Overlapping design and build cycles in product development

Product development time is a major component of the total time it takes to bring a product to market. Overlapping is the process of starting a downstream operation (such as manufacturing) before completing the upstream operation (such as design). There is an inherent risk in overlapping as a build-assembly may not be compatible with a subsequent assembly, requiring reconciliation work on the overlapped tasks. The ensuing trade-off between this risk, and the project time saved, is shown to possess some unique characteristics among different modes of overlapping. We study the optimization model of the trade-off in general, and analyze some special cases to establish interesting insights on overlapping. These include: advantage of overlapping in different scenarios, special properties of optimal overlap, and impact of parameter values on overlapping decisions. We show that several properties of a single overlap can be extended to multiple overlaps, and establish a limit to overlapping based on administrative cost of implementing overlap and shapes of cost functions. The critical role of the administrative cost (of coordinating overlaps) is also borne out by the model.     

Optimal overlapping and functional interaction in product development

Overlapping of development stages and interaction between different functions are regarded as important strategies for reducing development lead time. However, overlapping typically requires additional costs for rework and functional interaction increases communication time. This paper presents an analytical model to improve project performance by balancing the positive and negative effects of overlapping and functional interaction. We first investigate the progress of downstream development, which is essential to derive the optimal overlapping policies. We find that the downstream progress increases over time when the upstream evolution is fast or linear, but it is indefinite when the upstream evolution is slow. Then, we present optimal overlapping policies taking into account the complexity of downstream progress. The impact of different project properties, such as the dependency between development stages and the opportunity cost of time, on overlapping policies is discussed. Finally, we derive the optimal functional interaction strategy when the optimal overlapping is followed. The methodology is illustrated with a case study at a handset design company.     

Three time-based scale formulations for the two-stage lot sizing and scheduling in process industries

In this paper, we propose three novel mathematical models for the two-stage lot-sizing and scheduling problems present in many process industries. The problem shares a continuous or quasi-continuous production feature upstream and a discrete manufacturing feature downstream, which must be synchronized. Different time-based scale representations are discussed. The first formulation encompasses a discrete-time representation. The second one is a hybrid continuous-discrete model. The last formulation is based on a continuous-time model representation. Computational tests with state-of-the-art MIP solver show that the discrete-time representation provides better feasible solutions in short running time. On the other hand, the hybrid model achieves better solutions for longer computational times and was able to prove optimality more often. The continuous-type model is the most flexible of the three for incorporating additional operational requirements, at a cost of having the worst computational performance.     

An optimization-based model for maximizing the benefits of fast-track construction activities

Fast-track construction projects have become more popular in recent years in response to growing industry demand. By allowing downstream construction activities to start with incomplete information from upstream design activities, fast-tracking (through overlapping) allows for shorter project duration at the expense of potential rework. This leaves practitioners with the challenge of determining the optimal fast-tracking strategy to meet project schedule requirements while avoiding excessive amounts of rework. This paper presents an optimization-based model that serves as a decision support tool in scheduling fast-track construction activities. The model takes into consideration information exchange between upstream and downstream activities and uses the concepts of sensitivity and evolution to maximize the net benefits of fast-tracking. The model is illustrated on an ongoing construction project, which was analysed under various overlapping scenarios. The results indicate substantial time savings depending on the speed of evolution and sensitivity. The project schedule can be shortened by up to 50 days without causing excessive amounts of rework.     

供应中断风险下采购与定价决策分析

供应中断是供应链上的企业可能面临的问题,运用合理的采购策略可以帮助企业有效缓解供应中断风险。本文研究了供应中断下供应商和制造商之间的纵向竞争和两个制造商之间的横向竞争问题。供应商制定批发价,两个制造商采用不同的采购策略进行产量博弈,其中一个制造商采用紧急双源订货策略,另一个采用可靠单源订货策略。论文采用了多阶段博弈模型,分析了制造商之间的合谋与竞争两种行为,求出了供应商和制造商的最优决策,比较了这两种行为对供应商和制造商的影响。通过数值分析,讨论了成本参数和可靠性参数对于最优订货量的影响以及对于采用不同订货策略的制造商期望利润的影响。     

An inventory model with partial backordering and unit backorder cost linearly increasing with the waiting time

