A numerical method in optimal production and setup scheduling ofstochastic manufacturing systems

In this paper, we consider optimal production and setup scheduling in a failure-prone manufacturing system consisting of a single machine. The system can produce several types-of products, but at any given time it can only produce one type of product. A setup is required if production is to be switched from one type of product to another. The decision variables are a sequence of setups and a production plan. The objective of the problem is to minimize the cost of setup, production, and surplus. An approximate optimality condition is given together with a computational algorithm for solving the optimal control problem     

Stochastic dynamic job shops and hierarchical production planning

This paper presents an asymptotic analysis of hierarchical production planning in a general manufacturing system consisting of a network of unreliable machines producing a variety of products. The concept of a dynamic job shop is introduced by interpreting the system as a directed graph, and the structure of the system dynamics is characterized for its use in the asymptotic analysis. The optimal control problem for the system is a state-constrained problem, since the number of parts in any buffer between any two machines must remain nonnegative. A limiting problem is introduced in which the stochastic machine capacities are replaced by corresponding equilibrium mean capacities, as the rate of change in machine states approaches infinity. The value function of the original problem is shown to converge to that of the limiting problem, and the convergence rate is obtained. Furthermore, near-optimal controls for the original problem are constructed from near-optimal controls of the limiting problem, and an error estimate is obtained on the near optimality of the constructed controls     

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。     

印染行业不可靠生产系统生产控制模型

基于印染行业自身特性,建立了适合于该行业特点的不可靠生产系统的生产控制模型。该模型不但考虑了生产设备时有故障和修复事件的发生,而且也把由于生产系统操作条件及生产原料属性的波动造成合格产品呈随机分布的情况纳入模型框架,其中当不同产品间生产切换时,所需切换时间及切换费用也被引入模型,并假设此时设备的故障过程为Markov过程。结合单设备单产品情况,给出了其最优生产控制策略。为实现印染行业生产的优化控制及建立完善的MES系统提供了理论支持。     

Simultaneous control of maintenance and production rates of a manufacturing system with defective products

In the past three decades, studies of simultaneous maintenance and production planning have been focusing on age-dependent machine failure and inventory. This paper presents the interaction between defective products and optimal control of production rate, lead time and inventory. Our aim is to minimize the expected discounted overall cost due to maintenance activities, inventory holding and backlogs. Through Condition-Based Maintenance, we monitor in a real time the manufacturing system’s health by describing N operational states. We consider two maintenance states of a machine controlled by two decision variables: production and maintenance rates. The optimal policy is characterized by the dynamic programming solution to a piecewise deterministic optimal control problem. A numerical illustration and a sensitive analysis are developed with a set of parameters calibrated on an existing manufacturing system.     

Scheduling of an unreliable manufacturing system with nonresumable setups

This paper considers the scheduling of a manufacturing system with nonresumable setup changes. The system considered involves an unreliable machine that can produce two part types. The switchover from one part type to the other incurs a given constant setup time. The setups are nonresumable, i.e. after a machine repair completion, a setup decision has to be made. The parts have specified constant processing time and constant demand rate. We give a continuous dynamic programming formulation of the problem, which is solved numerically. The optimal setup switching policies are shown to be hedging corridors. Two heuristics, for the determination of the hedging levels, are provided. We show, through simulation, that the two heuristics exhibit good performance.     

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     

考虑机器检修的热轧钢管批量计划方法

本文从无缝钢管生产实际中提取并定义了周期性机器检修环境下的钢管热轧批量计划问题,基于无缝钢管生产的特殊性,将该问题抽象为一类考虑机器检修和机器调整时间的单机调度问题,并建立了以最小化机器闲置和机器调整时间为目标的数学模型.针对批量间的机器调整时间取决于钢管规格的变化这一特性,提出了最小调整时间排序规则,证明了该规则在不考虑检修计划时具有最优性.进而,以此为基础建立了循环求解框架,并设计了两阶段启发式算法.基于实际生产数据设计了多种问题规模的实验,验证了算法的有效性,并从实际应用角度对结果进行了分析.     

