Optimal production run length with imperfect production processes and backorder in fuzzy random environment

This article considers the economic production run time problem with imperfect production processes and allowable shortages. The elapsed time until the production process shifts is assumed to be a fuzzy random variable, and fuzzy random total cost per unit time model is constructed. The expectation theory and signed distance are employed to transform the fuzzy random model into crisp model. An effective approximate algorithm is developed to search for the optimal production run length. Furthermore, numerical examples are provided to illustrate the results of proposed model.     

考虑机器故障的串行生产系统控制策略优化

针对多级串行生产系统,考虑存在机器故障和随机需求,对生产及雇佣的控制策略进行研究。以最小平均总成本为目标,建立基于（Q,r）库存策略的优化模型;鉴于求解复杂性,提出一种改进的网格自适应直接搜索算法（MADS-GA）,为避免陷入局部最优和提高收敛速度,算法中加入了停滞阻止策略;对研究实例进行求解,并与已有算法比较。结果表明,所提出的算法收敛速度和寻优能力更优,能有效优化串行生产系统的控制策略,降低平均总成本。     

Multi-objective imperfect maintenance optimization for production system with an intermediate buffer

In several production systems, buffer stocks are built between consecutive machines to ensure the continuity of supply during interruptions of service caused by breakdowns or planned maintenance actions. However, in previous research, maintenance planning is performed individually without considering buffer stocks. In order to balance the trade-offs between them, in this study, an integrated model of buffer stocks and imperfective preventive maintenance for a production system is proposed. This paper considers a repairable machine subject to random failure for a production system by considering buffer stocks. First, the random failure rate of a machine becomes larger with the increase of the number of random failures. Thus, the renewal process is used to describe the number of random failures. Then, by considering the imperfect maintenance action reduced the age of the machine partially, a mathematical model is developed in order to determine the optimal values of the two decision variables which characterize the proposed maintenance strategy and which are: the size of the buffer stock and the maintenance interval. The optimal values are those which minimize the average total cost per time unit including maintenance cost, inventory holding cost and shortage cost, and satisfy the availability constraint. Finally, a heuristic procedure is used to solve the proposed model, and one experiment is used to evaluate the performance of the proposed methods for joint optimization between buffer stocks and maintenance policy. The results show that the proposed methods have a better performance for the joint optimization problem and can be able to obtain a relatively good solution in a short computation time.     

Integrated production and delivery with single machine and multiple vehicles

This paper considers a class of multi-objective production–distribution scheduling problem with a single machine and multiple vehicles. The objective is to minimize the vehicle delivery cost and the total customer waiting time. It is assumed that the manufacturer’s production department has a single machine to process orders. The distribution department has multiple vehicles to deliver multiple orders to multiple customers after the orders have been processed. Since each delivery involves multiple customers, it involves a vehicle routing problem. Most previous research work attempts at tackling this problem focus on single-objective optimization system. This paper builds a multi-objective mathematical model for the problem. Through deep analysis, this paper proposes that for each non-dominated solution in the Pareto solution set, the orders in the same delivery batch are processed contiguously and their processing order is immaterial. Thus we can view the orders in the same delivery batch as a block. The blocks should be processed in ascending order of the values of their average workload. All the analysis results are embedded into a non-dominated genetic algorithm with the elite strategy (PD-NSGA-II). The performance of the algorithm is tested through random data. It is shown that the proposed algorithm can offer high-quality solutions in reasonable time.     

Analysis of optimal production and advertising policies

In this paper, the joint production and advertising control model proposed by Parlar is extended to include a time dependent depreciation rate of goodwill (sales), the salvage value of inventory unsold, and the salvage value of goodwill. For an arbitrary form for the production cost function, necessary conditions for optimal production and advertising rates are obtained using the maximum principle. For specific forms (quadratic and linear) for the production cost function, optimal production and advertising policies are investigated. In addition, the solution technique used by Parlar to deal with the pure state inequality constraint is shown to be incorrect, and thus correct analyses to the problem are presented. An algorithm is developed to solve the necessary conditions and numerical examples are presented to illustrate the solution     

Analysis of a dynamic lot‐sizing problem with production capacity constraint

We study a capacitated dynamic lot‐sizing problem with special cost structure involving setup cost, freight cost, production cost, and inventory holding cost. We investigate two cases of the problem categorized by whether the maximal production capacity in one period is an integral multiple of the capacity of a container and reveal the special structure of an optimal solution for each case. In the case where the maximal production capacity is an integral multiple of a container's capacity, the T‐period problem is solved using polynomial effort by a network algorithm. For the other case, the problem is transformed into a shortest path problem, and a network‐based algorithm combining dynamic programming is proposed to solve it in polynomial time. Numerical examples are presented to illustrate application of the algorithms to solve the two cases of the problem.     

