Managing disruption in an imperfect production–inventory system

In this paper, a disruption recovery model is developed for an imperfect single-stage production–inventory system. For it, the system may unexpectedly face either a single disruption or a mix of multiple dependent and/or independent disruptions. The system is usually run according to a user defined production–inventory policy. We have formulated a mathematical model for rescheduling the production plan, after the occurrence of a single disruption, which maximizes the total profit during the recovery time window. The model thereby generates a revised plan after the occurrence of the disruption. The mathematical model, developed for a single disruption, is solved by using both a pattern search and a genetic algorithm, and the results are compared using a good number of randomly generated disruption test problems. We also consider multiple disruptions, that occur one after another as a series, for which a new occurrence may or may not affect the revised plan of earlier occurrences. We have developed a new dynamic solution approach that is capable of dealing with multiple disruptions on a real-time basis. Some numerical examples and a set of sensitivity analysis are presented to explain the usefulness and benefits of the developed model. The proposed quantitative approach helps decision makers to make prompt and accurate decisions for managing disruption.     

Training and testing a self-adaptive multi-operator evolutionary algorithm for constrained optimization

Over the last two decades, many different evolutionary algorithms (EAs) have been introduced for solving constrained optimization problems (COPs). Due to the variability of the characteristics in different COPs, no single algorithm performs consistently over a range of practical problems. To design and refine an algorithm, numerous trial-and-error runs are often performed in order to choose a suitable search operator and the parameters. However, even by trial-and-error, one may not find an appropriate search operator and parameters. In this paper, we have applied the concept of training and testing with a self-adaptive multi-operator based evolutionary algorithm to find suitable parameters. The training and testing sets are decided based on the mathematical properties of 60 problems from two well-known specialized benchmark test sets. The experimental results provide interesting insights and a new way of choosing parameters.     

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.     

考虑缺货的模糊随机缺陷生产系统

针对不可靠的生产过程,研究了生产故障时间为模糊随机变量且允许缺货的缺陷生产系统.建立含缺货费和模糊随机重修费的经济生产批量模型.基于可信性理论,建立其期望费用模型,揭示了费用函数的性质,并证明了使费用最小的最优生产时间的存在性和唯一性,从而确定了最优生产时间的上下界.基于此,设计了最优生产时间的二分法求解过程.最后通过算例验证了所提出模型的有效性,并分析了缺货费用、重修费用和缺陷产品比例对最优生产策略的影响.     

Multi-operator based evolutionary algorithms for solving constrained optimization problems

Over the last two decades, many sophisticated evolutionary algorithms have been introduced for solving constrained optimization problems. Due to the variability of characteristics in different COPs, no single algorithm performs consistently over a range of problems. In this paper, for a better coverage of the problem characteristics, we introduce an algorithm framework that uses multiple search operators in each generation. The appropriate mix of the search operators, for any given problem, is determined adaptively. The framework is tested by implementing two different algorithms. The performance of the algorithms is judged by solving 60 test instances taken from two constrained optimization benchmark sets from specialized literature. The first algorithm, which is a multi-operator based genetic algorithm (GA), shows a significant improvement over different versions of GA (each with a single one of these operators). The second algorithm, using differential evolution (DE), also confirms the benefit of the multi-operator algorithm by providing better and consistent solutions. The overall results demonstrated that both GA and DE based algorithms show competitive, if not better, performance as compared to the state of the art algorithms.     

A mathematical model on EPQ for stochastic demand in an imperfect production system

In the paper, we develop an EPQ (economic production quantity) inventory model to determine the optimal buffer inventory for stochastic demand in the market during preventive maintenance or repair of a manufacturing facility with an EPQ (economic production quantity) model in an imperfect production system. Preventive maintenance, an essential element of the just-in-time structure, may cause shortage which is reduced by buffer inventory. The products are sold with the free minimal repair warranty (FRW) policy. The production system may undergo “out-of-control” state from “in-control” state, after a certain time that follows a probability density function. The defective (non-conforming) items in “in-control” or “out-of-control” state are reworked at a cost just after the regular production time. Finally, an expected cost function regarding the inventory cost, unit production cost, preventive maintenance cost and shortage cost is minimized analytically. We develop another case where the buffer inventory as well as the production rate are decision variables and the expected unit cost considering the above cost functions is optimized also. The numerical examples are provided to illustrate the behaviour and application of the model. Sensitivity analysis of the model with respect to key parameters of the system is carried out.     

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.     

