Multi-product batch production on a single machine—A problem revisited

When several products are processed one at a time on a single machine, the conventional approach of computing the economic batch quantity for each product cannot apply. An example for six products is considered, where the total production capacity on regular time is inadequate, so that overtime has to be used at an extra cost. A simple method is described for solving this problem when each product is produced once during a production cycle, the objective being to minimize the total set-up and holding costs per day. Schedules which involve batch splitting can reduce these costs further, and a guideline is proposed for the construction of sub-cycles. The results compare favourably with lower bounds computed for the purpose.     

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.     

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。     

Integrated supply,production and distribution scheduling under disruption risks

This paper presents a bi-objective stochastic mixed integer programming approach for a joint selection of suppliers and scheduling of production and distribution in a multi-echelon supply chain subject to local and regional disruption risks. Two conflicting problem objectives are minimization of cost and maximization of service level. The three shipping methods are considered for distribution of products: batch shipping with a single shipment of different customer orders, batch shipping with multiple shipments of different customer orders and individual shipping of each customer order immediately after its completion. The stochastic combinatorial optimization problem is formulated as a time-indexed mixed integer program with the weighted-sum aggregation of the two objective functions. The supply portfolio is determined by binary selection and fractional allocation variables while time-indexed assignment variables determine the production and distribution schedules. The problem formulation incorporates supply–production, production–distribution and supply–distribution coordinating constraints to efficiently coordinate supply, production and distribution schedules. Numerical examples modelled after an electronics supply chain and computational results are presented and some managerial insights are reported. The findings indicate that for all shipping methods, the service-oriented supply portfolio is more diversified than the cost-oriented portfolio and the more cost-oriented decision-making, the more delayed the expected supply, production and distribution schedules.     

Optimal Solutions for the Single Batch,Flow Shop,Lot‐streaming Problem with Equal Sublots

Lot streaming is the process of splitting a production lot into sublots and then scheduling the sublots in overlapping fashion on the machines in order to improve the performance of the production system. Implementation of this concept arises in several batch production environments. These include, among others, printed circuit board assembly and semiconductor fabrication. There are several limitations in the lot‐streaming models available in the literature which affect their usefulness in reality. In this paper, we consider the single batch, flow shop, lot‐streaming problem but relax several of these limitations. The main contribution of this paper is to provide the production manager with a way of splitting a lot in order to optimize performance under various measures of performance and setup time considerations. In addition, the insight of the proposed procedure can be used to tackle more general versions of the problem considered.     

PRODUCTION SCHEDULING OF CONTINUOUS FLOW LINES: MULTIPLE PRODUCTS WITH SETUP TIMES AND COSTS

The problem of production planning and setup scheduling of multiple products on a single facility is studied in this paper. The facility can only produce one product at a time. A setup is required when the production switches from one type of product to another. Both setup times and setup costs are considered. The objective is to determine the setup schedule and production rate for each product that minimize the average total costs, which include the inventory, backlog, and setup costs. Under the assumption of a constant production rate, we obtain the optimal cyclic rotation schedule for the multiple products system. Besides the decision variables studied in the classical economic lot scheduling problem (ELSP), the production rate is also a decision variable in our model. We prove that our solutions improve the results of the classical ELSP.     

基于合作博弈的易腐性产品运输设施选择的费用分配

易腐性产品的价值会随着时间而损失,运输易腐性产品时,客户除了支付运输费用外还需要承担产品的价值损失。本文把易腐性产品的价值损失和运输费用之和作为总费用,应用合作博弈理论,把易腐性产品的运输设施选择的费用分配问题构造成费用分配博弈,证明了在易腐性产品线性价值损失的情况下,运输设施选择博弈的核心非空,且为子模博弈,并讨论核仁、夏普利值、τ-值等解。论文最后讨论了有约束运输的设施选择的费用分配博弈的解的情况,说明其核心也许为空,并提出了进一步研究的方向。     

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.     

