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.*     

Scheduling concurrent production over a finite planning horizon: polynomially solvable cases

The paper analyzes a manufacturing system made up of one workstation which is able to produce concurrently a number of product types with controllable production rates in response to time-dependent product demands. Given a finite planning horizon, the objective is to minimize production cost, which is incurred when the workstation is not idle and inventory and backlog costs, which are incurred when the meeting of demand results in inventory surpluses and shortages. With the aid of the maximum principle, optimal production regimes are derived and continuous-time scheduling is reduced to a combinatorial problem of sequencing and timing the regimes. The problem is proved to be polynomially solvable if demand does not exceed the capacity of the workstation or it is steadily pressing and the costs are “agreeable”.

Scope and purpose

Efficient utilization of modern flexible manufacturing systems is heavily dependent on proper scheduling of products throughout the available facilities. Scheduling of a workstation which produces concurrently a number of product types with controllable production rates in response to continuous, time-dependent demand is under consideration. Similar to the systems considered by many authors in recent years, a buffer with unlimited capacity is placed after the workstation for each product type. The objective is to minimize inventory storage, backlog and production costs over a finite planning horizon. Numerical approaches are commonly used to approximate the optimal solution for similar problems. The key contribution of this work is that the continuous-time scheduling problem is reduced to a combinatorial problem, exactly solvable in polynomial time if demand does not exceed the capacity of the workstation or the manufacturing system is organized such that the early production and storage of a product to reduce later backlogs are justified.     

Projecting on-time performance for deterministic schedules in dynamic environments

Manufacturing in a world class environment demands a high level of customer service. The production control department is responsible for achieving this high level of service through accurate planning and scheduling. The ability to achieve such a high level of customer service is limited by the scheduling tools currently available. Production planning is typically performed using MRP infinite capacity, fixed lead-time, backward scheduling. The work in each MRP time-bucket is then sequenced to develop a schedule. The production floor however, is not a static environment. Dynamic events, that cannot be scheduled, degrade production performance relative to the projected schedule. In this paper the relationship between dynamic events and schedule degradation is examined. Common approaches to production scheduling underestimate the effect of capacity loading relative to unplanned events and schedule achievability. These dynamic events exhaust capacity previously allocated to production orders. To hedge against such known, but unscheduled events, production control can schedule resources to a level less than full capacity. The size of the capacity hedge and the duration of the unplanned event dictate the time to recover from the backlog created by these dynamic events. A performance metric is developed to measure the ability to achieve customer promise dates. A machine loading policy is also presented to achieve the optimal capacity hedge point that will maximize this performance measure. The results are compared to simulated failures to examine the accuracy of the predicted performance degradation. The results suggest a trade-off of throughput for improved performance to customer promise date.     

串行生产线的集成最优生产控制与能力规划

研究了制造系统串行生产线生产控制和生产能力规划的集成优化方法。给出了串行生产线最优生产控制及生产能力规划问题的数学模型,通过粒子群优化算法来求解这一模型,通过Matlab进行了仿真,并对仿真结果进行了分析。     

Brand image and brand dilution in the fashion industry

We develop a dynamic optimal control model of a fashion designer's challenge of maintaining brand image in the face of short-term profit opportunities through expanded sales that risk brand dilution in the longer-run. The key state variable is the brand's reputation, and the key decision is sales volume. Depending on the brand's capacity to command higher prices, one of two regimes is observed. If the price markups relative to production costs are modest, then the optimal solution may simply be to exploit whatever value can be derived from the brand in the short-run and retire the brand when that capacity is fully diluted. However, if the price markups are more substantial, then an existing brand should be preserved. It may even be worth incurring short-term losses while increasing the brand's reputation, even if starting a new brand name from scratch is not optimal.     

Analytical study on multi-product production planning with outsourcing

This paper studies a problem on multi-product capacitated production planning with outsourcing. The context of the problem is about an enterprise that manufactures multiple products in multiple periods for stochastic demands. Manufacturers usually have two alternative modes for the production: one is to outsource parts from outside suppliers and then assemble them; the other is to in-house manufacture parts and then assemble them. Each mode has its relative merits. In addition, the capacity constraint by in-house manufacturing is also taken into account. This paper investigates how to balance the trade-off between the two modes. An analytical approach is proposed to study the optimal decision on the above two modes for all products during each planning period. Some findings are drawn out from this analytical study. Numerical experiments show the significant cost reduction can be obtained using the proposed decision model.     

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.     

