Hierarchical stochastic production planning for the highest business benefit

This paper addresses the hierarchical stochastic production planning (HSPP) problem of flexible automated workshops (FAWs), each with a number of flexible manufacturing systems (FMSs) the part-transfer between which is a delay of a time period. The problem not only includes uncertainties in the demand, capacities, material supply, processing times, necessity for rework, and scrap, but also considers multiple products and multiple time periods. The objective is to develop a production plan which tells each FMS how many parts to produce and when to produce them so as to obtain the highest business benefit. Herein, the HSPP problem is formulated by a stochastic nonlinear programming model whose constraints are linear but whose objective function is piecewise linear. For the convenience of solving the stochastic nonlinear programming model above, it is approximately transformed into a deterministic nonlinear programming model and further into a linear programming model. Because the scale of the model for a general workshop is too large to be solved by the simplex method on a personal computer within acceptable time, Karmarkar's algorithm and an interaction/prediction algorithm, respectively, are used to solve the model, the former for the medium or small scale problems and the latter for the large scale problems. By the implementation of the above-mentioned algorithms and through many HSPP examples, Karmarkar's algorithm, the interaction/prediction algorithm and the linear programming method in Matlab 5.0 are compared, the result of which shows that the proposed approaches are very effective and suitable for not only “push” production but also “pull” production.     

A stochastic model for the analysis of a two-machine flexible manufacturing cell

This paper presents a stochastic model to determine the performance of a flexible manufacturing cell (FMC) under variable operational conditions, including random machining times, random loading and unloading times, and random pallet transfer times. The FMC under study consists of two machines, pallet handling system, and a loading/unloading robot. After delivering the blanks by the pallet to the cell, the robot loads the first machine followed by the second. Unloading of a part starts with the machine that finishes its part first, followed by the next machine. When the machining of all parts on the pallet is completed, the handling system moves the pallet with finished parts out and brings in a new pallet with blanks. A model with these characteristics turns out to be a Markov chain with a transition matrix of size 5n+3, where n is the number of parts on the pallet. In this paper, we present exact numerical solutions and economic analysis to evaluate FMC systems, to determine optimal pallet capacity and robot speed that minimize total FMC cost per unit of production.     

最优递阶随机生产计划与控制

研究了敏捷制造车间(AMW)中的最优递阶随机生产计划与控制问题.首先根据实际需要建立关联方程有延迟的车间生产的随机非线性规划模型,即一种求解动态优化问题的静态优化模型.为求解方便将其转化成确定非线性规划模型并通过引进约束进一步转化成线性规划模型.然后,提出分别用卡马卡算法和基于卡马卡算法的关联预测法进行求解,并编制了相应软件.算例研究表明所提方法是非常有效的.     

Hierarchical production planning for complex manufacturing systems

A hierarchical approach to production planning for complex manufacturing systems is presented. A single facility comprising a number of work-centers that produce multiple part types is considered. The planning horizon includes a sequence of time periods, and the demand for all part types is assumed known. The production planning problem consists of minimizing the holding costs for all part types, as well as the work-in-process and the backlogging costs for the end items. We present a two-level hierarchy that is based on aggregating parts to part families, work-centers to manufacturing cells and time periods to aggregate time periods. The solution at the aggregate level is imposed as a constraint to the detailed level problems which are formulated for each manufacturing cell separately. This architecture uses a rolling horizon strategy to perform the production management function. We have employed perturbation analysis techniques to adjust certain parameters of the optimization problems at the detailed level to reach a near-optimal detailed production plan. Numerical results for several realistic example problems are presented and the solutions obtained from the hierarchical and monolithic approaches are compared. The results indicate that the hierarchical approach offers major advantages in computational efficiency, while the loss of optimality is acceptable.     

A robust hierarchical production planning for a capacitated two-stage production system

In this paper, we propose a robust hierarchical production planning approach for a two-stage real world capacitated production system operating in an uncertain environment. The first stage of the system produces a set of semi-finished products having relatively stable annual demands, and the second finishing stage produces finished products having highly variable weekly demands. The fixed production setup costs incurred at the first stage are considerably high. Fixed production setup costs incurred at the second stage are fairly small compared to those of the first stage. We propose an integrated hierarchical planning model, where semi-finished products from the first stage (i.e. the aggregate level) are disaggregated into finished products to be produced in the second stage (i.e. the operational level). As a result of the relatively stable demands and the high setup costs experienced at the first stage, a cyclical aggregate planning model is proposed for production planning at the upper level of the hierarchical plan. Based on this aggregate plan, a modified periodic review policy is then proposed for production planning at the lower level. Finally, a coupling plan, linking the two planning levels, is proposed to ensure the feasibility of the disaggregation process at every period.     

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.     

