A novel flexible model for lot sizing and scheduling with non-triangular,period overlapping and carryover setups in different machine configurations

This paper develops and tests an efficient mixed integer programming model for capacitated lot sizing and scheduling with non-triangular and sequence-dependent setup times and costs incorporating all necessary features of setup carryover and overlapping on different machine configurations. The model’s formulation is based on the asymmetric travelling salesman problem and allows multiple lots of a product within a period. The model conserves the setup state when no product is being processed over successive periods, allows starting a setup in a period and ending it in the next period, permits ending a setup in a period and starting production in the next period(s), and enforces a minimum lot size over multiple periods. This new comprehensive model thus relaxes all limitations of physical separation between the periods. The model is first developed for a single machine and then extended to other machine configurations, including parallel machines and flexible flow lines. Computational tests demonstrate the flexibility and comprehensiveness of the proposed models.     

Rule-based production planning in flexible manufacturing systems

Production planning in flexible manufacturing may require the solution of a large-scale discrete-event dynamic stochastic optimization problem, due to the complexity of the system to be optimized, and to the occurrence of discrete events (new orders and hard failures). The production planning problem is here approached for a multistage multipart-type manufacturing shop, where each work cell can share its processing time among the different types of parts. The solution of this problem is obtained by an open-loop-feedback control strategy, updated each time a new event occurs. At each event time, two coupled problems are solved: 1) a product-order scheduling problem, conditioned on estimated values of the production capacities of all component work cells; and 2) a production-capacity planning problem, conditioned on predefined sequences of the product orders to be processed. In particular, the article aims at defining a production planning procedure that integrates both analytical tools, derived from mathematical programming, and knowledge-based rules, coming from experience. The objective is to formulate a hybrid (knowledge-based/analytical) planning architecture, and to analyze its use for multicell multipart-type manufacturing systems.     

An efficient heuristic for scheduling batches of parts in a flexible flow system

Flexible manufacturing systems (FMSs) are a class of automated systems that can be used to improve productivity in batch manufacturing. Four stages of decision making have been defined for an FMS—the design, planning, scheduling, and control stages. This research focuses on the planning stage, and specifically in the area of scheduling batches of parts through the system. The literature to date on the FMS planning stage has mostly focused on the machine grouping, tool loading, and parttype selection problems. Our research carries the literature a step further by addressing the problem of scheduling batches of parts. Due to the use of serial-access material-handling systems in many FMSs, the batch-scheduling problem is modeled for a flexible flow system (FFS). This model explicitly accounts for setup times between batches that are dependent on their processing sequence. A heuristic procedure is developed for this batch-scheduling problem—the Maximum Savings (MS) heuristic. The MS heuristic is based upon the savings in time associated with a particular sequence and selecting the one with the maximum savings. It uses a two-phase method, with the savings being calculated in phase I, while a branch-and-bound procedure is employed to seek the best heuristic solution in phase II. Extensive computational results are provided for a wide variety of problems. The results show that the MS heuristic provides good-quality solutions.     

An Efficient Heuristic Approach to Recognize the Infeasibility of a Loading Problem

The success of hierarchical production planning approaches for flexible manufacturing systems lies in the consistency of decision outcomes at various decision levels. For instance, the loading problem, which is solved at a lower level, may not yield a feasible loading solution to a set of part types selected at a higher level. This paper attemps to address the issue of recognizing the infeasibility of a loading solution. We present a modified loading model that includes a penalty for each operation not assigned to any machine. We develop a Lagrangian-based heuristic procedure and provide a sufficient condition on the quality of heuristic solutions that, if satisfied, will enable us to use the heuristic solutions to recognize the infeasibility of a loading problem. The proposed model and the dual-based heuristic can be effectively incorporated in an FMS hierarchical production planning approach that finds a good loading solution by iteratively comparing different part grouping scenarios.     

Scheduling parallel machines with major and minor setup times

This article discusses the problem of scheduling a large set of parts on an FMS so as to minimize the total completion time. Here, the FMS consists of a set of parallel identical machines. Setup time is incurred whenever a machine switches from one type of part to another. The setup time may be large or small depending on whether or not the two part types belong to the same family. This article describes a fast heuristic for this scheduling problem and derives a lower bound on the optimal solution. In computational tests using random data and data from an IBM card test line, the heuristic archieves nearly optimal schedules.     

An iterative approach to system setup problems in flexible manufacturing systems

System setup problems in flexible manufacturing systems deal with short-term planning problems such as part type selection, machine grouping, operation assignment, tooling, fixture and pallet allocation, and routing. In this article, we consider three of the subproblems: part type selection, machine grouping, and loading. We suggest a heuristic approach to solve the subproblems consistently with the objective of maximizing the expected production rate. The proposed procedure includes routines to generate all possible machine grouping alternatives for a given set of machines, to obtain optimal target workloads for each grouping alternative, and to allocate operations and tools to machine groups. These routines are executed iteratively until a good solution to the system setup problem is obtained. Computational experience is reported.     

