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.     

Robust Algorithms for Preemptive Scheduling

Preemptive scheduling problems on parallel machines are classic problems. Given the goal of minimizing the makespan, they are polynomially solvable even for the most general model of unrelated machines. In these problems, a set of jobs is to be assigned to run on a set of m machines. A job can be split into parts arbitrarily and these parts are to be assigned to time slots on the machines without parallelism, that is, for every job, at most one of its parts can be processed at each time. Motivated by sensitivity analysis and online algorithms, we investigate the problem of designing robust algorithms for constructing preemptive schedules. Robust algorithms receive one piece of input at a time. They may change a small portion of the solution as an additional part of the input is revealed. The capacity of change is based on the size of the new piece of input. For scheduling problems, the supremum ratio between the total size of the jobs (or parts of jobs) which may be re-scheduled upon the arrival of a new job j, and the size of j, is called migration factor. We design a strongly optimal algorithm with the migration factor $1-\frac{1}{m}$ for identical machines. Strongly optimal algorithms avoid idle time and create solutions where the (non-increasingly) sorted vector of completion times of the machines is lexicographically minimal. In the case of identical machines this results not only in makespan minimization, but the created solution is also optimal with respect to any ? _p norm (for p>1). We show that an algorithm of a smaller migration factor cannot be optimal with respect to makespan or any other ? _p norm, thus the result is best possible in this sense as well. We further show that neither uniformly related machines nor identical machines with restricted assignment admit an optimal algorithm with a constant migration factor. This lower bound holds both for makespan minimization and for any ? _p norm. Finally, we analyze the case of two machines and show that in this case it is still possible to maintain an optimal schedule with a small migration factor in the cases of two uniformly related machines and two identical machines with restricted assignment.     

A maximum principle based combined method for scheduling in a flexible manufacturing system

A continuous time dynamic model of discrete scheduling problems for a large class of manufacturing systems is considered in the present paper. The realistic manufacturing based on multi-level bills of materials, flexible machines, controllable buffers and deterministic demand profiles is modeled in the canonical form of optimal control. Carrying buffer costs are minimized by controlling production rates of all machines that can be set up instantly. The maximum principle for the model is studied and properties of the optimal production regimes are revealed. The solution method developed rests on the iterative approach generalizing the method of projected gradient, but takes advantage of the analytical properties of the optimal solution to reduce significantly computational efforts. Computational experiments presented demonstrate effectiveness of the approach in comparison with pure iterative method.     

Stohastic optimal production control problem with corrective maintenance

We consider a production control problem in a manufacturing system with failure-prone machines and a constant demand rate. The objective is to minimise a discounted inventory holding and backlog cost over an infinite planning horizon. The availability of the machines is improved through a corrective maintenance strategy. The decision variables are the production and the machine repair rates, which influence the inventory levels and the system capacity, respectively. It is shown that, for constant demand rates and exponential failure and repair times distributions of the machines, the hedging point policy is optimal. Such a policy is modified herein and parameterised by factors representing the thresholds of involved products and switching inventory levels for corrective maintenance. With the obtained policy, simulation experiments are combined to experimental design and response surface methodology to estimate the optimal production and corrective maintenance policies, respectively. The usefulness of the proposed approach is illustrated through a numerical example.     

Optimal control of pull manufacturing systems

We consider the problem of optimal control of pull manufacturing systems. We study a fluid model of a flow shop, with buffer holding costs nondecreasing along the route. The system is subject to a constant exogenous demand, thus incurring additional shortfall/inventory costs. The objective is to determine the optimal control for the production rate at each machine in the system. We exhibit a decomposition of the flow shop into “sections” of contiguous machines, where, in each section, the head machine is the bottleneck for the downstream system. We exhibit the form of an optimal control and show that it is characterized by a set of “deferral times”, one for each head machine. Machines which are upstream of a head machine simply adopt a “just-in-time” production policy. The head machines initially stay idle for a period equal to their deferral time and thereafter produce as fast as possible, until the initial shortfall is eliminated. The optimal values of these deferral times are simply obtained by solving a set of quadratic programming problems. We also exhibit special cases of re-entrant lines, for which the optimal control is similarly computable     