On the receding horizon hierarchical optimal control of manufacturing systems

This paper concerns the development of a hierarchical framework for the integrated planning and scheduling of a class of manufacturing systems. In this framework, dynamic optimization plays an important role in order to define control strategies that, by taking into account the dynamic nature of these systems, minimize customized cost functionals subject to state and control constraints. The proposed architecture is composed of a set of hierarchical levels where a two-way information flow, assuming the form of a state feedback control, is obtained through a receding horizon control scheme. The averaging effect of the receding horizon control scheme enables this deterministic approach to handle random and unexpected events at all levels of the hierarchy. At a given level, production targets to the subsystems immediately below are defined by solving appropriate optimal control problems. Efficient iterative algorithms based on optimality conditions are used to yield control strategies in the form of production rates for the various subsystems. At the lower level, this control strategy is further refined in such a way that all sequences of operations are fully specified. The minimum cost sensitivity information provided in the optimal control formulation supports a mechanism, based on the notion of a critical machine, which plays an important role in the exploitation of the available flexibility. Finally, an important point to note is that our approach is particularly suited to further integration of the production system into a larger supply chain management framework, which is well supported by recent developments in hybrid systems theory.     

A genetics-based approach for aggregated production planning in afuzzy environment

Due to the nondeterministic nature of the business environment of a manufacturing enterprise, it is more appropriate to describe the aggregated production planning by using a fuzzy mathematical programming model. In this paper, a genetics-based inexact approach is proposed to imitate the human decision procedure for production planning. Instead of locating one exact optimal solution, the proposed approach finds a family of inexact solutions within an acceptable level by adopting a mutation operator to move along a weighted gradient direction. Then, a decision maker can select a preferred solution by examining a convex combination of the solutions in the family via the human-computer interaction. Our computational experiments illustrate how the enterprise managers can be more satisfied by this new approach than others     

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.     

Modelling the effect of demand variations on the performance of a production system

Modelling the effect of demand variations on a production system manufacturing multiple products is discussed. The various system costs involved in the production system, namely set-up cost and inventory cost incurred due to change in demands for the products with respect to products and planning periods are estimated. A statistical modelling is presented for determining the production capacity and inventory level requirement to satisfy the customer to a certain level decided by the management. Two important factors, (i) number of types of products and (ii) multiple planning horizons are considered to identify the costs as well as the production capacity and inventory level requirements. A statistical method, analysis of variance (ANOVA) is used to study the variations in the demands and costs involved. Finally, an example is presented to explain the application and the behaviour of the statistical model.     

A GENETIC ALGORITHM FOR THE ECONOMIC MANPOWER SHIFT PLANNING PROBLEM

A modified genetic algorithm (GA) is presented for the solution of the economic manpower shift planning (EMSP) problem. This is an NP-hard capacity planning problem arising in various industrial settings including the packing stage of production in process industries and maintenance operations. Given a set of independent jobs, their production targets, and a planning horizon, EMSP seeks the manpower to be planned for each workday shift in order to complete all the jobs within the specified time horizon at minimum cost. These are the key innovative aspects of the developed GA: (1) it uses a problem-specific encoding of the solution structure at the genotypic level; (2) it adopts a special greedy algorithm for mapping genotypes to phenotypes (i.e., to actual EMSP solutions); (3) it employs an adaptive parameter control scheme to adjust the mutation rate during its run. Extensive experiments over various industrial simulated environments and comparisons with the best existing EMSP heuristic (namely the block planning greedy algorithm) show the superiority of the proposed solution approach in terms of solution quality. Furthermore, comparisons to the results obtained by the standard CPLEX optimizer showed the proposed solution's performance to be very satisfactory.     

Graphical tools for production planning in small medium industries (SMIs) based on pinch analysis

Small medium industries (SMIs) routinely face supply variations in their production cycle. Such firms are typically characterised by limited resources and insufficiency of funds. Thus, SMIs need simple solutions to cope with the production planning issues. Pinch analysis has been proven as a strategy for planning of efficient use of scarce resources. Recently, it has been extended to various production planning problems. In this paper, a simple novel graphical approach is proposed to address two common production planning problems in SMI's, which are warehouse space allocation and production capacity planning. Two industrial case studies are shown in this paper to illustrate the proposed approach.     

轮手一体机器人能量次优重构规划方法

模块化机器人的重构规划中,由于各模块的目标分配与其轨迹规划之间的耦合关系导致组合爆炸问题.本文提出一种基于简化模型的能量次优规划方法,将重构规划问题转化为最优控制问题,实现目标分配与轨迹规划的解耦.通过求解由Hamilton-Jacobi-Bellman（HJB）方程描述的最优控制问题,得到简化模型的值函数和最优轨迹.各模块的运动目标由值函数的吸引域决定.通过在最优轨迹附近的次优区域内搜索得到实际运动轨迹,提高了搜索效率.仿真实验结果表明,该方法能够选择合适的模块组合,并能在障碍物环境中生成满足机器人动力学约束的运动轨迹.     