Switching curve policy for manufacturing systems with no backlogpermitted

For failure-prone manufacturing systems with deterministic machine up time, the switching curve policy, which has a special property and can be characterized by a single parameter, was shown to be optimal. In previous work, the problem of optimal production rate control was studied under the assumption that backlog is allowed. In this paper, the authors consider manufacturing systems in which backlog is not permitted. The authors show that the switching curve policy is still optimal in this case. They also consider the system model in which one machine has three states: down, idle, and operational. This model can reduce maintenance times of the machine, and then reduce its maintenance costs     

Optimal production control in a discrete manufacturing system withunreliable machines and random demands

We consider a production control problem in a manufacturing system with a failure-prone machine and a stochastic demand. The objective is to minimize a discounted inventory holding and backlog cost over an infinite planning horizon. The optimal production control of continuous, stochastic manufacturing systems with a failure-prone machine and a constant demand has been considered in Akella and Kumar (1986). However, the problem of optimal production control for discrete stochastic manufacturing systems with uncertain demands remains open. In this paper, we investigate a case where the exogenous demand forms a homogeneous Poisson flow. Primarily, we show that the optimal production control for such a system is of the threshold control type. In addition, the explicit form of production control policy and the objective functions are provided. Numerical examples are included to demonstrate the results obtained in the paper and to compare with the one in Akella and Kumar     

Multi-product production quantity model with repair failure and partial backordering

In this paper, a production quantity model with random defective items, service level constraints and repair failure is studied. The existence of only one machine results in limited production capacity and partial backordering. The aim of this research is to determine the optimal cycle length, optimal production quantity and optimal backordered quantity of each product such that the expected total cost (holding, shortage, production, setup, defective items and repair costs) is minimized. Two numerical examples and sensitivity analysis are provided to illustrate the practical usage of the proposed method.     

Production and maintenance control for manufacturing systems

This paper addresses the production and maintenance control problem of a failure prone manufacturing system consisting of one machine and producing one part type. The machine is assumed to have three working states: good, average and bad, and a failure state. In the three working states, the machine can produce parts and some of these parts are rejected with a rate depending on the machine state. In the failure state, no part is produced. The state transition of the machine is governed by a continuous-time Markov process. The jump rates from average and bad states to the good state are the preventive maintenance rates and the one from failure state to good state is the corrective maintenance rate. The production rate and the maintenance rates are optimized     

Stochastic proportionate flowshop scheduling with setups

This paper addresses the problem of scheduling n jobs on a proportionate two-machine flowshop where the machines are subject to random breakdowns and setup times are considered separate from processing times. The considered performance measure is makespan. Sequences that minimize makespan with probability 1 are obtained when the first or the second machine is subject to random breakdowns without making any assumptions about downtime distributions or counting processes. It is assumed that the processing and setup times on one machine dominate the corresponding times on the other machine. In the case that processing and setup times on the first and second machines are proportionate, it is shown that the longest processing time (LPT) rule gives an optimal solution when only the first machine is subject to breakdowns, while the shortest processing time (SPT) rule yields an optimal solution when only the second machine suffers breakdowns.     

A multi-machine multi-product EPQ problem for an imperfect manufacturing system considering utilization and allocation decisions

This paper considers a multi-product problem with non-identical machines. This manufacturing system consists of various machine types with different production capacities, production costs, setup times, production rates and failure rates. One of the major issues in the planning phase of a manufacturing system is to take the best decision about which machines must be utilized to manufacture which items. As a result, the decision makers face three critical questions: what machines must be purchased, which items should be allocated to each machine, and what is the optimal cycle length. These decisions must be made to minimize system costs including utilization, setup, production, holding and scrap costs. The multi-machine multi-product economic production quantity (EPQ) problem for an imperfect manufacturing system is formulated as a mixed integer non-linear programming (MINLP), where the convexity property of multi-product single machine EPQ model is used to convert the problem into a bi-level decision-making problem. In the first level, decisions about machine utilization and items allocation are made. After, in the second level the optimal cycle length for each machine is determined. To solve the problem at hand, a hybrid genetic algorithm (HGA) is proposed integrating genetic algorithm and derivatives method. In the proposed HGA, the solutions of the first level are obtained randomly and then, for the second level, the derivatives method is applied to obtain optimal cycle length based on solutions of the first level. Finally, the results of HGA method are compared to the results of general algebraic modeling system (GAMS) and it is found that HGA method has better and more efficient results. Also, a numerical experimentation and a sensitivity analysis of the model are done.     

A time-decomposition method for sequence-dependent setup schedulingunder pressing demand conditions

This paper develops a method for continuous-time scheduling problems in flexible manufacturing systems. The objective is to find the optimal schedule subject to different production constraints: precedence constraints (bills of materials), sequence-dependent setup times, finite machine capacities, and pressing demands. Differential equations along with mixed constraints are used to model production and setup processes in a canonical form of optimal control. The proposed approach to the search for the optimal solution is based on the maximum principle analysis and time-decomposition methodology. To develop fast near-optimal solution algorithms for sizable problems, we replace the general problem with a number of sub-problems so that solving them iteratively provides tight lower and upper estimates of the optimal solution     

Production/inventory systems with a stochastic production rate under a continuous review policy