柔性自动化车间生产计划的最优分解

研究了柔性自动化车间生产计划的最优分解问题,首先根据实际需要建立车间生产计划的非线性规划模型,然后为求解方便将其转化成线性规划模型,由于这种模型对于一般车间来讲其规模已经很大,很难在微机上用单纯形法求争,为此,提出分别用卡马卡算法和一种新的基于卡马卡算法的关联预测法来求解车间生产计划的最优分解问题,并编制了相应软件,最后通过算例研究,比较了卡马卡算法、基于卡马卡算法的关联预测法和Matlab中的线性规划法,结果表明所提方法是非常有效的。     

Hierarchical multi-agent planning for flexible assembly of large-scale lunar facilities

Several national space agencies and commercial aerospace companies plan to set up lunar bases with large-scale facilities that rely on multiple lunar robots’ assembly. Mission planning is necessary to achieve efficient multi-robot cooperation. This paper aims at autonomous multi-robot planning for the flexible assembly of the large-scale lunar facility, considering the harsh lunar environment, mission time optimization, and joint actions. The lunar robots and modules are scattered around the mission area without fixed assembly lines. Thus, the traditional assembly planning methods ignoring the optimal selection of modules are unable to handle this problem. We propose a hierarchical multi-agent planning method based on two-stage two-sided matching (HMAP-TTM) to solve this critical problem. First, the distributed planning framework with multi-replica public agents is introduced, ensuring robot plan knowledge consistency through public agents’ communication. Second, the hierarchical task graph (HTG) divides the mission into task layers based on task dependency knowledge. Third, we develop a novel two-stage two-sided matching algorithm. Time-optimal plans emerge from the matching games among public and private agents in each layer of HTG. Agents make decisions in the game based on action knowledge updated during planning. Finally, an assembly mission is presented to prove the method’s effectiveness. The simulation results show that the HMAP-TTM can generate plans with shorter mission time and require smaller communication costs than the baseline methods.     

面向大规模定制的柔性生产计划研究

针对大规模定制条件下传统生产计划在主生产计划、产品结构管理和生产计划过程三个方面柔性不足的问题,应用模块化方法构建了双层柔性主生产计划、产品族结构模型和"PUSH/PULL"结合的生产计划过程模型,在此基础上,构建了柔性的生产计划体系结构。通过实证分析,验证了该体系结构可实现快速响应大规模定制下产品多样化的需求。     

需求随机的变质性产品生产计划模型

研究了能力约束的有限计划展望期生产计划问题,各周期的需求随机,库存产品存在变质且变质率为常数。建立了问题的期望值模型,目标函数为极小化生产准备成本、生产成本、库存成本的期望值。提出了随机模拟、遗传算法和启发式算法相结合的求解算法。用数值实例对模型和算法进行了验证,优化结果表明模型和算法是有效的。     

面向柔性制造车间的多目标RFID网络规划方法

针对具有多种覆盖需求的柔性制造车间RFID网络规划问题,以部署成本、阅读器干扰与阅读器效能为多优化目标,提出一种分层聚类、冗余消减与梯度下降方法集成的RFID网络规划方法,采用分层聚类算法确定RFID初始数量与部署位置,采用冗余阅读器消减算法优化RFID数量,采用梯度下降算法优化RFID部署位置从而实现网络规划多目标优化。实验研究表明,提出的方法在多目标综合性能方面优于传统基于分层聚类方法、遗传算法、粒子群与冗余消减混合方法的RFID网络规划方法,验证了该方法的有效性。     

An algorithm for production planning in a flexible production system

In this paper, we consider the problem of determining the production rate, production batch size, and production sequence when production rate, setup cost, and unit processing cost are sequence-dependent. Using a standard lot sizing model with backorder, a tabu search algorithm for solving this problem is proposed. The algorithm is tested on some random test problems and its performance is compared with random sequencing. Computational results show that the proposed algorithm is very efficient.     

Multi-objective supply planning for two-level assembly systems with stochastic lead times

This paper considers two-level assembly systems whose lead times of components are stochastic with known discrete random distributions. In such a system, supply planning requires determination of release dates of components at level 2 in order to minimize expected holding cost and to maximize customer service. Hnaien et al. [Hnaien F, Delorme X, Dolgui A. Multi-objective optimization for inventory control in two-level assembly systems under uncertainty of lead times. Computers and Operations Research 2010; 37:1835-43] have recently examined this problem, trying to solve it through multi-objective genetic algorithms. However, some reconsideration in their paper is unavoidable. The main problem with Hnaien et al. proposal is their wrong mathematical model. In addition, the proposed algorithms do not work properly in large-scale instances. In the current paper, this model is corrected and solved via a new approach based on NSGA-II that is called Guided NSGA-II. This approach tries to guide search toward preferable regions in the solution space. According to the statistical analyses, the guided NSGA-II has the higher performance in comparison with the basic NSGA-II used by Hnaien et al. Moreover, the wrongly reported characteristics of the Pareto front shape provided by Hnaien et al. are modified.     