An optimal weather condition dependent approach for emission planning in urban areas

The urban air quality strongly depends on the weather conditions. When unfavorable weather conditions are forecasted, it is desirable to reduce a certain amount of pollutant emissions to maintain a given level of air quality. In this paper, we propose and demonstrate a new approach to find the optimal reduction, and we contribute to the methodology of decision support of short-term emission control. This approach is based on weather forecasts and state-of-the-art 3-dimensional numerical air-quality prediction models by solving an optimal control problem with the emission cuts as the control variables. The objective of the optimal problem is to minimize the total cost due to the emission cuts, subject to feasibility constraints, system-governing model constraints, and target constraints. When a high-resolution numerical model is used as the state constraint, the problem can become a very high dimensional one. A practical approach to solving this problem with high dimension is proposed, based on the adjoint technique.The proposed approach is demonstrated with two computational test cases in Jinan, China for the control of sulfur dioxide. The results show the capability and computational efficiency of the method and suggest a promising potential for emission planning applications based on weather forecasts.     

Coordinated procurement/inspection and production model under inspection errors

In this study, we investigate integrating the acquisition of input materials, material inspection and production planning, where type I and type II inspection errors are allowed, and the unit acquisition cost is dependent on the average quality level. This study aims to find an optimal purchase lot size (or here, equivalently, the fixed production rate multiplied by the production run time), input quality level and the associated inspection policy that minimize the total cost per item including the order cost, materials purchase cost, setup cost, inventory holding cost, and the quality-related cost. Furthermore, the boundaries, conditions and properties for the optimal production run time are obtained under an optimal inspection policy when the input material quality level is fixed. These findings will facilitate the establishing of an efficient algorithm for an optimal solution. The study demonstrates that a partial inspection approach could dominate over both the commonly used policies of full or no inspection, which is different from a previous report where the optimal inspection policy is either full or no inspection. A numerical example is performed to evaluate the impact of the two types of inspection errors and the process deterioration because of a nonconforming process input on the optimal solution, where a Weibull shift distribution is used to simulate the process failure time. Finally, conclusions are addressed.     

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.     

Pallet operation sequencing based on network part program logic

CAPP systems play a relevant role in aiding planners during setup planning, operation sequencing and pallet configuration activities. The support and automation granted by these techniques, together with the use of non-linear process planning logic, lead to a reduction in the planning time and costs, thus making manufacturers more competitive. This paper presents an approach that integrating process and production planning leads to the definition at the shop-floor level of the optimal operation sequence to machine all of the workpieces on a pallet using a four-axis machine tool. Part programs of non-production movements for each possible sequence of two operations are automatically generated at the shop-floor level and are simulated to obtain the non-production time. The complete sequence of operations is then defined on the basis of the minimisation of the estimated non-production time. This minimisation is performed using a mathematical model that defines a good sequence of operations. Four algorithms are adopted to analyse the proposed solution and to reduce the gap from optimality. The approach is tested on some cases taken from literature and on a real case. The real case was provided by a company that produces mechanical components. The obtained results underline a reduction on production and planning time, and consequently an increment in the company profit.     

Dynamically Integrated Manufacturing Systems (DIMS)—A Multiagent Approach

Manufacturing businesses in today's market are facing immense pressures to react rapidly to dynamic variations in demand distributions across products and changing product mixes. To cope with the pressures requires dynamically integrated manufacturing systems (DIMS) that can manage optimal fulfillment of customer orders while simultaneously considering alternative system structures to suit changing conditions. This paper presents a multiagent approach to DIMS, where production planning and control decisions are integrated with systems reconfiguration and restructure. A multiagent framework, referred to as a hierarchical autonomous agent network, is proposed to model complex manufacturing systems, their structures, and constraints. It allows the hierarchical structures of complex systems to be modeled while avoiding centralized control in classical hierarchical/hybrid frameworks. Subsystems interact heterarchically with product orders to carry out optimal planning and scheduling. An agent coordination algorithm, operating iteratively under the control of a genetic algorithm, is developed to enable optimal planning and control decisions for order fulfillment to be made through interactions between agents. This algorithm also allows the structural constraints of systems to be relaxed gradually during agent interaction, so that planning and control are first carried out under existing constraints, but when satisfactory solutions cannot be found, subsystems are allowed to regroup to form new configurations. Frequently used configurations are detected and evaluated for system restructure. The approach also enables Petri-net models of new system structures to be generated dynamically and the structures to be evaluated through agent-based discrete event simulation.