is random. Assuming that there is at most one order outstanding at any point in time, we first address the case with the general production time distribution. We show that the optimal order policy is characterized by a reorder point and the optimal rationing policy is characterized by time‐dependent rationing levels. We then approximate the production time distribution with a phase‐type distribution and show that the optimal policy can be characterized by a reorder point and state‐dependent rationing levels. Using the Erlang production time distribution, we generalize the model to a tandem MTS system in which there may be multiple outstanding orders. We introduce a state‐transformation approach to perform the structural analysis and show that both the reorder point and rationing levels are state dependent. We show the monotonicity of the optimal reorder point and rationing levels for the outstanding orders, and generate new theoretical and managerial insights from the research findings.     

A SINGLE-MACHINE SCHEDULING MODEL WITH FIXED-INTERVAL DELIVERIES

We consider an environment where a production facility modeled as a single machine needs to assign delivery dates to several orders and find a feasible sequence. Tardy jobs are not allowed. The delivery dates are to be at prespecified fixed intervals. The objective is to minimize the due date penalty and the cost of earliness. We provide a dynamic programming-based solution procedure that runs in polynomial time. We develop several dominance results that reduced the computational requirement by an order of magnitude in our computational study.     

An Investigation of Scheduling Policies in a Dual-Constrained Manufacturing Cell*

In previous group scheduling studies, labor has essentially been ignored by assuming that enough labor is assigned to each machine in the cell. In reality, however, management usually does not have the resources to employ a laborer at each machine in the cell (i.e., machines need to share labor). Both labor scheduling and group scheduling heuristics need to be administered to manage the cell effectively. This study develops and examines scheduling procedures for a dual-constrained (i.e., machine and labor) manufacturing cell. Eleven decision rules are developed and tested under 16 different experimental conditions. The experimental factors used are interarrival time distribution, cell load, setup-to-run-time ratio, and transfer-to-run-time ratio. Results show that interarrival time distribution and cell load have the greatest impact on the performance of the cell. This suggests that effective production planning aimed at reducing job arrival variation and leveling the cell load can substantially improve cell performance. Among the experimental factors, setup and transfer-to-run-time ratio factors had the strongest influence on the rankings of the decision rules. These rankings were fairly robust across all experimental conditions and performance measures. The results also indicated that the inclusion of labor as a contraint in the cell had a significant impact on the performance of several group scheduling heuristics. Finally, it was shown that the best performing decision rules consider both transfer time and subfamily setup times.     

On the integration of due date setting and order release control

This paper calls for a paradigm shift in the production control literature away from assuming due date setting and order release are two independent decision levels. When order release is controlled, jobs do not enter the shop floor directly but are retained in a pre-shop pool and released to meet certain performance targets. This makes the setting of accurate planned release dates – the point at which jobs transition from the pool to the shop floor – a key consideration when setting due dates. We develop a new approach to estimating planned release dates to be embedded in the Workload Control (WLC) concept. Our approach is unique as it anticipates the release decision as part of the due date setting procedure. This makes a second independent release decision superfluous and avoids a major cause of tardiness – deviations between (i) the planned release date used when calculating the delivery time allowance and (ii) the actual, realised release date. Simulation is used to compare the performance of WLC using two decision levels with the new single-level approach where the release decision is anticipated when setting the due date. Performance improvements are shown to be robust to uncertainty in processing time estimates.     

Customer order scheduling to minimize total weighted completion time

In this paper we study the scheduling problem in which each customer order consists of several jobs of different types, which are to be processed on m facilities. Each facility is dedicated to the processing of only one type of jobs. All jobs of an order have to be delivered to the customer at the same time. The objective is to schedule all the orders to minimize the total weighted order completion time. While the problem has been shown to be unary NP-hard, we develop a heuristics to tackle the problem and analyze its worst-case performance.