A single production facility is dedicated to producing one product with completed units going directly into inventory. The unit production time is a random variable. The demand for the product is given by a Poisson process and is supplied directly from inventory when available, or is backordered until it is produced by the production facility. Relevant costs are a linear inventory holding cost, a linear backorder cost, and a fixed setup cost for initiating a production run. The objective is to find a control policy that minimizes the expected cost per time unit.The problem may be modeled as an M/G/1 queueing system, for which the optimal decision policy is a two-critical-number policy. Cost expressions are derived as functions of the policy parameters, and based on convexity properties of these cost expressions, an efficient search procedure is proposed for finding the optimal policy. Computational test results demonstrating the efficiency of the search procedure and the behavior of the optimal policy are presented.     

A heuristic approach for single-machine scheduling with due dates and class setups

The single-machine sequence-independent class setup scheduling problem is examined in this paper. It is assumed that jobs are classified into classes and a setup is required between jobs of different classes, but not of the same class. Furthermore, this setup time is fixed and depends only on the current job. Since the problem is NP-hard, a heuristic algorithm is proposed to find an approximate schedule that minimizes the maximum lateness on a set of jobs. The algorithm can easily be modified to solve the maximum tardiness problems as well. The accuracy of the heuristic algorithm in generating near optimal solutions is empirically evaluated.Scope and purposeFor batch manufacturing, it maybe desirable to produce many items of the same type, or class, at the same run in order to save the setup cost. However, committing facilities to long production runs for one product may inevitably make others tardy. Small batch size may conform urgent jobs to their delivery date, but one of the consequences would be the loss of productive efficiency due to numerous setups. Therefore, scheduling is basically a trade-off between the inherently conflicting efficiency measure and due-date compliance. This paper considers a single-machine scheduling problem in which jobs are classified into classes and a setup is required between jobs of different classes. The setup time is fixed and depends only on the current job. This problem is called a sequence-independent class setup problem and is NP-complete.     

Scheduling one-part-type serial manufacturing system under periodic demand: a solvable case

The paper studies one-part type, multiple-stage production system with periodic demands. A buffer of infinite capacity is placed after each machine. Inventory flow through buffers is controlled by machine production rates. The objective is to find a cyclic production rate, which minimizes all inventory-related expenses over an infinite planning horizon. With the aid of the maximum principle, optimal production policies are derived and the continuous-time scheduling problem is reduced to a discrete timing problem. As a result, a polynomial-time algorithm is suggested to calculate the optimal production rate. A numerical example is used to illustrate the algorithm.Scope and purposeNumerical and heuristic approaches have been suggested for production control of automated-serial-manufacturing systems. These approaches try to derive production control policies that would minimize overall costs related to inventory, backlog, and production. The quality of these approaches is often difficult to assess, and they can be time-consuming to implement. Therefore, increasing attention has been directed to optimal control policies of production systems that can be derived precisely and quickly. This paper addresses a special case of the production system manufacturing a single product type to meet a periodic demand. Given a certain assumption on cost relationship, we derive a fast and simple scheduling algorithm that calculates the optimal policy.     

Optimal Flow Control for Continuous-time Scheduling in Flexible Manufacturing Systems

This paper introduces a new approach to continuous-time optimal scheduling problems for a large class of manufacturing systems. This class belongs to a make-to-order production environment, based on multi-level bills of materials, flexible flow shops with setup effects and finite capacities on the shop floor. So far the setup and production planning had to be decomposed into two levels; the present model allows treating these two issues on one level, thus potentially achieving better production results. The proposed approach states the problem in terms of optimal control and investigates control strategies by means of the maximum principle for the problems with constraints on state variables. A numerical method concludes this investigation, sustaining the effectiveness of the approach on a robotic cell example.*     

机床产品制造系统能效的最优控制

本文结合机床产品制造系统的能量流特性,研究机床产品制造系统能效的最优控制.首先,利用无线传感器网络,构建制造系统能效感知网络,并设计了网络能量高效的通信协议,实时获取制造系统的能效数据.进而,利用能效感知数据,分别从单机设备局部优化与综合资源全局优化两方面,设计能效优化控制算法.根据单机设备任意两工步间空载能耗特性,给出单机设备空载能效最优控制模型.同时,建立以缩短生产周期、减少机器空转时间、提高产品合格率为优化目标的综合生产资源能效多目标优化方案.考虑到所论综合资源能效优化问题是离散组合优化问题,本文提出了文化基因支配排序粒子群算法进行求解,并采用层次分析(analysis hierarchy process,AHP)决策方法从Pareto解集中选取最优综合能效的优化策略.最后,利用实例与仿真相结合的方法,验证了文中所提方法的有效性.