A hierarchic approach to production planning and scheduling of a flexible manufacturing system

The paper deals with the problem of improving the machine utilization of a flexible manufacturing cell. Limited tool magazine space of the machines turns out to be a relevant bottleneck. A hierarchic approach for this problem is proposed. At the upper level, sets of parts that can be concurrently processed (batches) are determined. At the lower levels, batches are sequenced, linked, and scheduled. Methods taken from the literature are used for the solution of the latter subproblems, and an original mixed integer programming model is formulated to determine batches. The proposed methods are discussed on the basis of computational experience carried out on real instances.     

On stochastic dynamic programming for solving large-scale planning problems under uncertainty

The stochastic dynamic programming approach outlined here, makes use of the scenario tree in a back-to-front scheme. The multi-period stochastic problems, related to the subtrees whose root nodes are the starting nodes (i.e., scenario groups), are solved at each given stage along the time horizon. Each subproblem considers the effect of the stochasticity of the uncertain parameters from the periods of the given stage, by using curves that estimate the expected future value (EFV) of the objective function. Each subproblem is solved for a set of reference levels of the variables that also have nonzero elements in any of the previous stages besides the given stage. An appropriate sensitivity analysis of the objective function for each reference level of the linking variables allows us to estimate the EFV curves applicable to the scenario groups from the previous stages, until the curves for the first stage have been computed. An application of the scheme to the problem of production planning with logical constraints is presented. The aim of the problem consists of obtaining the planning of tactical production over the scenarios along the time horizon. The expected total cost is minimized to satisfy the product demand. Some computational experience is reported. The proposed approach compares favorably with a state-of-the-art optimization engine in instances on a very large scale.     

A stochastic algorithm for makespan minimized multi-agent path planning in discrete space

Makespan minimized multi-agent path planning (MAPP) requires the minimization of the time taken by the slowest agents to reach its destination. The resulting minimax objective function is non-smooth and the search for an optimal solution in MAPP can be intractable. In this work, a maximum entropy function is adopted to approximate the minimax objective function. An iterative algorithm named probabilistic iterative makespan minimization (PIMM) is then proposed to approximate a makespan minimized MAPP solution by solving a sequence of computationally hard MAPP minimization problems with a linear objective function. At each iteration, a novel local search algorithm called probabilistic iterative path coordination (PIPC) is used to find a sufficiently good solution for each MAPP minimization problem. Experimental results from comparative studies with existing MAPP algorithms show that the proposed algorithm strikes a good tradeoff between the quality of the makespan minimized solution and the computational cost incurred.     

Analytical study on multi-product production planning with outsourcing

This paper studies a problem on multi-product capacitated production planning with outsourcing. The context of the problem is about an enterprise that manufactures multiple products in multiple periods for stochastic demands. Manufacturers usually have two alternative modes for the production: one is to outsource parts from outside suppliers and then assemble them; the other is to in-house manufacture parts and then assemble them. Each mode has its relative merits. In addition, the capacity constraint by in-house manufacturing is also taken into account. This paper investigates how to balance the trade-off between the two modes. An analytical approach is proposed to study the optimal decision on the above two modes for all products during each planning period. Some findings are drawn out from this analytical study. Numerical experiments show the significant cost reduction can be obtained using the proposed decision model.     

钢铁企业年度生产计划的研究

针对多分厂、多机型的钢铁企业年度生产计划问题,建立一个以提高经济效益为目的,包含生产工艺、资源和能力等约束的多层递阶优化数学模型,并研究了模型的算法．该算法首先从产品结构的角度将多层问题转换为两层模型,然后对此两层模型利用遗传算法和二阶段法进行求解．仿真结果表明了该模型和算法的有效性和可行性．     

An enhanced genetic algorithm for automated assembly planning

Automated assembly planning reduces manufacturing manpower requirements and helps simplify product assembly planning, by clearly defining input data, and input data format, needed to complete an assembly plan. In addition, automation provides the computational power needed to find optimal or near-optimal assembly plans, even for complex mechanical products. As a result, modern manufacturing systems use, to an ever greater extent, automated assembly planning rather than technician-scheduled assembly planning. Thus, many current research reports describe efforts to develop more efficient automated assembly planning algorithms. Genetic algorithms show particular promise for automated assembly planning. As a result, several recent research reports present assembly planners based upon traditional genetic algorithms. Although prior genetic assembly planners find improved assembly plans with some success, they also tend to converge prematurely at local-optimal solutions. Thus, we present an assembly planner, based upon an enhanced genetic algorithm, that demonstrates improved searching characteristics over an assembly planner based upon a traditional genetic algorithm. In particular, our planner finds optimal or near-optimal solutions more reliably and more quickly than an assembly planner that uses a traditional genetic algorithm.     

A robust dynamic planning strategy for lot-sizing problems with stochastic demands

We consider the question of generating robust plans for production planning problems under uncertainty. In particular, we present an alternative approach to generate robust solutions for lot-sizing problems with stochastic demand. The proposed approach is dynamic and includes a decision rule that guides the planner. The decision rule parameters are determined so that the number of expected planning adaptations and their magnitudes are under control. The robust approach and its related models are presented together with some computational results to show how it performs compared to other approaches.