As the implementation of JIT practice becomes increasingly popular, each echelon in a supply chain tends to carry fewer inventories, and thus the whole supply chain is made more vulnerable to lost sales and/or backorders. The purpose of this paper is to recast the inventory model to be more relevant to current situations, where the penalty cost for a shortage occurrence at a downstream stage in a supply chain is continually transmitted to the upstream stages. The supplier, in this case, at the upstream of the supply chain is responsible for all the downstream shortages due to the chain reaction of its backlog. The current paper proposes a model in which the backorder cost per unit time is a linearly increasing function of shortage time, and it claims that the optimal policy for the supplier is setting the optimal shortage time per inventory cycle to minimize its total relevant cost in a JIT environment.     

Simultaneous Job Scheduling and Resource Allocation on Parallel Machines

Most deterministic production scheduling models assume that the processing time of a job on a machine is fixed externally and known in advance of scheduling. However, in most realistic situations, apart from the machines, it requires additional resources to process jobs, and the processing time of a job is determined internally by the amount of the resources allocated. In these situations, both the cost associated with the job schedule and the cost of the resources allocated should be taken into account. Therefore, job scheduling and resource allocation should be carefully coordinated and optimized jointly in order to achieve an overall cost-effective schedule. In this paper, we study a parallel-machine scheduling model involving both job processing and resource allocation. The processing time of a job is non-increasing with the cost of the allocated resources. The objective is to minimize the total cost including the cost measured by a scheduling criterion and the cost of all allocated resources. We consider two particular problems of this model, one with the scheduling criterion being the total weighted completion time, and the other with that being the weighted number of tardy jobs. We develop a column generation based branch and bound method for finding optimal solutions for these NP-hard problems. The method first formulates the problems as set partitioning type formulations, and then solves the resulting formulations exactly by branch and bound. In the branch and bound, linear relaxations of the set partitioning type formulations are decomposed into master problems and single-machine subproblems and solved by a column generation approach. The algorithms developed based on this method are capable of solving the two problems with a medium size to optimality within a reasonable computational time.     

Adaptive policies for multi-mode project scheduling under uncertainty

In this paper we propose an adaptive model for multi-mode project scheduling under uncertainty. We assume that there is a due date for concluding the project and a tardiness penalty for failing to meet this due date, and that several distinct modes may be used to undertake each activity. We define scheduling policies based on a set of thresholds. The starting time of the activity is compared with those thresholds in order to define the execution mode.We propose a procedure, based on the electromagnetism heuristic, for choosing a scheduling policy. In computational tests, we conclude that the adaptive scheduling policy found by using the model and the heuristic solution procedure is consistently better than the optimal non-adaptive policy. When the different modes have very different characteristics and there is a reasonable difference between the average duration of the project and the due date, the cost advantage of the adaptive policy becomes very significant.     

Exploiting process plan flexibility in production scheduling: A multi-objective approach

When solving a product/process design problem, we must exploit the available degrees of freedom to cope with a variety of issues. Alternative process plans can be generated for a given product, and choosing one of them has implications on manufacturing functions downstream, including planning/scheduling. Flexible process plans can be exploited in real time to react to machine failures, but they are also relevant for off-line scheduling. On the one hand, we should select a process plan in order to avoid creating bottleneck machines, which would deteriorate the schedule quality; on the other one we should aim at minimizing costs. Assessing the tradeoff between these possibly conflicting objectives is difficult; actually, it is a multi-objective problem, for which available scheduling packages offer little support. Since coping with a multi-objective scheduling problem with flexible process plans by an exact optimization algorithm is out of the question, we propose a hierarchical approach, based on a decomposition into a machine loading and a scheduling sub-problem. The aim of machine loading is to generate a set of efficient (non-dominated) solutions with respect to the load balancing and cost objectives, leaving to the user the task of selecting a compromise solution. Solving the machine loading sub-problem essentially amounts to selecting a process plan for each job and to routing jobs to the machines; then a schedule must be determined. In this paper we deal only with the machine loading sub-problem, as many scheduling methods are already available for the problem with fixed process plans. The machine loading problem is formulated as a bicriterion integer programming model, and two different heuristics are proposed, one based on surrogate duality theory and one based on a genetic descent algorithm. The heuristics are tested on a set of benchmark problems.     