On finite-horizon control of genetic regulatory networks with multiple hard-constraints

Background

Probabilistic Boolean Networks (PBNs) provide a convenient tool for studying genetic regulatory networks. There are three major approaches to develop intervention strategies: (1) resetting the state of the PBN to a desirable initial state and letting the network evolve from there, (2) changing the steady-state behavior of the genetic network by minimally altering the rule-based structure and (3) manipulating external control variables which alter the transition probabilities of the network and therefore desirably affects the dynamic evolution. Many literatures study various types of external control problems, with a common drawback of ignoring the number of times that external control(s) can be applied.

Results

This paper studies the intervention problem by manipulating multiple external controls in a finite time interval in a PBN. The maximum numbers of times that each control method can be applied are given. We treat the problem as an optimization problem with multi-constraints. Here we introduce an algorithm, the "Reserving Place Algorithm'', to find all optimal intervention strategies. Given a fixed number of times that a certain control method is applied, the algorithm can provide all the sub-optimal control policies. Theoretical analysis for the upper bound of the computational cost is also given. We also develop a heuristic algorithm based on Genetic Algorithm, to find the possible optimal intervention strategy for networks of large size.

Conclusions

Studying the finite-horizon control problem with multiple hard-constraints is meaningful. The problem proposed is NP-hard. The Reserving Place Algorithm can provide more than one optimal intervention strategies if there are. Moreover, the algorithm can find all the sub-optimal control strategies corresponding to the number of times that certain control method is conducted. To speed up the computational time, a heuristic algorithm based on Genetic Algorithm is proposed for genetic networks of large size.

     

Process flexibility and inventory flexibility via product substitution

This paper studies the optimal control of and interaction between two types of flexibility under Markov models of demand and production: process flexibility and inventory flexibility. In our model, process flexibility is generated by a multi-functional production facility that can produce two types of products, and inventory flexibility is manifested in firm-driven one-way product substitution. Both process flexibility and inventory flexibility are important drivers of supply chain performance and are strategic design considerations. To analyze the interaction between these two types of flexibility, we model a dynamically controlled two-product, make-to-stock system with stochastic processing times and stochastic demand. We characterize the complex joint optimal production and post-production policy for a special case and numerically show that a simply structured multi-threshold policy is a near-optimal heuristic policy for the general case. We gain further insight into the impact of system parameters on the value of process flexibility and inventory flexibility via a comprehensive numerical study. We find that for a wide range of capacity and cost parameters, process flexibility and inventory flexibility complement each other, so pursuing both forms of flexibility is effective.     

Iterative pass optimization of sequence data

The problem of determining the minimum-cost hypothetical ancestral sequences for a given cladogram is known to be NP-complete. This "tree alignment" problem has motivated the considerable effort placed in multiple sequence alignment procedures. Wheeler in 1996 proposed a heuristic method, direct optimization, to calculate cladogram costs without the intervention of multiple sequence alignment. This method, though more efficient in time and more effective in cladogram length than many alignment-based procedures, greedily optimizes nodes based on descendent information only. In their proposal of an exact multiple alignment solution, Sankoff et al. in 1976 described a heuristic procedure--the iterative improvement method--to create alignments at internal nodes by solving a series of median problems. The combination of a three-sequence direct optimization with iterative improvement and a branch-length-based cladogram cost procedure, provides an algorithm that frequently results in superior (i.e., lower) cladogram costs. This iterative pass optimization is both computation and memory intensive, but economies can be made to reduce this burden. An example in arthropod systematics is discussed.     

Average-Cost Optimal Policies for an Unreliable Flexible Multiproduct Machine

This paper is concerned with optimal production planning on a single failure-prone flexible machine that produces N distinct part types. The machine is flexible in the sense that no setup is required for switching from production of one part type to another. We consider the problem of controlling production rates to minimize the expected long-run average cost of product surpluses over time. We assume constant unit holding and shortage costs and constant demand rates for the part types. Moreover, the costs are assumed to be the same for all products. We provide an explicit optimal solution for the problem.     

