Optimisation of PM scheduling for multi-component systems – a simulated annealing approach

Proper planning of preventive maintenance (PM) is crucial in many industries such as oil transmission pipelines, automotive and food industries. A critical decision in the PM plans is to determine frequencies and types of maintenance actions in order to achieve a certain level of system availability with a minimum total cost. In this paper, we consider the problem of obtaining availability-based non-periodic optimal PM planning for systems with deteriorating components. The objective is to sustain a certain level of availability with the minimal total maintenance-related costs. In the proposed approach, the planning horizon is divided into some inspection periods of equal intervals. For any given interval, a decision must be made to perform one of the three actions on each component; inspection, preventive repair and preventive replacement. Any of these activities has different effects on the reliability of the components and the corresponding distinct costs based on the required recourses. The cost function includes the cost for repair, replacement, system downtime and random failures. System availability and PM resources are the main constraints considered. Since the proposed model is combinatorial in nature involving non-linear decision variables, a simulated annealing algorithm is employed to provide good solutions within a reasonable time.     

Contribution of simulation to the optimization of inspection plans for multi-stage manufacturing systems

In this paper we develop a new mathematical model to optimize inspection plans for multi-stage manufacturing systems with possible misclassification errors. The presented model minimizes total inspection related costs while still assuring a required output quality. Because of the complexity of the proposed mathematical model, a simulation algorithm is presented to model the multistage manufacturing system subject to inspection and to estimate the resulting inspection costs. We use the popular Arena simulation software to implement our simulation algorithm and then we utilize OptQuest, Arena’s built-in optimization package, to find the optimal inspection plan. Finally, a numerical example is presented and simulation experiments are also conducted in order to examine the effects of several model parameters.     

Optimal non-periodic inspection scheme for a multi-component repairable system using A1 search algorithm

This paper proposes an approach for finding an optimal non-periodic inspection scheme on a finite time horizon for a multi-component repairable system. The system consists of several components, each of which is subjected to soft failure. Soft failures of each component do not cause the system to stop functioning, but increase the system operating costs and are detected only if inspection is performed. Thus, the system is inspected at the scheduled inspection instances and if any of its components is found to have failed, the failed component is minimally repaired. The system’s expected total cost associated with a given inspection scheme includes inspection costs, repair costs, and the penalty costs that are incurred due to the time delay between the actual occurrence of a soft failure of the components and its detection at an inspection. The objective is to determine the optimal inspection scheme which minimizes system’s expected total cost.In the proposed approach, the system’s expected total cost is first formulated in terms of inspection scheme. Then, A¹ search algorithm, with a proposed heuristic cost function for calculating lower bounds, is employed to search through alternative inspection schemes to determine the optimal one. The proposed approach is illustrated through a numerical example.     

Optimal policy for set-up time reduction in a multistage production inventory system

A batch production-inventory system consisting of multiple stages with an optimal policy of set-up time reduction and a fixed increment cost are discussed. The ratio of set-up time reduction as a decision variable under various cases of demand in the batch production-inventory model is considered. The ratio of set-up time reduction and lot size are solved simultaneously to obtain an optimal value of the total annual cost. A numerical example is presented to demonstrate the accuracy of the proposed method.     

Implementing an optimal policy for set-up time reduction in an economic production quantity model

An economic production quantity (EPQ) system consisting of single and multiple items with an optimal policy of set-up time reduction and a fixed increment cost are discussed in the present study. The set-up time reduction ratio as a decision variable under various cases of demand in the EPQ model is considered. It is assumed that the set-up cost is linearly related to the set-up time. The set-up time reduction ratio and the lot size are solved simultaneously to obtain an optimal value of the total annual cost. Numerical examples are presented to demonstrate the accuracy of the proposed method.     