Economic lot scheduling with uncontrolled co-production

The aim of this paper is to analyze the effects of uncontrolled co-production on the production planning and lot scheduling of multiple products. Co-production occurs when a proportion of a certain production comes out as another product. This is typical in the process industry where quality and process specifications can lead to diversified products. We assume that there is no demand substitution and each product has its own market. Furthermore, we assume that co-production cannot be controlled due to technical and/or cost considerations. We introduce two models that extend the common cycle economic lot scheduling (ELSP) setting to include uncontrolled co-production. In the first model we do not allow for shortages and derive the optimal cycle time expression. In the second model, we allow for planned backorders and characterize the optimal solution in closed form. We provide a numerical study to gain insight about co-production. It seems that the cycle time increases with co-production rate and utilization of the system. The effect of co-production on long-term average cost does not exhibit a certain characteristic.     

基于倒箱移动路径的集装箱堆场提箱作业优化模型

集装箱堆场提箱作业优化的目标是通过对倒箱搬运过程的优化使总作业成本最小。本文分析了正面吊设备的提箱作业过程,对作业规则和约束建立数学模型,在分析倒箱移动路径的基础上,提出了提箱作业优化模型。该模型为两层嵌套的组合优化模型,外层子模型针对提箱订单实现倒箱策略优化;内层子模型针对每一步倒箱作业寻找使倒箱作业成本最小的移动路径。提出了求解该模型的算法流程。最后,通过数值算例验证了优化模型的有效性。与传统人工作业方式的比较结果表明:本优化模型能够明显降低提箱作业成本。     

The effect of testing equipment shift on optimal decisions in a repetitive testing process

Repetitive testing process is commonly used in the final testing stage of semiconductor manufacturing to ensure high outgoing product quality and to reduce testing errors. The decision on testing lot size and the number of testing repetitions ultimately determines the effectiveness of the testing process. Setting the retest rule is often difficult in practice due to uncertainties in the incoming product quality and testing equipment condition. In this paper, we study a repetitive testing process where the testing equipment may shift randomly to an inferior state. We develop a cost model that helps us to make optimal decisions on retesting rule. Through numerical analysis, we provide practical insights about the effects of testing equipment shift rate, testing errors, and different costs such as cost of testing and cost of rejecting conforming products on the optimal decision and the system performance. We find that significant penalty may result if the potential testing equipment shift is ignored.     

Simultaneous engineering approach to an integrated design and process planning

To support integration of design and process planning, a reference model has been developed. This reference model represents the basis for a new methodology for integrated design and process planning which enables a Simultaneous Engineering approach in the early stages of product development. The reference model consists of four partial models. These are the activity model, the information model, the technical system model and the model of integrating methods. Using these models, the methodology enables a concurrent processing of design and process planning activities with regard to different components of a product. Furthermore, the methodology covers planning methods as well as execution methods, to support early transmission of information to downstream activities and a feedback of information to upstream activities within the process chain of design and process planning.     

具有两种运输方式选择的物流排序问题

本文研究了单机环境下,有两种运输方式可供选择的集成生产和运输的排序问题。有多个工件需要在一台机器上进行加工,工件生产完后需要分批运到客户处。有两种运输方式,普通运输和特快运输可供选择。制造商需要安排工件的加工顺序,选择合适的运输方式和出发时间,以极小化相应的时间目标与运输费用的加权和。研究了排序理论中主要的两个目标函数,分析了问题的复杂性,对于这些问题给出了它们的最优算法。     

基于多技能多渠道变成本的物流联络中心排班

物流联络中心的人力成本随着坐席拥有的技能、服务渠道的多少以及服务时段的不同而不同,对人员进行合理班次设计以节省人力成本尤为必要。考虑现实联络中心工作时间的连续与中断、技能组和渠道组的匹配等,提出采用分阶段法优化班次。首先给出不考虑时间中断的坐席的排班模型A,求得排班方案;接下来,在此基础上将中断时间约束加入,建立模型B,求得班次覆盖矩阵;最后加入排班调整约束,建立模型C,对多技能组中各渠道组进行调整,给出最符合实际情况的最优排班调整方案。数值实验结合物流企业实例和各方案的比较,验证了模型的有效性。该方法为联络中心排班提供了新思路,对其它服务行业的排班也具有一定的参考价值。     