An enhanced model for the integrated production and transportation problem in a multiple vehicles environment

Solving an integrated production and transportation problem (IPTP) is a very challenging task in semiconductor manufacturing with turnkey service. A wafer fabricator needs to coordinate with outsourcing factories in the processes including circuit probing testing, integrated circuit assembly, and final testing for buyers. The jobs are clustered by their product types, and they must be processed by groups of outsourcing factories in various stages in the manufacturing process. Furthermore, the job production cost depends on various product types and different outsourcing factories. Since the IPTP involves constraints on job clusters, job-cluster dependent production cost, factory setup cost, process capabilities, and transportation cost with multiple vehicles, it is very difficult to solve when the problem size becomes large. Therefore, heuristic tools may be necessary to solve the problem. In this paper, we first formulate the IPTP as a mixed integer linear programming problem to minimize the total production and transportation cost. An efficient genetic algorithm (GA) is proposed next to tackle the problem when it becomes too complicated. The objectives are to minimize total costs, where the costs include production cost and transportation cost, under the environment with backup capacities and multiple vehicles, and to determine an appropriate production and distribution plan. The results demonstrate that the proposed GA model is an effective and accurate tool.     

Robust planning in optimization for production system subject to random machine breakdown and failure in rework

This study is concerned with robust planning in optimization, specifically in determining the optimal run time for production system that is subject to random breakdowns under abort/resume (AR) control policy and failure in rework. In most real-life production processes, generation of defective items and breakdowns of manufacturing equipment are inevitable. In this study, random defective rate is assumed and all manufactured items are screened. The perfect quality, reworkable and scrap items are identified and separated; failure-in-rework is assumed. The system is also subject to random machine breakdown; and when it occurs, the AR policy is adopted. Under such policy, the production of the interrupted lot will be immediately resumed when the machine is restored. Mathematical modeling and derivation of the production-inventory cost functions for both systems with/without breakdowns are presented. The renewal reward theorem is used to cope with the variable cycle length when integrating cost functions. The long-run average cost per unit time is obtained. Theorems on convexity and on bounds of production run time are proposed and proved. A recursive searching algorithm is developed for locating the optimal run time that minimizes the expected production-inventory costs. A numerical example with sensitivity analysis is provided to give insight into the optimal operational control of such an unreliable system.     

HBBA: hybrid algorithm for buffer allocation in tandem production lines

In this paper, we consider the problem of buffer space allocation for a tandem production line with unreliable machines. This problem has various formulations all aiming to answer the question: how much buffer storage to allocate between the processing stations? Many authors use the knapsack-type formulation of this problem. We investigate the problem with a broader statement. The criterion depends on the average steady-state production rate of the line and the buffer equipment acquisition cost. We evaluate black-box complexity of this problem and propose a hybrid optimization algorithm (HBBA), combining the genetic and branch-and-bound approaches. HBBA is excellent in computational time. HBBA uses a Markov model aggregation technique for goal function evaluation. Nevertheless, HBBA is more general and can be used with other production rate evaluation techniques.     

预制构件并行生产线资源配置与生产调度集成优化

并行生产线和特定工序生产资源共享模式可以显著改善客户满意度并节约成本.针对预制构件并行生产线资源配置与生产调度集成优化问题,基于分解策略和交替迭代优化思想,提出一种交替式混合果蝇-禁忌搜索算法(AHFOA＿TS)以最小化拖期惩罚费用.首先,通过快速启发式方法产生一较好初始解;然后,固定资源配置方案,为提高算法局部搜索能力,通过集成多种局部搜索方式,设计一种离散果蝇优化算法优化订单指派及调度方案;最后,固定订单指派及调度方案,为减少无效搜索次数,设计一种基于双层变异算子和精英劣解交叉策略的混合禁忌搜索算法以优化资源配置方案,如此两个阶段交替运行直至满足终止条件.此外,设计4种基于交替搜索框架的智能优化算法用于比较.计算结果表明, AHFOA＿TS算法能够更有效求解预制构件生产线资源配置和生产调度集成优化问题.     