Optimal non-periodic inspection scheme for a multi-component repairable system using A search algorithm

This paper proposes an approach for finding an optimal non-periodic inspection scheme on a finite time horizon for a multi-component repairable system. The system consists of several components, each of which is subjected to soft failure. Soft failures of each component do not cause the system to stop functioning, but increase the system operating costs and are detected only if inspection is performed. Thus, the system is inspected at the scheduled inspection instances and if any of its components is found to have failed, the failed component is minimally repaired. The system’s expected total cost associated with a given inspection scheme includes inspection costs, repair costs, and the penalty costs that are incurred due to the time delay between the actual occurrence of a soft failure of the components and its detection at an inspection. The objective is to determine the optimal inspection scheme which minimizes system’s expected total cost.     

Application of ant colony optimization algorithm in process planning optimization

One objective of process planning optimization is to cut down the total cost for machining process, and the ant colony optimization (ACO) algorithm is used for the optimization in this paper. Firstly, the process planning problem, considering the selection of machining resources, operations sequence optimization and the manufacturing constraints, is mapped to a weighted graph and is converted to a constraint-based traveling salesman problem. The operation sets for each manufacturing features are mapped to city groups, the costs for machining processes (including machine cost and tool cost) are converted to the weights of the cities; the costs for preparing processes (including machine changing, tool changing and set-up changing) are converted to the ‘distance’ between cities. Then, the mathematical model for process planning problem is constructed by considering the machining constraints and goal of optimization. The ACO algorithm has been employed to solve the proposed mathematical model. In order to ensure the feasibility of the process plans, the Constraint Matrix and State Matrix are used in this algorithm to show the state of the operations and the searching range of the candidate operations. Two prismatic parts are used to compare the ACO algorithm with tabu search, simulated annealing and genetic algorithm. The computing results show that the ACO algorithm performs well in process planning optimization than other three algorithms.     

Optimal inspection interval for a k-out-of-n system with non-identical components

In this paper, we develop a continuous-time discrete-state model for periodic inspection of a k-out-of-n cold-standby system with non-identical components. A perfect switching system detects the components’ failures, and the failed component(s) are repaired during the next inspection interval, and then added to the standby queue. The system can be in different states depending on the combination of working components and the order of the components on the standby queue at the beginning of an inspection interval. We present a matrix-based approach to determine the system states and calculate the system-states transition probabilities and the transition matrix. We calculate the expected total cost of the inspection intervals by determining the system state at the beginning and end of each inspection interval and calculating the inspection cost matrix. The expected total inspection cost consists of the system downtime cost, components repair cost, system repair cost, and system inspection costs. Finally, we minimize the system’s expected total cost by determining the system’s optimal inspection interval. The results show that determining the optimal inspection interval decreases the system's total inspection interval cost up to 60 % in comparison with the cases when the inspection interval is selected arbitrarily.     

软计算求解分布式多工厂多顾客的供应链准时化生产计划问题

描述了分布式多工厂、多顾客的供应链准时化生产计划问题,以实现最小化提前／拖期惩罚费用、生产成本、产品运输费用之和为目标建立了数学模型,将遗传算法与模糊逻辑相结合,设计了软计算方法求解模型,采用基于规则方法的模糊规则量化方法求解模糊决策,并将模糊决策嵌入遗传算法,使得算法具有比分枝定界法更快的寻优能力和更广的适应范围。实例计算结果表明了该模型和算法的有效性和应用潜力。     

Multiproduct production/inventory control under random demands

Studies the optimal production/inventory control policy for a single machine multiproduct production system. The machine produces to fill the end-product inventory stock and the demand is satisfied from the inventory when available; unsatisfied demand is backlogged until the product becomes available as the result of production. For each product, the demand follows a Poisson process and the unit processing time is known. When the machine switches production from one product to another, it incurs a set-up time and a set-up cost. The relevant costs include the set-up cost, a cost per unit time while the machine is running, and linear costs for inventory and backlogging. This problem is modeled as a semi-Markov decision process using the criterion of minimizing expected total cost with discounting over an infinite horizon. Procedures for computing near-optimal policies and their error bounds are developed. The error bound given by the authors' procedure is shown to be much tighter than the one given by the “norm-based” approach. Computational test results are presented to show the structure of the near-optimal policy and how its accuracy is affected by the system characteristics such as capacity utilization and set-up time     