Bayesian reliability demonstration with multiple independent tasks

^** Corresponding author. Email: frank.coolen{at}durham.ac.uk We consider optimal testing of a system in order to demonstratereliability with regard to its use in a process after testing,where the system has to function for different types of tasks,which we assume to be independent. We explicitly assume thattesting reveals zero failures. The optimal numbers of tasksto be tested are derived by optimisation of a cost criterion,taking into account the costs of testing and the costs of failuresin the process after testing, assuming that such failures arenot catastrophic to the system. Cost and time constraints ontesting are also included in the analysis. We focus on studyof the optimal numbers of tests for different types of tasks,depending on the arrival rate of tasks in the process and thecosts involved. We briefly compare the results of this studywith optimal test numbers in a similar setting, but with analternative optimality criterion which is more suitable in caseof catastrophic failures, as presented elsewhere. For thesetwo different optimality criteria, the optimal numbers to betested depend similarly on the costs of testing per type andon the arrival rates of tasks in the process after testing.     

Group sequential comparison of two binomial proportions under ranked set sampling design

Ranked set sampling (RSS) is a technique for incorporating auxiliary (concomitant) information into estimation and testing procedures right at the design stage. In this paper, we propose group sequential testing procedures for comparing two treatments with binary outcomes under an RSS scheme with perfect ranking. We compare the power, the average sample sizes and type I errors of the proposed tests to those of the group sequential tests based on simple random sampling schemes. We illustrate the usefulness of the methodology by using data from a clinical trial on leukemia.     

随机环境下基于成本经济的项目调度权衡优化研究

针对随机环境下项目前摄性调度与反应性调度在应对不确定因素过程中起到的不同作用,从成本经济角度出发,研究了如何通过两种调度方法的权衡实现项目计划与执行的最优配合。在此基础上构建了基于成本的前摄反应调度权衡模型,通过对鲁棒性成本与调整成本进行量化分析,实现两种调度方案的最佳权衡。考虑到问题的NP难属性,设计了基于混合变邻域禁忌搜索的随机两点启发式算法,并通过大规模算例测试验证了算法的有效性。结果表明,根据承包商对成本的敏感度,前摄性调度与反应性调度在应对不确定性因素干扰中承担的工作量会随着成本权衡比的变化而发生改变,逐渐从前摄性方法为主过渡到以反应性方法为主。最后,从项目管理角度给出了有价值的管理启示。     

Scheduling and lot sizing models for the single-vendor multi-buyer problem under consignment stock partnership

We consider a centralized supply chain composed of a single vendor serving multiple buyers and operating under consignment stock arrangement. Solving the general problem is hard as it requires finding optimal delivery schedule to the buyers and optimal production lot sizes. We first provide a nonlinear mixed integer programming formulation for the general scheduling and lot sizing problem. We show that the problem is NP-hard in general. We reformulate the problem under the assumption of ‘zero-switch rule’. We also provide a simple sequence independent lower bound to the solution of the general model. We then propose a heuristic procedure to generate a near-optimal delivery schedule. We assess the cost performance of that heuristic by conducting sensitivity analysis on the key model parameters. The results show that the proposed heuristic promises substantial supply-chain cost savings that increase as the number of buyers increases.     

Optimal maintenance scheduling for a complex manufacturing system subject to deterioration

We address the problem of determining inspection strategy and replacement policy for a deteriorating complex multi-component manufacturing system whose state is partially observable. We develop inspection and replacement scheduling models and other simple maintenance scheduling models via employing an imperfect repair model coupled with a damage process induced by operational conditions. The system state in performance of the imperfectly repaired system is modelled using a proportional intensity model incorporating a damage process and a virtual age process caused by repair. The system is monitored at periodic times and maintenance actions are carried out in response to the observed system state. Decisions to perform imperfect repair and replacement are based on the system state and crossing of a replacement threshold. The model proposed here aims at joint determination of a cost-optimal inspection and replacement policy along with an optimal level of maintenance which result in low maintenance cost and high operational performance and reliability of the system. To demonstrate the use of the model in practical applications a numerical example is provided. Solutions to optimal system parameters are obtained and the response of the model to these parameters is examined. Finally some features of the model are demonstrated. The approach presented provides a framework so that different scenario can be explored.