Necessity constraint in two plant optimal production problem with imprecise parameters

The purpose of this paper is to present and solve a real-life problem of two plants producing the same item under fuzzy-stochastic environment. Here, an item alongwith random defective units is produced at two different plants situated in different locations under a single management. The rates of demand, production and defectiveness at these places are different. Demands of the item are primarily met locally from the respective plants but if a stock-out situation occurs in a plant, immediately some stock, from the other plant if available, is rushed to the stock-out plant. The demands are known but production rates are unknown, functions of time are taken as control variables. The available budget for the management house is imprecise. The holding, shortage and transportation costs are assumed to be imprecise and represented by fuzzy numbers which are transformed to corresponding interval numbers. Following interval mathematics and nearest interval approximation, the objective function is changed to respective multi-objective functions and thus the single-objective fuzzy problem is reduced to a crisp multi-objective decision making (MODM) problem. The MODM problem is then again transformed to a single crisp objective function with the help of weighted sum method. Using fuzzy relations, the imprecise budget constraint expressed in the form of necessity constraint is transformed into an equivalent crisp one. Then, total cost consisting of production, holding, shortage and transportation (from one plant to another) costs is expressed as an optimal control problem and solved using weighted sum method, the Kuhn-Tucker conditions, Pontryagin’s Optimal Control principle and generalized reduced gradient (GRG) technique. The model has been illustrated by numerical data. The optimum results are presented in both tabular and graphical forms.     

Computational aspects of an extended EMQ model with variable production rate

The paper considers a generalized economic manufacturing quantity (EMQ) model with stochastic machine breakdown and repair in which the time to machine failure, corrective and preventive repair times are all assumed to be random variables. The model is formulated under general failure and general repair time distributions, treating the machine production rate (speed) as a decision variable. As the stress condition of the machine changes with the production rate, the failure rate is assumed to be dependent on the production rate. The model is further extended to the case where certain safety stocks are hold in inventory to protect against possible stockout during machine repair. The solution procedure and computational algorithms of the associated constrained optimization problems are provided. Numerical examples are taken to determine the optimal production policies by the proposed algorithms and examine the sensitivity of the model parameters.Several economic manufacturing quantity (EMQ) models for unreliable manufacturing systems have been developed in the literature even for general failure and general repair (corrective) time distributions. In these studies, preventive repair has not been considered in a general way and efforts have been made to derive the production control and maintenance policy for inflexible manufacturing systems, where the machine capacity is pre-determined. The purpose of this article is to formulate a generalized EMQ model for a flexible unreliable manufacturing system in which (i) the time to machine failure and repair (corrective and preventive) times follow general probability distributions and (ii) the machine failure rate is dependent on the production rate. Consideration of a variable production rate makes the model hard to analyze completely. So, attempt has also been made to get into its computational aspects by developing solution algorithms.     

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.     

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.     

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.     

A discrete-time Markov production-inventory model with machine breakdowns

A machine produces an item at a constant rate, which is assumed to be greater than the demand rate, and the demand is assumed to be known and constant. While operating, the machine can fail, and upon failure it requires service. The machine times-to-failure and repair times are random, and during repairs, demand is backordered as long as the backordering level does not exceed a prescribed amount, after which demand is lost. By considering time to be of discrete units and the times-to-failure and repair times to be geometrically distributed, we model the production-inventory system as a Markov chain and develop an efficient algorithm to compute the potentials that are used to formulate the cost function. The model results are then compared to simulation results where time is treated as a continuous parameter.     

Distribution of the minimal completion time of parallel tasks in multi-reward semi-Markov models

The completion time of parallel tasks executed on a randomly varying system is represented as the barrier hitting time in a multi-reward stochastic model. The work produced by the system is calculated by means of two types of functionals that account for different mechanisms of accumulation of the reward in physical systems. The work requirement of each parallel task is assigned as an absorbing barrier acting on the corresponding functional. The distribution of the first time at which one of the functionals hits its barrier is investigated. If the barrier levels are assumed to be PH random variables, the hitting time becomes a PH random variable and the completion time problem is converted into the solution of a suitable expanded Markov chain.     

Inverse data envelopment analysis model to preserve relative efficiency values: The case of variable returns to scale

This paper studies the inverse Data Envelopment Analysis (inverse DEA) for the case of variable returns to scale (inverse BCC). The developed inverse BCC model can preserve relative efficiency values of all decision making units (DMUs) in a new production possibility set composing of all current DMUs and a perturbed DMU with new input and output values. We consider the inverse BCC model for a resource allocation problem, where increases of some outputs and decreases of the other outputs of the considered DMU can be taken into account simultaneously. The inverse BCC problem is in the form of a multi-objective nonlinear programming model (MONLP), which is not easy to solve. We propose a linear programming model, which gives a Pareto-efficient solution to the inverse BCC problem. However, there exists at least an optimal solution to the proposed model if and only if the new output vector is in the set of current production possibility set. The proposed approach is illustrated via a case study of a motorcycle-part company.     