软计算求解分布式多工厂单件制造业的提前/拖期生产计划问题

描述了分布式多工厂单件制造企业准时化生产计划问题, 以实现最小化提前/拖期惩罚费用、生产成本、产品运输费用之和为目标建立了0-1规划数学模型; 设计了基于模糊规则量化的方法求解模糊决策, 并将模糊决策嵌入到遗传算法中的软计算方法求解模型, 使得算法具有比分枝定界法更快速的寻找优解的能力以及更广泛的适应范围. 结果表明了该模型和算法的有效性和应用潜力.     

The impact of OPT and TPM on the economic production quantity

In manufacturing systems, the material flow is influenced by a number of factors, such as batching policies, capacity of machines, machine breakdowns, etc. Realizing the role of batching policies and reliability of machines in production systems, a mathematical model is presented here for determining optimal batching policies with the objective of improving the speed of material flow considering machine breakdowns and batch splitting and forming. This model is employed for studying (i) the significance of total preventive maintenance (TPM); (ii) the use of the optimized production technology (OPT) concept in batching policies; and (iii) the influence of a set-up cost reduction programme on the performance of manufacturing systems. The basic criterion considered for optimizing the batch sizes is the minimization of total system cost (TSC). An example problem is solved to explain the application of the model.     

A condition-based maintenance policy for a production system under excessive environmental degradation

In this paper a condition-based maintenance model is proposed for a single-unit system of production of goods and services. The system is subject to random deterioration which impacts not only the product quality but also the environment. We assume that the environment degrades whenever a specific level of system deterioration is reached. The proposed maintenance model aims to assess the degradation in such a way to reduce the deterioration of the environment. To control this deterioration, inspections are performed and after which the system is preventively replaced or left as it is. Preventive replacement occurs whenever the level of the system degradation reaches a specific level threshold. The objective is to determine optimal inspection dates which minimize the average total cost per unit of time in the infinite horizon. Cost function is composed of inspection and maintenance costs in addition to a penalty cost due to environmental deterioration. The maintenance optimization model is formally derived. On the basis of Nelder–Mead method, inspection dates as optimal solutions are computed. A numerical example is provided to illustrate the proposed maintenance model.     

A Dynamic Inspection Model for Wearing Production Systems

The aim of this paper is to correlate the deterioration process of a production system with the items control process and, as a consequence, with the equipment inspection policy. The objective is to consider how the wear of the manufacturing system influences the values of the control process parameters and how these parameters have to be changed in accordance with the need to maintain optimal (working) conditions. Adopting a Weibull failure-time distribution, it is shown how these parameters must be changed (at different times t ) in order to maintain optimal working conditions. To test the inspection model, a weighted cost function dependent on the time loss for the production of defective units and for the production shut-down (in order to make an inspection to control the state of the system) is developed.     

基于模糊决策与进化算法的生产设备布局优化

为解决复杂情况下制造系统的生产设备布局优化问题,提出了一种将模糊决策与进化算法相结合的设备布局优化方法。进一步完善了优化模型,优化目标包括总成本最小、设备相邻要求最大化和面积利用率最大化等优化目标;其中总成本最小目标考虑了物料搬运成本,设备重置导致的设备拆装、移动成本,生产停工造成的产能损失成本。该方法考虑了用户对于成本、利用率及相邻性要求等存在的满意度、优先度等模糊情况,基于模糊决策理论,对多目标优化模型进行了模糊化处理,设计了模糊适应度函数,用以根据用户的优先关系评价pareto解集。基于求解模型的特点,对多目标进化算法的染色体编码方式与交叉、变异等遗传操作方式进行改进,以提高求解该模型的实用性与效率。最后以实际案例的优化结果证明了该方法的有效性。     

Continuous review inventory model with controllable lead time,lost sales rate and order processing cost when the received quantity is uncertain