Economic Manufacturing Quantity and Its Integrating Implications

Several contradictions are noted among the Economic Order Quantity (EOQ), Just‐In‐Time (JIT), and Optimized Production Technology (OPT) approaches and the economic framework for profit maximization. A fundamental model referred to as the Economic Manufacturing Quantity (EMO) is developed and examined for its integrating implications for the three approaches. An implication for the classic EOQ approach is that the balance between setup and inventory carrying costs is valid when a production facility is operating at or below a certain critical level but not when operating above that level. An implication for the JIT approach is that one must reduce setup cost at non‐bottlenecks and setup time at bottlenecks to reduce inventory. An implication for the OPT approach is that trade‐offs between setup and inventory carrying costs may indeed be ignored while determining process batch sizes, provided each facility in a production system is operating at or above Its critical level. Economic theoretic analysis of the EMO model provides a basis for unification of JIT which advocates stability in operating level as a key to improved productivity and quality, and OPT that advocates maximizing operating level with resultant emphasis on bottlenecks as a key to increased profits. This unifying basis states that a profit‐maximizing production facility or system will operate at the full and stable level as long as market demand remains relatively sensitive to price and operating at the full (maximum) level provides positive unit contribution.     

Balancing Production and Distribution in Paper Manufacturing

A paper manufacturing plant minimizes its production cost by using long production runs that combine the demands from its various customers. As jobs are completed, they are released to distribution for delivery. Deliveries are made by railcars, each of which is dedicated to one customer. Long production runs imply that maximizing railcar utilization requires holding the cars over several days or holding completed jobs within the loading facility. Each of these methods imposes a cost onto the distribution function. We find how distribution can minimize its cost, given production's schedule. We then consider the problem of minimizing the company's overall cost of both production and distribution. A computational study using general data illustrates that the distribution cost is reduced by 25.80% through our proposed scheme, and that the overall cost is reduced an additional 4.40% through our coordination mechanism. An optimal algorithm is derived for a specific plant's operations.     

Notes and Communications REPLANNING FREQUENCIES FOR MASTER PRODUCTION SCHEDULES

Updating production plans typically is achieved by rolling the planning horizon forward one period at a time, each time including the latest information in order to determine the best course of action to pursue in the present period. Theoretical planning-horizon studies have identified the conditions by which the production decisions in the current and some specified number of future periods remain optimal given some set of future demands. Motivated by these findings, this study addresses the replanning frequency in a hierarchical production planning problem where no planning-horizon theorems are available. In this problem the aggregate production plan and the master production schedule are linked by a rolling-horizon practice. Empirical experimentation indicates that under certain cost and demand conditions the master production schedule need not be updated every period. If a schedule does not need to be updated for several periods, the schedule for these periods can be frozen to provide stability for planning components at lower levels in the bill of material of the products. The results of this study thus provide some reference for the determination of the frozen portion of the master production schedule.     

Sequencing heuristics for dependent setups in a continuous process industry

In this paper we address the scheduling of Biaxially Oriented Polypropylene (BOPP) film production, which belongs to the plastics industry and is a continuous process. Scheduling problems in BOPP film production involve processing different thickness settings of films on a common facility. Customer orders of the same thickness setting are usually grouped together as a production batch and a setup time is incurred whenever the batch is switched. However, there is usually more than one batch for the same thickness setting because of the due date constraints of the orders. Therefore, there is a need to develop a batching and sequencing scheme that minimizes the total setup time, or equivalently the makespan, under the due date constraint. In this paper heuristics are developed to generate a near-optimal solution for the problem. The heuristics are evaluated by an optimal solution procedure and are tested by using the actual data from a plant making the BOPP film. Comparison of the heuristics with the results of the current system has demonstrated a significant reduction in total setup time.     

随机需求下联合选址-库存模型研究

研究了一类具有季节性需求特性的商品的联合选址-库存模型。在传统的无容量限制的固定费用设施选址问题中考虑了分销中心的运作库存和安全库存的影响,以及规模经济效应和风险分摊效应,同时考虑了季节性商品未来需求的不确定性,将订货决策作为模型的决策变量,建立了一类随机需求下以期望销售收益最大化为目标函数的联合选址-库存模型,拓展了已有的联合选址-库存模型。该模型是一个混合整数规划问题,给出了求解该问题的基于拉格朗日松弛算法的两阶段算法,最后通过随机生成四组不同规模的数值算例,得到的计算结果表明拉格朗日松弛算法可以有效地求解该问题。     