Maintenance scheduling and production control of multiple-machine manufacturing systems

This paper deals with the production and preventive maintenance control problem for a multiple-machine manufacturing system. The objective of such a problem is to find the production and preventive maintenance rates for the machines so as to minimize the total cost of inventory/backlog, repair and preventive maintenance. A two-level hierarchical control model is presented, and the structure of the control policy for both identical and non-identical manufacturing systems is described using parameters, referred to here as input factors. By combining analytical formalism with simulation-based statistical tools such as experimental design and response surface methodology, an approximation of the optimal control policies and values of input factors are determined. The results obtained extend those available in existing literature to cover non-identical machine manufacturing systems. A numerical example and a sensitivity analysis are presented in order to illustrate the robustness of the proposed approach. The extension of the proposed production and preventive maintenance policies to cover large systems (multiple machines, multiple products) is discussed.     

Optimal threshold control in discrete failure-prone manufacturingsystems

Bielecki and Kumar (1988) show that the threshold or hedging-point production policies are optimal in a continuous manufacturing system, even if production ability is uncertain. Their analysis assumes constant demand and processing time. In this paper, we consider a discrete manufacturing system in which production capacity, demand, and processing time are all nondeterministic. We formulate the problem into a discrete Markovian production model, and explore the most cost-effective control policy for such a system. With two more sources of uncertainty, we find that the threshold control policies are optimal among all feasible policies when the long run average cost is to be minimized. This extends Bielecki and Kumar's result which shows that the threshold policies are optimal among a subset of feasible policies     

Real-time capacity requirement planning for make-to-order manufacturing with variable time-window orders

In a make-to-stock (MTS) manufacturing environment using material requirement planning (MRP), checking the capacity feasibility of a master production schedule (MPS) requires capacity requirement planning (CRP) that can be easily calculated. The time window of an order is the time interval from its ready date to its due date. In a make-to-order (MTO) manufacturing environment, the CRP method checks whether a set of orders with different time windows can be scheduled for timely completion. This corporate-level CRP problem has long perplexed MTO contract manufacturers, such as those in the fashion industry. This study therefore develops an efficient and effective CRP approach that considers orders with variable time windows. Real-time capacity feasibility can be checked on both the corporate planning and detailed operational scheduling levels by applying the preemptive earliest due date (PEDD) rule to a single machine problem. This simple and efficient dispatching rule can assess the impact on capacity consumption each time an inquiry order is received or select a set of pre-prioritized orders that can be feasibly scheduled. The efficiency of a supply chain network is affected by its overall lead time, which includes time spent on order processing, manufacturing, and transportation. The proposed approach significantly reduces the order processing time and enhances supply chain efficiency.     

Capacity planning with ant colony optimization for TFT-LCD array manufacturing

Array manufacturing in thin film transistor-liquid crystal display (TFT-LCD) production network is characterized as a capital-intensive and capacity-constrained production system with re-entrance and batch operations. Effectively using associated machines through optimal capacity planning and order scheduling decisions is a critical issue for array manufacturing. This study develops a capacity planning system (CPS) for TFT-LCD array manufacturing. CPS uses information including master production schedule, order due date, process routing, processing time, and number of machines. In addition, CPS derives the order release time, estimated machine start and finish time, machine allocation, and order completion time to maximize machine workload, improve lateness, and eliminate setup time. This research also develops ant colony optimization (ACO) to seek the optimal order release schedule to maximize a combination of the above objectives. The preliminary experiments are first applied to identify the optimal tuning parameters of the ACO algorithm. Computational experiments are then conducted to evaluate the significance and the robustness of the proposed algorithm compared with other competitive algorithms by full factorial experimental design.     