Multi-objective decision making model under fuzzy random environment and its application to inventory problems

In this paper, we concentrate on developing a fuzzy random multi-objective model about inventory problems. By giving some definitions and discussing some properties of fuzzy random variable, we design a method of solving solution sets of fuzzy random multi-objective programming problems. These are applied to numerical inventory problems in which all inventory costs, purchasing and selling prices in the objectives and constraints are assumed to be fuzzy random variables in nature, and then the impreciseness of fuzzy random variables in the above objectives and constraints are transformed into fuzzy variables which are similar trapezoidal fuzzy numbers. The exact parameters of fuzzy membership function and probability density function can be obtained through fuzzy random simulating the past dates. By comparing the results with those from the fuzzy multi-objective models, we believe that the proposed fuzzy random multi-objective model and hybrid intelligent algorithm provide significant solutions to construct other inventory models with fuzzy random variables in real life.     

Optimization of the finite production rate model with scrap,rework and stochastic machine breakdown

This study employs mathematical modeling along with a recursive searching algorithm to determine the optimal run time for an imperfect finite production rate model with scrap, rework, and stochastic machine breakdown. In real-life manufacturing systems, generation of defective items and machine breakdown are inevitable. The objective of this paper is to address these issues and to be able to derive the optimal production run time. It is assumed that the proposed manufacturing system produces defective items randomly, a portion of them is considered to be scrap, and the other portion can be repaired through rework. Further, the proposed system is subject to random breakdown and when it occurs, the abort/resume (AR) policy is adopted. Under such an inventory control policy, the production of the interrupted lot will be resumed immediately when machine is fixed and restored. Mathematical modeling along with a recursive searching algorithm is used for deriving the replenishment policy for such a realistic production system.     

Optimal maintenance of stochastically deteriorating systems

A machine maintenance problem were the deterioration of the machine is subject to additive random noise is considered. The objective is then to maximize the discounted net return of the machine. Furthermore, it is also required that the machine maintains a sufficiently good quality state with certain degrees of confidence in part or whole of the machine life span. This problem can be formulated as a constrained stochastic optimal control problem. It is then shown that the stochastic optimal control problem can be converted into an equivalent deterministic optimal control problem and subsequently solved by the technique of control parametrization. Numerical examples are presented to illustrate some of the interesting features of the model.     

Scheduling optimization of a stochastic flexible job-shop system with time-varying machine failure rate

Due to environmental circumstances encountered in manufacturing processes, operating machines need to be maintained preventively, so as to ensure satisfactory operating condition. This paper investigates a scheduling problem in a flexible job-shop system with maintenance considerations where each operation can be processed by a machine out of a set of capable machines, and so, jobs may have alternative routes. Machine failure rates are assumed to be time-varying. This is a real assumption comes from a fact in realistic environments, where failure rate of a machine is variable when environmental situations like shop temperature, shop light, shop humidity or even worker skill change significantly. Moreover, in order to more close the addressed problem into the situations encountered in real world, the processing times and due dates are considered to be stochastic parameters. A mixed integer linear programming (MILP) model is constructed for addressed problem with the objective of number of tardy jobs and a minimum total availability constraint. Then a simulation-optimization framework based on a simulated annealing (SA) optimizer and Monte Carlo (MC) simulator is presented to solve the problem.     

Multi-choice multi-objective mathematical programming model for integrated production planning: a case study

This article develops a multi-choice multi-objective linear programming model in order to solve an integrated production planning problem of a steel plant. The aim of the integrated production planning problem is to integrate the planning sub-functions into a single planning operation. The sub-functions are formulated by considering the capacity of different units of the plant, cost of raw materials from various territories, demands of customers in different geographical locations, time constraint for delivery the products, production cost and production rate at different stages of production process. Departure cost is also considered in the formulation of mathematical programming model. Some of the parameters are decided from a set of possible choices, therefore such parameters are considered as multi-choice type. Multi-choice mathematical programming problem cannot be solved directly. Therefore an equivalent multi-objective mathematical programming model is established in order to find the optimal solution of the problem. Computation of the mathematical programming model is performed with the practical production data of a plant to study the methodology.     

基于分布式神经动态优化的综合能源系统多目标优化调度EI北大核心CSCD

研究了基于神经动态优化的综合能源系统(Integrated energy systems,IES)分布式多目标优化调度问题.首先,将IES元件单元(包含负荷)作为独立的决策主体,联合考量其运行成本和排放成本,并计及多能源设备间的传输损耗,提出了IES多目标优化调度模型,该模型可描述为一类非凸多目标优化问题.其次,针对此类问题的求解,提出了一种基于神经动力学系统的分布式多目标优化算法,该算法基于动态权重的神经网络模型,可以解决不可分离的不等式约束问题.该算法计算负担小,收敛速度快,并且易于硬件实现.仿真结果表明,所提算法能同时协调综合能源系统的经济性和环境性这两个冲突的目标,且获得了整个帕累托前沿,有效降低了综合能源系统的污染物排放量和综合运行成本.     