Loading problems with tool management in flexible manufacturing systems: A few integer programming models

In automated production systems like flexible manufacturing systems (FMSs), an important issue is to find an adequate workload for each machine for each time period. Many integer linear programming (ILP) models have been proposed to solve the FMS loading problems, but not all of them take tools into account. Those that do not consider tooling are quite unrealistic, especially when setup times are important with respect to processing times. When tool loading has to be handled by the model, the load assignment may have to be changed completely. In this article we consider FMSs with a tool management of the following type: the system works in time periods whose durations are fixed or not; and tools are loaded on the machines at the beginning of each time period and stay there for the whole time period. Tool changes may occur only at the end of each time period when the system is stopped. We present some integer programming models for handling these situations with several types of objectives. Emphasis is laid on the ILP formulations. Computational complexities are discussed.     

Analysis of a two-stage, flexible production system with unreliable machines, finite buffers and non-negligible setups

We analyze a Markov model of a two-stage production system capable of producing two part types. Each stage consists of an unreliable machine and the different stages are decoupled by two intermediate buffers of finite capacity, one for each part type. Unlike previous work, we specifically consider non-negligible machine setup times during changeovers and also assume that machine failure probabilities are dependent on the part type being produced. We assume that machine processing times, repair/failure times and setup times are exponentially distributed and may have different mean rates for each machine and for each part-type. We describe a solution method to evaluate the system performance that reduces the total number of equations to be solved from a multiplicative function to an additive function of buffer sizes. This model may then be integrated with a new decomposition method for analyzing longer lines. The results show the relative influence of different factors on system performance and thus provide guidance to the optimal choice of system parameters such as buffer sizes.     

Comparison of three flow line layouts with unreliable machines and profit maximization

Manufacturing system design is a complex challenge when a new factory is being built. Although some factories produce the same product, the layouts of the factories may be different. Manufacturing systems for automotive engines can be modelled with several types of queueing networks with finite buffers and unreliable machines. In this paper, three types of layout structures which are commonly used in automotive engine shops are compared with respect to maximizing profit that is determined by throughput and the investment cost of buffers. We assume that the service times are constant but inhomogeneous, and the time to failure and the time to repair are exponentially distributed. To solve this problem we used approximation methods which are based on aggregation and overlapping decomposition for computing performance measures, and a gradient search method for finding an optimal buffer allocation.     

Models for capacity acquisition decisions considering operational costs

In this article, we study a capacity acquisition problem by considering technology choice and operational factors in a stochastic environment. The motivation for our work comes from developments in modern flexible technologies and a problem encountered in a real industrial setting. We study the impact of operational factors such as setup times, demand patterns, and inventory/back order costs on the decisions of capacity acquisition and technology choice. We consider three alternatives in capacity and technology decisions: (i) a flexible system, (ii) a dedicated system, and (iii) a combination of these two systems. For each system, we develop a model that integrates investment decisions and operational decisions to determine an optimal amount of capacity to purchase and the time and the types of parts to produce. The objective is to minimize the capacity acquisition cost at the beginning of the planning horizon and the total expected operational costs over an infinite planning horizon. To solve the problem in this article, a solution procedure is proposed. Managerial insights are also derived from extensive computational results.     

Scheduling algorithms for a two-machine flexible manufacturing system

The flexible manufacturing system (FMS) considered in this paper is composed of two CNC machines working in series—a punching machine and a bending machine connected through rollers acting as a buffer system of finite capacity. The main difference between the present problem and the standard two-machine flow shop problem with finite intermediate capacity is precisely the buffer system, which in our problem consists of two stacks of parts supported by rollers: the first stack contains the output of the punching machine, while the second stack contains the input for the bending machine. When the second stack is empty, the first stack may be moved over. Furthermore, the capacity of each stack depends on the particular part type being processed. The FMS can manufacture a wide range of parts of different types. Processing times on the two machines are usually different so that an unbalance results in their total workload. Furthermore, whenever there is a change of the part type in production, the machines must be properly reset—that is, some tools need to be changed or repositioned. A second important difference between the present problem and the usual two-machine flow shop problem is the objective. Given a list ofp part types to be produced in known quantities, the problem considered here is how to sequence or alternate the production of the required part types so as to achieve various hierarchical targets: minimize the makespan (the total time needed to complete production) and, for instance, compress the idle periods of the machine with less workload into a few long enough intervals that could be utilized for maintenance or other reasons. Although Johnson's rule is optimal in some particular cases, the problem addressed in the paper isNP-hard in general: heuristic procedures are therefore provided.     

A framework for capacity planning and machine configuration in flexible assembly systems

We consider the problem of simultaneously determining the number of machines (and/or workers), the assignment of tasks (and related tools and components) to these machines, and the number of jobs circulating in a flexible assembly system (FAS), to satisfy steady-state throughput requirements for a family of similar products at minimum cost. We focus on situations where there are precedence relations among the various tasks, as is common in assembly systems. We present a framework for solving this problem based on a heuristic decomposition approach which involves the solution of only a few types of sub-problems. We demonstrate the efficiency and effectiveness of the overall procedure using a number of example problems.     