Buffer size design linked to reliability performance: A simulative study

Material flow along a Flow Production Line may be disrupted by machine failures or variable processing times. In particular, Automatic Flow Production Lines are often affected by the presence of micro-down-times (i.e. speed losses due to work-pieces blocking or congestion, momentary stiff or stuck pieces on machines, etc.), which can penalize the productivity of the system and increase losses in availability for the whole plant. Moreover, micro-breakdowns cause inability of the system not to respond to sudden changes in demand due to capacity restrictions.Intermediate buffers built between the various machines in an asynchronous automatic (or semi-automatic) production line may increase the reliability of the whole system by limiting the consequences of micro-downtime, and saving companies from making inadequate purchases of oversized equipment.In this paper a new efficiency simulative study for the allocation of storage capacity in serial production lines is developed and a new experimental cross matrix is provided as a tool to determine the optimal buffer size. Thus, this research studies the relationship of machines’ availability and buffers size, in order to stress a new paradigm: the buffer design for availability (BDFA).Using a simulation approach, this paper describes the effects of workstation reliability parameters on buffer capacity level, developing a set of simple guidelines to support and help designers and practitioners in the rapid and robust buffer design issue.     

Hidden Markov model-based autonomous manufacturing task orchestration in smart shop floors

Smart manufacturing requires flexible production organization and management to handle the dynamic customer requirements rapidly and efficiently. In the context of smart manufacturing, work-in-progress (WIP), machines, and other physical resources in smart shop floors are endowed with intelligence, such as self-perception and self-decision-making. In this situation, the manufacturing task orchestration in such smart shop floors becomes autonomous, which is different from the traditional one that is centrally set and managed. The manufacturing tasks are accomplished with the help of autonomous communication between the WIP and the machines. This paper firstly clarifies the logic of autonomous manufacturing, in which the core idea is the autonomous communication and collaboration between the WIP and the machines during production. Furthermore, the autonomous manufacturing task orchestration (AMTO) problem is described. An improved hidden Markov model (HMM) is proposed to formulate the problem and generate an optimal AMTO solution for a certain process flow. A demonstrative case is implemented to verify the feasibility of the proposed model and method. The results show that HMM can give suggestions on AMTO and dynamically adjust the situation based on the real-time manufacturing data.     

Robust invariant sets for constrained storage systems

Several items are produced and stored into n buffers in order to supply an external demand without interruptions. We consider the classical problem of determining control laws and smallest buffer levels guaranteeing that an unknown bounded demand is always satisfied. A simple model with n decoupled integrators and n additive bounded disturbances is employed. The coupling arises from bounds on the total production capacity and on the total demand. Invariant set theory for linear and switched linear systems is exploited to compute robust positive invariant sets and controlled robust invariant sets for two commonly adopted scheduling policies. This paper provides the explicit expression of the invariant sets for any arbitrary n.     

A continuous-time integrated model for discrete control of production flows in a multi-level bills of material environment

An integrated dynamic model for discrete production scheduling and continuous capacity expansion is presented in this paper. The modeled manufacturing system, based on multi-level bills of materials, is characterized by flexible machines with negligible setups and production rates fixed for the current capacity. Make-to-stock formulation of the problem is studied and optimal behavior of the system is determined with the help of the maximum principle. A fast time-decomposition algorithm is suggested to locate the optimal solution.     

PWB装配线综合生产能力计划模型及其近似求解算法

提出了多产品柔性制造环境中市场需求确定动态且完全由生产满足的条件下PWB 装配线的再设计模型.由于该模型为大规模混合整数规划问题,提出了一种首先求解若干递 归线性规划以减小搜索空间,然后应用启发式搜索的近似求解方法.实际问题的计算结果表 明了所提出算法的有效性.     