具有传感器增益退化、传输时延和丢包的离线状态估计器

研究了具有传感器增益退化、数据传输时延和丢包的网络化状态估计问题,传感器增益退化现象通过统计特性已知的随机变量来描述,数据包时延和丢失发生于传感器量测输出向远程处理中心传送过程中,将各时延的发生描述为随机过程,在远程处理中心端建立只存储最新时刻数据包的时延-丢包模型,考虑到利用每一时刻实时的时延值和丢包情况,设计了一种离线的无偏估计器,推导出最小方差原则下的离线最优估计器增益.最后,通过算例仿真验证所设计离线状态估计器的有效性.     

Determining the prices of remanufactured products,capacity of internal workstations and the contracting strategy within queuing framework

This paper studies a remanufacturing facility with several types of incoming nonconforming products and different independent remanufacturing workstations. The workstations have limited capacities so that an outsourcing strategy can be practiced. Each workstation is modeled with an M/M/1/k queuing system considering k as a decision variable. Additionally, a binary decision variable is taken into account to determine the contracting strategy along with some decision variables for the prices of remanufactured products. Thus, a bi-objective mixed-integer nonlinear programming is built to obtain optimal values of the decision variables. The first objective attempts to maximize the total profit and the second minimizes the average length of queuing at workstations. To solve the complex bi-objective mixed-integer nonlinear programming problem, the best out of six multi-objective decision-making (MODM) methods is selected in order to make the bi-objective optimization problem a single-objective one. Afterward, a genetic algorithm (GA) is developed to find a near-optimum solution of the single-objective problem. Besides, all of the important parameters of the algorithm are calibrated using regression analysis. To validate the results obtained, the solutions of some test problems are compared to the ones obtained by the GAMS software. The applicability of the proposed model and the solution procedure are shown with an illustrative example.     

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.     

Robust ℋ︁∞ sliding mode control for nonlinear stochastic systems with multiple data packet losses

In this paper, an ??_∞ sliding mode control (SMC) problem is studied for a class of discrete‐time nonlinear stochastic systems with multiple data packet losses. The phenomenon of data packet losses, which is assumed to occur in a random way, is taken into consideration in the process of data transmission through both the state‐feedback loop and the measurement output. The probability for the data packet loss for each individual state variable is governed by a corresponding individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. The discrete‐time system considered is also subject to norm‐bounded parameter uncertainties and external nonlinear disturbances, which enter the system state equation in both matched and unmatched ways. A novel stochastic discrete‐time switching function is proposed to facilitate the sliding mode controller design. Sufficient conditions are derived by means of the linear matrix inequality (LMI) approach. It is shown that the system dynamics in the specified sliding surface is exponentially stable in the mean square with a prescribed ??_∞ noise attenuation level if an LMI with an equality constraint is feasible. A discrete‐time SMC controller is designed capable of guaranteeing the discrete‐time sliding mode reaching condition of the specified sliding surface with probability 1. Finally, a simulation example is given to show the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

具有传感器增益退化、随机时延和丢包的分布式融合估计器

研究了具有传感器增益退化、模型不确定性、数据传输时延和丢包的网络化多传感器分布式融合估计问题,模型的不确定性描述为系统矩阵受到随机扰动,传感器增益退化现象通过统计特性已知的随机变量来描述,随机时延和丢包现象存在于局部最优状态估计向融合中心传输的过程中.首先,设计了一种局部最优无偏估计器,然后将传输时延描述为随机过程,并在融合中心端建立符合存储规则的时延-丢包模型,利用最优线性无偏估计方法,导出最小方差意义下的分布式融合估计器.最后,通过算例仿真证明所设计融合估计器的有效性.     

Optimization of storage sizes and controls strategy in industrial production systems

The determination of optimal storage sizes and optimal control strategy for an industrial production system is treated as a stochastic feedback optimization problem. The stochastic character of the problem is due to the randomly varying production modes of the different production units of the system. The resulting average net profit during a given interval of time and under given circumstances is taken as the value of the objective function corresponding to these circumstances. The problem is then to choose the sizes of storages and the control strategy, or the control law, in an optimal way so that the value of the objective function is maximized. However, in order to make the problem realistic and the obtained results practically applicable, the choice of control strategy has to be restricted to a carefully chosen class of feasible strategies.The described method is used for solving some actual dimensioning and planning problems at a pulp and paper mill. The approximately optimal storage sizes and control strategy are found by means of computer simulation. It is found that deviations in the storage sizes from the optimal value lead necessarily to considerable yearly losses due to either production restrictions caused by too small containers or high price of oversized storages.