Derivative and GA-based methods in metamodeling of back-propagation neural networks for constrained approximate optimization

Artificial neural networks (ANN) have been extensively used as global approximation tools in the context of approximate optimization. ANN traditionally minimizes the absolute difference between target outputs and approximate outputs thereby resulting in approximate optimal solutions being sometimes actually infeasible when it is used as a metamodel for inequality constraint functions. The paper explores the development of the efficient back-propagation neural network (BPN)-based metamodel that ensures the constraint feasibility of approximate optimal solution. The BPN architecture is optimized via two approaches of both derivative-based method and genetic algorithm (GA) to determine interconnection weights between layers in the network. The verification of the proposed approach is examined by adopting a standard ten-bar truss problem. Finally, a GA-based approximate optimization of suspension with an optical flying head is conducted to enhance the shock resistance capability in addition to dynamic characteristics.     

Modeling and analysis for multi-period, multi-product and multi-resource production scheduling

This study presents a framework for solving the multi-period, multi-product and multi-resource production-scheduling (M³PS) problem. Practically, the main concern for an M³PS problem is how to satisfy two management policies: (1) each product is manufactured in a continuous manner so that once the product is on a production line, it will complete its production procedure without interruption, and (2) the number of the product's types is limited during one period. By defining the decision variables and taking into account the machine's capacity and the customers' demand, a mixed integer programming (MIP) Model is formulated. To solve this MIP problem, a two-phase approach is proposed. In phase 1, the search space of the MIP Model is transformed into a preliminary pattern by a heuristic mining algorithm so that a hyper assignment problem can be formed as a reference model to be solved. In phase 2, a stochastic global optimization procedure that incorporates a genetic algorithm with neighborhood search techniques is designed to obtain the optimal solution. A numerical experiment is presented with an illustration, and it shows that the proposed model is adequate to cope with complicate scheduling problems.     

远程生产管理系统在钢铁厂中的应用

远程生产管理系统可以实时采集、查看生产数据。通过此系统,用户可以在线对比、分析生产线数据,判断生产线状况。本系统能够将数据保存下来,为解决问题提供了数据,节约时间,提高工作效率。     

A naive genetic approach for non-stationary constrained problems

An algorithm to be effective for solving non-stationary problems should be robust, adaptive to the changing environment and efficient. Genetic algorithms (GAs) are increasingly being used to solve non-stationary problems. We use GA with a new approach of gene induction (Bhatia and Basu in Soft Comput 8(1):1–9, 2003) to solve non-stationary constrained problems. The approach combines high value genes to form chromosomes from the initial population itself. The efficacy of the method is demonstrated on non-stationary versions of 0/1 knapsack and pure-integer programming problems. The results obtained with the approach are compared with those obtained with feedback thermodynamical genetic algorithm (FTDGA) (Mori et al. in 5th parallel problem solving from nature, number 1498 in LNCS, pp 149–157, 1998). It shows that gene-induction approach is more accurate and requires less time compared to the FTDGA.A preliminary version of the paper appeared in the proceedings of the 5th international conference on advances in pattern recognition (Basu and Bhatia 2003).     

Open pit mine production schedule optimization using a hybrid of maximum-flow and genetic algorithms

Production scheduling is a critical activity for the long-term production planning of open pit mining operations. It deals with the effective management of resources and maximizes cash flows to generate higher profits over the life of a mine. Production scheduling problems determine that blocks be mined and processed over a number of periods subjected to mining and processing constraints, which makes the problem more complex. The complexity is further increased due to the uncertainty in the input parameters. In this study, the maximum flow algorithm with a genetic algorithm is used to generate the long-term production schedule. The graph structure for maximum flow is created for multiple periods under uncertainty, and the flow in the arcs is controlled by a genetic algorithm to develop a production schedule. Numerical results for realistic instances are provided to indicate the efficiency of the solutions.     

A constrained genetic algorithm for decentralized control system structure selection and optimization

A genetic algorithm is applied to the automatic synthesis of decentralized MIMO control systems incorporating both feedback and feedforward components. The design approach relies on a robust performance objective formulation, which defines the limiting trade-off between performances of the output channels. The method is demonstrated on the synthesis of typical MIMO control systems.     