Dynamic instabilities and stabilization methods in distributedreal-time scheduling of manufacturing systems

The paper concerns policies for sequencing material through a flexible manufacturing system to meet desired production goals for each part type. The authors demonstrate by examples that cyclic material flow and certain distributed scheduling policies can lead to instability in the sense that the required buffer levels are unbounded. This can be the case even when the set-up times for changing part types are zero. Sufficient conditions are then derived under which a class of distributed policies is stable. Finally, a general supervisory mechanism is presented which will stabilize any scheduling policy (i.e. maintain bounded buffer sizes at all machines) while satisfying the desired production rates     

Joint admission,production sequencing,and production rate control for a two-class make-to-order manufacturing system

Today's manufacturing industry faces a number of challenges related to the rapid delivery of products with a high degree of variety. Striking a balance between the effectiveness in capacity utilization and the rapidness in order-fulfillment is a substantial challenge for manufacturing companies. This work aims to provide a theoretical basis from which to address this practical question. To this end, we address the problem of coordinating the admission, production sequencing, and production rate controls for a two-class make-to-order manufacturing system. Formulating the problem as a Markov decision process model, we identify the structural properties of optimal control policies under both discounted and average profit criteria. We show that the cμ rule is optimal for production sequencing and the optimal admission and production rate control policies can be characterized by the state-dependent threshold levels, provided that the production times are not associated with customer class. We also show that the optimal production rates are monotone in the system state, as in the case of a single class queueing system, and that the lower priority class can be preferred to the higher priority class in order admission under a certain condition on the system parameters. Our numerical study demonstrates that a considerable economic benefit can be achieved if the production rate is dynamically controlled between the minimum and maximum rates rather than fixed to the mean rate of these values. Finally, we present a heuristic policy that is described by linear switching functions for the control of order admission and a selection rule for the control of production rate. We compare the performance of our heuristic to the optimal policy using a numerical experiment, revealing that the heuristic provides near optimal solutions to test example problems and is robust to the system parameters.     

Dynamics and design of a class of parameterized manufacturing flowcontrollers

The optimal production control of failure prone flexible manufacturing systems has received considerable attention. Analytically intractable optimality conditions render near optimal controller design the only available option for realistic size systems. This paper deals with a class of suboptimal feedback control policies that are parameterized over a finite set. In-depth analysis of the dynamics of the controlled system is undertaken and important properties of these dynamics are proven for the first time for multiple part-type systems. These properties provide the theoretical justification of an infinitesimal perturbation analysis-based controller parameter optimization technique whose validity has been previously supported by empirical evidence     

Pade approximants for the transient optimization of hedging controlpolicies in manufacturing

Part production is considered over a finite horizon in a single-part multiple-failure mode manufacturing system. When the rate of demand for parts is constant, for Markovian machine-mode dynamics and for convex running cost functions associated with part inventories or backlogs, it is known that optimal part-production policies are of the so-called hedging type. For the infinite-horizon case, such policies are characterized by a set of constant critical machine-mode dependent inventory levels that must be aimed at and maintained whenever possible. For the finite-horizon (transient) case, the critical levels still exist, but they are now time-varying and in general very difficult to characterize. Thus, in an attempt to render the problem tractable, transient production optimization is sought within the (suboptimal) class of time-invariant hedging control policies, a renewal equation is developed for the cost functional over finite horizon under an arbitrary time-invariant hedging control policy     

Reliability evaluation for a manufacturing network with multiple production lines

This paper focuses on performance evaluation of a manufacturing system with multiple production lines based on the network-analysis perspective. Due to failure, partial failure, or maintenance, the capacity of each machine is stochastic (i.e., multi-state). Hence, the manufacturing system can be constructed as a stochastic-flow network, named manufacturing network herein. This paper intends to measure the probability that the manufacturing network can satisfy customers’ orders. Such a probability is referred to as the system reliability. A graphical representation is first proposed to transform a manufacturing system into a manufacturing network. Thereafter, we decompose the manufacturing network into general processing paths and reworking paths. Three algorithms are subsequently developed for different scenarios and multiple production lines to generate the minimal capacity vectors that machines should provide to satisfy demand. The system reliability can be derived in terms of such capacity vectors afterwards.     

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.