A stochastic production planning problem with nonlinear cost

Most production planning models are deterministic and often assume a linear relation between production volume and production cost. In this paper, we investigate a production planning problem in a steel production process considering the energy consumption cost which is a nonlinear function of the production quantity. Due to the uncertain environment, the production demands are stochastic. Taking a scenario-based approach to express the stochastic demands according to the knowledge of planners on the demand distributions, we formulate the stochastic production planning problem as a mixed integer nonlinear programming (MINLP) model.Approximated with the piecewise linear functions, the MINLP model is transformed into a mixed integer linear programming model. The approximation error can be improved by adjusting the linearization ranges repeatedly. Based on the piecewise linearization, a stepwise Lagrangian relaxation (SLR) heuristic for the problem is proposed where variable splitting is introduced during Lagrangian relaxation (LR). After decomposition, one subproblem is solved by linear programming and the other is solved by an effective polynomial time algorithm. The SLR heuristic is tested on a large set of problem instances and the results show that the algorithm generates solutions very close to optimums in an acceptable time. The impact of demand uncertainty on the solution is studied by a computational discussion on scenario generation.     

An optimization algorithm for production systems

As the scale of rule-based expert systems increases, the efficiency of production systems becomes a pressing concern. Recently developed production systems thus enable users to specify an appropriate ordering or clustering of join operations. Various efficiency heuristics have been introduced to optimize production rules manually. However, since the heuristics often conflict With each other, users have to proceed by trial and error. The problem addressed in this paper is how to automatically determine efficient join structures for production system programs. Our algorithm does not directly apply efficiency heuristics to programs, but rather enumerates possible join structures under various constraints and selects the best one. For this purpose, the cost model for production systems is introduced to estimate the run-time cost of join operations. Evaluation results demonstrate that the proposed algorithm can generate programs that are as efficient as those obtained by manual optimization, and thus can reduce the burden of manual optimization     

A hybrid ant colony algorithm for U-line balancing and rebalancing in just-in-time production environment

U-line balancing is an important problem for designing a new U-line. It is about combining a finite set of tasks to form workstations optimally with the restriction of given precedence relationships in a new U-line. As the demand varies, the U-line should be rebalanced to eliminate waste and improve the production efficiency as part of just-in-time principles. If all machines can be moved freely, the rebalancing problem equals to the balancing problem. In practice, some machines are stationary or need certain moving cost. In this paper, U-line rebalancing problem is formalized with respect to minimization the moving cost of machines and labor cost. The walking time of operators is considered to avoid generating awkward walking path. A new hybrid algorithm of ant colony optimization and filtered beam search is presented to solve the problem. The hybrid algorithm adopts the framework of ant colony optimization. In the process of constructing path, each ant explores several nodes for one step and chooses the best one by global and local evaluation at a given probability. Computational results show that the proposed algorithm performs quite effectively for solving U-line balancing problems in the literature by comparing to the existing solutions. Finally, the proposed algorithm for solving U-line rebalancing problem is demonstrated with an example and also yields optimal solutions.     

考虑中间库存缓冲区的设备不完美预防维修策略研究

针对带有库存缓冲区的设备维修问题,提出了随机故障设备的不完美预防维修策略。首先,考虑设备随机故障率随故障次数的增多而变大的情况,基于准更新过程,建立随机故障设备的故障次数表达式。其次,结合设备故障次数表达式,综合考虑维修成本和库存缓冲成本的基础上,构建了设备生产成本模型,以缓冲库存量和预防维修周期为自变量,以生产成本为目标函数。获得设备的最优维修策略和最佳库存缓冲量。最后,通过算例分析验证了模型的有效性,为生产线设计的可行性提供了依据。     

Dynamic joint pricing and production policy for perishable products

A joint dynamic pricing and production problem for perishable products without shortages is considered. The demand rate is price‐dependent and time‐varying. This paper constructs an optimal control model to maximize the total profit under a general nonlinear production cost function. The feature of the optimal joint dynamic pricing and production policy is analyzed by solving the corresponding optimal control problem on the basis of improved Pontryagin's maximum principle. Then, an effective algorithm is designed to obtain the optimal joint policy. The case of the joint static optimal policy is also investigated and compared with the dynamic one. Finally, numerical examples are presented to illustrate the effectiveness of the proposed methods, and some managerial implications are provided for the management of perishable items.     