集配中心模式下供应延迟干扰管理模型

针对集配中心模式下供应延迟导致制造商生产计划难以顺利执行这一难题,运用干扰管理思想,从客户满意度、订单处理顺序和生产惩罚成本三方面衡量制造商生产系统的扰动程度,建立车间生产调度干扰管理模型,设计用于求解该类问题的改进模拟退火算法,并通过算例验证干扰管理模型及算法的有效性,使调整方案尽可能偏离初始方案最小,也就是生产系统受到的扰动最小。与重调度方法相比,该模型可以在较小的订单顺序改变和成本增加的基础上,最大限度地减少客户加权不满意度,保留重要客户,增强客户群的稳定性。     

A sharp augmented Lagrangian-based method in constrained non-convex optimization

In this paper, a novel sharp Augmented Lagrangian-based global optimization method is developed for solving constrained non-convex optimization problems. The algorithm consists of outer and inner loops. At each inner iteration, the discrete gradient method is applied to minimize the sharp augmented Lagrangian function. Depending on the solution found the algorithm stops or updates the dual variables in the inner loop, or updates the upper or lower bounds by going to the outer loop. The convergence results for the proposed method are presented. The performance of the method is demonstrated using a wide range of nonlinear smooth and non-smooth constrained optimization test problems from the literature.     

Development of hybrid evolutionary algorithms for production scheduling of hot strip mill

A hot strip mill (HSM) produces hot rolled products from steel slabs, and is one of the most important production lines in a steel plant. The aim of HSM scheduling is to construct a rolling sequence that optimizes a set of given criteria under constraints. Due to the complexity in modeling the production process and optimizing the rolling sequence, the HSM scheduling is a challenging task for hot rolling production schedulers. This paper first introduces the HSM production process and requirements, and then reviews previous research on the modeling and optimization of the HSM scheduling problem. According to the practical requirements of hot rolling production, a mathematical model is formulated to describe two important scheduling sub-tasks: (1) selecting a subset of manufacturing orders and (2) generating an optimal rolling sequence from the selected manufacturing orders. Further, hybrid evolutionary algorithms with integration of genetic algorithm (GA) and extremal optimization (EO) are proposed to solve the HSM scheduling problem. Computational results on industrial data show that the proposed HSM scheduling solution can be applied in practice to provide satisfactory performance.     

Joint optimization of product tolerance design,process plan,and production plan in high-precision multi-product assembly

With the ever-increasing product variety faced by the manufacturing industry, investment efficiency can only be maintained by the application of multi-product assembly systems. In such systems, the product design, process planning, and production planning problems related to different products are strongly interconnected. Despite this, those interdependent decisions are typically made by different divisions of the company, by adopting a decomposed planning approach, which can easily result in excess production costs. In order to overcome this challenge, this paper proposes an integrated approach to solving the above problems, focusing on the decisions crucial for achieving the required tolerances in high-precision assembled products. The joint optimization problems related to product tolerance design and assembly resource configuration are first formulated as a mixed-integer linear program (MILP). Then, a large neighborhood search (LNS) algorithm, which combines classical mathematical programming and meta-heuristic techniques, is introduced to solve large instances of the problem. The efficiency of the method is demonstrated through an industrial case study, both in terms of computational efficiency and industrial effectiveness.     

Procedures for estimating desirable initial states of a production line: a comparative study

Two procedures for estimating initial states of a production line that ensure the line has a high probability of meeting the specified production target during a scheduled production shift are presented. The problem of determining desirable initial states is important in low variety, high volume production systems such as those from the automobile industry. One procedure is derived from design of experiments (DOE) theory whereas the other uses a genetic algorithm (GA). In the study it was determined that both procedures are straightforward to implement and produce good solutions to the problem. The results from the procedures are compared and their benefits and disadvantages are discussed.     

An economic production quantity model with random defective rate,rework process and backorders for a single stage production system

This paper revisits the economic production quantity (EPQ) model with rework process at a single-stage manufacturing system with planned backorders. It is well known that any imperfect production system of real life has random defective rates. In this direction, this paper extends an inventory model to allow random defective rates. Basically, three different inventory models are developed for three different distribution density functions such as uniform, triangular, and beta. The analytical derivation provides closed-form solution for each inventory model. We have made comparison tables of optimal results among the distribution functions. Some numerical examples and sensitivity analysis are given to illustrate the inventory models.     

用混合遗传算法求解虚拟企业生产计划

针对虚拟企业生产计划的特点,以各成员企业承担的生产任务为对象,以快速响应市场为目标,建立了生产任务计划的数学模型,并基于该模型,提出一种基于遗传算法与模拟退火算法混合的求解算法,充分发挥了遗传算法良好的全局搜索能力和模拟退火算法有效避免陷入局部极小的优点．从而提高了算法的全局寻优能力．数值仿真计算表明了该算法的良好收敛性和有效性．