The impact of random machine unavailability on inventory policies in a continuous improvement environment

There are production situations where a production facility (e.g. a machine) is used intermittently to produce lot sizes of certain products. Upon completion of production run, the facility may not be available for a random amount of time due to several reasons, such as: the facility needs to be maintained and the maintenance time is random due to unforeseen circumstances; or that the facility is leased by different manufacturers and the demand for the facility is random. As a result of machine unavailability, stock-out situations might arise. This paper extends the work of Abboud et al . (2000, Computers and Operations Research , 27 , 335-351) by assuming learning and forgetting in production. A new mathematical model is developed with numerical examples and sensitivity analysis provided. Furthermore, this paper determines how the overall inventory cost is influenced by the nature of the random variable that represents the unavailability time of the production facility.     

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.     

混合离散差分进化算法在单机批处理调度中的应用

本文研究单机批处理调度问题,批处理机有批次容量限制,批处理时间由每个批次所含作业中的最长作业处理时间决定。每个作业具有不同的大小、处理时间、提前拖期惩罚权重,所有作业具有公共交货期,且交货期无限晚。目标函数为最小化所有作业的加权提前拖期惩罚之和。该问题已被证明为NP难题,本研究找到了其最优解具有的一些性质,在此基础上利用它们提出了一种动态规划(DP)与差分进化(DE)算法相结合的混合离散差分进化(HDDE)算法来求解该问题,通过与传统的遗传算法、模拟退火算法和迭代贪婪算法进行对比,HDDE算法显示了更加强大的全局搜索能力。     

The Use of Flexible Manufacturing Capacity in Pharmaceutical Product Introductions*

This work considers the value of the flexibility offered by production facilities that can easily be configured to produce new products. We focus on technical uncertainty as the driver of this value, while prior works focused only on demand uncertainty. Specifically, we evaluate the use of process flexibility in the context of risky new product development in the pharmaceutical industry. Flexibility has value in this setting due to the time required to build dedicated capacity, the finite duration of patent protection, and the probability that the new product will not reach the market due to technical or regulatory reasons. Having flexible capacity generates real options, which enables firms to delay the decision about constructing product‐specific capacity until the technical uncertainty is resolved. In addition, initiating production in a flexible facility can enable the firm to optimize production processes in dedicated facilities. The stochastic dynamic optimization problem is formulated to analyze the optimal capacity and allocation decisions for a flexible facility, using data from existing literature. A solution to this problem is obtained using linear programming. The result of this analysis shows both the value of flexible capacity and the optimal capacity allocation. Due to the substantial costs involved with flexibility in this context, the optimal level of flexible capacity is relatively small, suggesting products be produced for only short periods before initiating construction of dedicated facilities.     

Offshore Remanufacturing with Variable Used Product Condition

We consider the acquisition and production decisions of a remanufacturer who acquires used products of variable condition and allocates remanufacturing activity to domestic and offshore facilities. The problem is formulated as a multicommodity network flow model with economies of scale and product obsolescence. We show that the remanufacturer's optimal strategy can be chosen from a finite set of simple policies in which each product is routed to a facility based on its condition. We then numerically investigate the impact of key parameters on optimal decisions regarding offshore remanufacturing.     

Optimal Policies for Perishable Products When Transportation to Export Market Is Disrupted

We consider a problem where a firm produces a variety of fresh products to supply two markets: an export market and a local market. A public transportation service is utilized to deliver the products to the export market, which is cheap, but its schedule is often disrupted severely. Each time this happens, the firm faces the following questions. (i) For a product that has been finished and is waiting for delivery to the export market, should it continue to wait, at an increasing risk of decay, and when should the waiting be terminated and the product be put to the local market? (ii) For a product that has not been finished, should its processing be postponed, so as to reduce the loss from decay after its completion? (iii) What is the best sequence to process the remaining products, according to the information available? We develop, in this study, a model to address these and other related questions. We find optimal policies that minimize the total expected loss in both the make‐to‐order and make‐to‐stock production systems, respectively. For each finished product, we reveal relationships among the desirable waiting time, the price at the local market, and the decaying cost. For unfinished products, we find the optimal start times and processing sequence. Numerical experiments are also conducted to evaluate the optimal policies.