Analysis of a multicriterial buffer capacity optimization problem for a production line

We consider a multicriterial optimization problem for volumes of buffers in a production line. We assume that the line has a series-parallel structure, and during its operation equipment stops occur due to failures, stops that are random in the moments when they arise and in their durations. The volumes of buffers are integer-valued and bounded from above. As criteria we consider the average production rate of the line, capital costs for installing buffers, and the inventory cost for intermediate products. To approximate the Pareto optimal set we use evolutionary algorithms SIBEA and SEMO. Problems with larger dimension experimentally support the advantage of the modified SEMO algorithm with respect to the hypervolume of the resulting set of points.     

Hierarchical stochastic production planning for flexible automation workshops

This paper presents the hierarchical stochastic production planning (HSPP) problem for flexible automation workshops (FAWs) in agile manufacturing environments, which is a multiple-period multiple-product problem with random material supply, demands, capacities, processing times, rework and waste products. To solve the HSPP problem, a mathematical model is built up first. Then, an algorithm for HSPP is deduced in detail by using a stochastic interaction/prediction approach. The corresponding software package named as stochastic interaction/prediction algorithm (SIPA) has been developed and is presented in this paper, through which examples of HSPP have been studied, and which show that the algorithm can optimally decompose medium-term random product demand plans of an FAW into short-term stochastic production plans to be executed by FMSs in the FAW. Finally, the application of the algorithm is presented in detail through one of those examples.     

Hybrid approach for buffer allocation in open serial production lines

The buffer allocation problem is an NP-hard combinatorial optimization problem involving the determination of the number of buffers in buffer locations required to increase the efficiency of a production line. Researchers in this field have proposed various optimization techniques to solve the problem for different types of production system configurations. In this study, a hybrid approach-based simulation optimization is proposed to determine the buffer sizes required in open serial production lines to maximize the average production rate of the system. This approach involves the use of a search tool and an evaluative tool. A hybrid approach using a genetic algorithm and simulated annealing is used as a search tool to create candidate buffer sizes. As an evaluative tool, discrete event simulation modeling is used to obtain the average production rate of the line. The performance of the proposed approach and the power of the hybridization are investigated for various serial line configurations. Promising results demonstrate the efficacy of the proposed hybrid approach for the buffer allocation problem in open serial lines.     

设备故障条件下柔性作业车间重调度方法

设备故障是生产实践中最为常见的一类不确定事件,它易对正常的生产计划造成影响。为了有效应对生产中的设备随机故障干扰,对设备随机故障条件下的柔性作业车间调度问题进行了研究,提出了一种基于组合策略的重调度方法。在重调度方法中,对重调度成本进行了系统分析并建立了重调度成本函数,设计了两种重调度策略,并结合免疫算法对遗传算法进行了改进,用于模型的求解计算。通过算例分析,验证了方法的可行性和有效性。实验结果表明,所提出方法能够更好地处理多种情况下的设备故障扰动。     

Random gradient-free method for online distributed optimization with strongly pseudoconvex cost functions

This paper focuses on the online distributed optimization problem based on multi-agent systems. In this problem, each agent can only access its own cost function and a convex set, and can only exchange local state information with its current neighbors through a time-varying digraph. In addition, the agents do not have access to the information about the current cost functions until decisions are made. Different from most existing works on online distributed optimization, here we consider the case where the cost functions are strongly pseudoconvex and real gradients of the cost functions are not available. To handle this problem, a random gradient-free online distributed algorithm involving the multi-point gradient estimator is proposed. Of particular interest is that under the proposed algorithm, each agent only uses the estimation information of gradients instead of the real gradient information to make decisions. The dynamic regret is employed to measure the proposed algorithm. We prove that if the cumulative deviation of the minimizer sequence grows within a certain rate, then the expectation of dynamic regret increases sublinearly. Finally, a simulation example is given to corroborate the validity of our results.