A production policy considering reworking of imperfect items and trade credit

Making production decisions that will reduce total cost is a goal that most manufacturers pursue actively. However, the traditional production model development assumed that all products are perfect quality, which is far from reality. Since trade credit is a popular payment method in today??s business environment, this paper analyzes the production problem under trade credit and imperfect product reworking conditions. This work extends the traditional production model by considering reworking imperfect items and trade credit to cope with realistic situations. The objective of this study is to determine the optimal production lot size while minimizing the total cost. This paper develops an easy-to-use algorithm to solve the problem described, provides numerical examples to illustrate the proposed solution procedure, and discusses the impact of various system parameters.     

Production planning of a flexible manufacturing system in a material requirements planning environment

Early flexible manufacturing system (FMS) production planning models exhibited a variety of planning objectives; typically, these objectives were independent of the overall production environment. More recently, some researchers have proposed hierarchical production planning and scheduling models for FMS. In this article, we examine production planning of FMS in a material requirements planning (MRP) environment. We propose a hierarchical structure that integrates FMS production planning into a closed-loop MRP system. This structure gives rise to the FMS/MRP rough-cut capacity planning (FMRCP) problem, the FMS/MRP grouping and loading (FMGL) problem, and the FMS/MRP detailed scheduling problem. We examine the FMRCP and FMGL problems in detail and present mathematical programming models for each of these problems. In particular, the FMRCP problem is modeled as a generalized assignment problem (GAP), and a GAP-based heuristic procedure is defined for the problem. We define a two-phase heuristic for the FMGL problem and present computational experience with both heuristics. The FMRCP heuristic is shown to solve problems that exhibit a dependent-demand relation within the FMS and with FMS capacity utilization as high as 99 percent. The FMGL heuristic requires very little CPU time and obtains solutions to the test problems that are on average within 1.5 percent of a theoretical lower bound. This FMS/MRP production planning framework, together with the resulting models, constitutes an important step in the integration of FMS technology with MRP production planning. The hierarchical planning mechanism directly provides for system-level MRP planning priorities to induce appropriate production planning and control objectives on the FMS while simultaneously allowing for necessary feedback from the FMS. Moreover, by demonstrating the tractability of the FMRCP and FMGL problems, this research establishes the necessary groundwork upon which to explore systemwide issues pertaining to the coordination of the hierarchical structure.     

最优化设计连续的自然保护区

生境破碎是导致生物多样性损失的重要原因之一,避免生境破碎的一个有效方式是建立连续的自然保护区使物种可在保护区内自由移动。不加选择地把大片土地都转为保护区是实现连续的一个途径,但资源是有限的,应当以最优的方式分配。如何最优化设计生态上和经济上都有效的保护区成为生物保护领域一个重要议题。从一组备选地块中选择一部分组成自然保护区,这样的问题主要有两种解法:启发式方法和最优化方法。启发式方法虽然灵活且运算速度快但不能保证最优解因而可能导致稀缺资源的浪费,最优化方法保证得到的解是最优的但建模和运算存在困难。建立一个线性整数规划模型用于设计一个最小的连续保护区,用Dantzig剪切法消除循环确保形成一个连续的树,对应一个连续的保护区,检验了模型的计算效率。结果显示,模型可在合理时间内解决一个包含100个备选地块和30个物种的连续保护区设计问题,计算效率显著优于同类目的的其它方法。以美国伊利诺伊州Cache河流域11种濒危鸟类的保护区设计为例说明了该方法的应用,设计了两种情况下连续的保护区。讨论了模型的局限和数据问题。     

Planning of distributed data production for High Energy and Nuclear Physics

Modern experiments in High Energy and Nuclear Physics heavily rely on distributed computations using multiple computational facilities across the world. One of the essential types of the computations is a distributed data production where petabytes of raw files from a single source has to be processed once (per production campaign) using thousands of CPUs at distant locations and the output has to be transferred back to that source. The data distribution over a large system does not necessary match the distribution of storage, network and CPU capacity. Therefore, bottlenecks may appear and lead to increased latency and degraded performance. In this paper we propose a new scheduling approach for distributed data production which is based on the network flow maximization model. In our approach a central planner defines how much input and output data should be transferred over each network link in order to maximize the computational throughput. Such plans are created periodically for a fixed planning time interval using up-to-date information on network, storage and CPU resources. The centrally created plans are executed in a distributed manner by dedicated services running at participating sites. Our simulations based on the log records from the data production framework of the experiment STAR (Solenoid Tracker at RHIC) have shown that the proposed model systematically provides a better performance compared to the simulated traditional techniques.