In practice the quantity received may not match the quantity ordered due to worker's strike, rejection during inspection, damage during transportation, human errors in counting, etc. Accordingly, the managers often must make decisions under uncertain quantity received circumstances. In this study, we investigate the continuous review inventory model with shortages include the case where the quantity received is uncertain, in which the lead time, lost sales rate and order processing cost are decision variables. Here, we consider the lead time crashing cost is an exponential function of lead time, and the order processing cost and lost sales rate are logarithmic functions of capital investment. The objective of this study is to minimize the total relevant cost by simultaneously optimizing the order quantity, lost sales rate and order processing cost. In addition, an efficient algorithm is developed to determine the optimal policy, and our approach is illustrated through a numerical example. From the results of numerical example, it can be shown that, the significant savings can be achieved through the reductions of order processing cost and lost sales rate.     

Robust manufacturing system design using multi objective genetic algorithms,Petri nets and Bayesian uncertainty representation

Decisions involving robust manufacturing system configuration design are often costly and involve long term allocation of resources. These decisions typically remain fixed for future planning horizons and failure to design a robust manufacturing system configuration can lead to high production and inventory costs, and lost sales costs. The designers need to find optimal design configurations by evaluating multiple decision variables (such as makespan and WIP) and considering different forms of manufacturing uncertainties (such as uncertainties in processing times and product demand). This paper presents a novel approach using multi objective genetic algorithms (GA), Petri nets and Bayesian model averaging (BMA) for robust design of manufacturing systems. The proposed approach is demonstrated on a manufacturing system configuration design problem to find optimal number of machines in different manufacturing cells for a manufacturing system producing multiple products. The objective function aims at minimizing makespan, mean WIP and number of machines, while considering uncertainties in processing times, equipment failure and repairs, and product demand. The integrated multi objective GA and Petri net based modeling framework coupled with Bayesian methods of uncertainty representation provides a single tool to design, analyze and simulate candidate models while considering distribution model and parameter uncertainties.     

制造系统的递阶滚动优化调度模型

研究的对象是只有一台不可靠（failure-prone)机器的非完全柔性制造系统，该系统能生产多种产品，但在同一时刻只能生产一种产品，并且当机器由生产一种产品向生产另一种产品切换时，需要考虑setup时间及其成本，待决策变量是setup序列及产品生产率，本文基于非完全柔性制造系统的特点，引入递阶层控的思想，采用新的递阶结构框架和阈值控制策略，对问题进行分解，建立了考虑setup时间及成本的递阶流率控制最优化调度模型，并给出了递阶的滚动优化算法，仿真结果表明，这种调度策略更易于工程实现。     

Simultaneous optimization of repair and control-limit policy in condition-based maintenance

In condition-based maintenance (CBM) planning, collected information from system condition monitoring is the basis of making decision about conducting the maintenance and repair activities. Recently, ample number of studies has been conducted in CBM field especially, in control-limit policy. In control-limit policy, using proportional Hazards model and results of monitoring system condition, one can estimate hazard rate function and its condition’s transition probability matrix. Then, considering replacement costs, optimal control-limit can be determined minimizing the average cost in the long run. The presented model considers repair policy and their implementation cost, and the assumptions of repair during interval inspection is ignored. Then, a model is presented to determine the optimal control-limit and the best repair policy, in which the average total cost per unit time in the long-run, is minimized. At the end, a numerical example is illustrated.     

Supply chain coordination with defective items and quantity discount

This study develops an integrated inventory system involving defective items and quantity discount for optimal pricing and ordering strategies. The model analysed in this study is one in which the buyer orders a quantity, the vendor produces more than buyer's order quantity in order to reduce set-up cost, and then he/she offers an all-units quantity discount to the buyer. Our objective is to determine the optimal order quantity, retail price, mark-up rate, and the number of shipments per production run from the vendor to the buyer, so that the entire supply chain joint total profit incurred has a maximum value. Furthermore, an algorithm of finding the optimal solution is developed. Numerical examples are provided to illustrate the theoretical results.