Planning the routing mix in FASs to minimize total transportation time

The routing mix problem in flexible assembly systems is considered. The problem consists of assigning the operations for each part to the machines, with the two objectives of balancing the machine workloads and minimizing the burden of the transportation system. These two objectives are sometimes conflicting, since the latter tends to support assigning operations to the same machine(s) as much as possible, and this may be bad for workload balancing. A linear programming problem is presented that, given a constraint on the workload of each machine, finds one solution that minimizes the overall time spent moving the parts from one machine to another. Since such a linear program may have an exponential number of variables, an efficient column generation technique to solve the problem is devised. The efficiency of the method is validated by experiments on a large number of random problems.     

Workload balance and part-transfer minimization in flexible manufacturing systems

Problems related to the flow management of a flexible manufacturing system (FMS) are here formulated in terms of combinatorial optimization. We consider a system consisting of several multitool automated machines, each one equipped with a possibly different tool set and linked to each other by a transportation system for part moving. The system operates with a given production mix. The focused flow-management problem is that of finding the part routings allowing for an optimal machine workload balancing. The problem is formulated in terms of a particular capacity assignment problem. With the proposed approach, a balanced solution can be achieved by routing parts on a limited number of different paths. Such a balancing routing can be found in polynomial time. We also give polynomial-time and-space algorithms for choosing, among all workload-balancing routings, the ones that minimize the global amount of part transfer among all machines.     

A heuristic algorithm for the loading problem in flexible manufacturing systems

The paper considers the loading problem in flexible manufacturing systems (FMSs). This problem involves the assignment to the machine tools of all operations and associated cutting tools required for part types that have been selected to be produced simultaneously. The loading problem is first formulated as a linear mixed 0–1 program with the objective to minimize the greatest workload assigned to each machine. A heuristic procedure is presented in which an assignment of operations to machine tools is obtained by solving a parameterized generalized assignment problem with an objective function that approximates the use of tool slots required by the operations assigned to the machines. The algorithm is coded in FORTRAN and tested on an IBM-compatible personal computer. Computational results are presented for different test problems to demonstrate the efficiency and effectiveness of the suggested procedure.     

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.     

Production Capacity Modeling of Alternative, Nonidentical, Flexible Machines

Analyzing the production capacity of a flexible manufacturing system consisting of a number of alternative, nonidentical, flexible machines, where each machine is capable of producing several different part types simultaneously (by flexibly allocating its production capacity among these part types), is not a trivial task. The production capacity set of such a system is naturally expressed in terms of the machine-specific production rates of all part types. In this paper we also express it in terms of the total production rates of all part types over all machines. More specifically, we express the capacity set as the convex hull of a set of points corresponding to all possible assignments of machines to part types, where in each assignment each machine allocates all its capacity to only one part type. First, we show that within each subset of assignments having a given number of machines assigned to each part type, there is a unique assignment that corresponds to an extreme point of the capacity set. Then, we propose a procedure for generating all the extreme points and facets of the capacity set. Numerical experience shows that when the number of part types is less than four, the size of the capacity set (measured in terms of the number of variables times the number of constraints) is smaller, if the capacity set is expressed in terms of the total production rates of all part types over all machines than if it is expressed in terms of the machine-specific production rates of all part types. When the number of part types is four or more, however, the opposite is true.     

A new branch and bound algorithm for loading problems in flexible manufacturing systems

Loading problems in flexible manufacturing systems involve assigning operations for selected part types and their associated tools to machines or machine groups. One of the objectives might be to maximize the expected production rate (throughput) of the system. Because of the difficulty in dealing with this objective directly, a commonly used surrogate objective is the closeness of the actual workload allocation to the continuous workload allocation that maximizes throughput. We test several measures of closeness and discuss correlations between these measures and throughput. Using the best measure, we show how to modify an existing branch and bound algorithm which was developed for the case of equal target workloads for all machine groups to accommodate unequal target workloads. We also develop a new branch and bound algorithm which can be used for both types of problems. The efficiency of the algorithm in finding optimal solutions is achieved through the application of better branching rules and improved dominance results. Computational results on randomly generated test problems indicate that the new algorithm performs well.     

Clustering algorithms to optimize the tool handling system management in an FMS

Tool management is recognized as a critical issue in flexible manufacturing facilities management. This article addresses the issue of tool management in a flexible system installed in an avionics components factory. The system is composed of two machining centers equipped with local tool magazines of limited capacity. A tool handling system is in charge of tool movements between the tool room and the two machines. Each machine is able to perform any operation, provided that it is equipped with the suitable tool. In this kind of installation, tool allocation must be determined, and tool movements must be synchronized in order to minimize operating costs, or, equivalently, maximize the productivity of the system. We propose an approach to production planning based on a clustering algorithm, which takes into account the tool requirements of each part program in the production batch. We also propose two different heuristics for the scheduling problem. A case study was conducted on the facility mentioned above. Two conflicting objectives can be identified for this kind of production system: the reduction of tools to be shared among machines and the reduction of workload unbalance. The tests and comparison made demonstrate how the proposed procedure leads to superior results in terms of both objectives.     

VRAA: virtualized resource auction and allocation based on incentive and penalty

Virtualization is widely used in cloud computing environments to efficiently manage resources, but it also raises several challenges. One of them is the fairness issue of resource allocation among virtual machines. Traditional virtualized resource allocation approaches distribute physical resources equally without taking into account the actual workload of each virtual machine and thus often leads to wasting. In this paper, we propose a virtualized resource auction and allocation model (VRAA) based on incentive and penalty to correct this wasting problem. In our approach, we use Nash equilibrium of cooperative games to fairly allocate resources among multiple virtual machines to maximize revenue of the system. To illustrate the effectiveness of the proposed approach, we then apply the basic laws of auction gaming to investigate how CPU allocation and contention can affect applications’ performance (i.e., response time), and its effect on CPU utilization. We find that in our VRAA model, the fairness index is high, and the resource allocation is closely proportional to the actual workloads of the virtual machines, so the wasting of resources is reduced. Experiment results show that our model is general, and can be applied to other virtualized non-CPU resources.     

Scheduling unrelated parallel machines in semiconductor manufacturing by problem reduction and local search heuristics

We investigate a difficult scheduling problem in a semiconductor manufacturing process that seeks to minimize the number of tardy jobs and makespan with sequence-dependent setup time, release time, due dates and tool constraints. We propose a mixed integer programming (MIP) formulation which treats tardy jobs as soft constraints so that our objective seeks the minimum weighted sum of makespan and heavily penalized tardy jobs. Although our polynomial-sized MIP formulation can correctly model this scheduling problem, it is so difficult that even a feasible solution can not be calculated efficiently for small-scale problems. We then propose a technique to estimate the upper bound for the number of jobs processed by a machine, and use it to effectively reduce the size of the MIP formulation. In order to handle real-world large-scale scheduling problems, we propose an efficient dispatching rule that assigns a job of the earliest due date to a machine with least recipe changeover (EDDLC) and try to re-optimize the solution by local search heuristics which involves interchange, translocation and transposition between assigned jobs. Our computational experiments indicate that EDDLC and our proposed reoptimization techniques are very efficient and effective. In particular, our method usually gives solutions very close to the exact optimum for smaller scheduling problems, and calculates good solutions for scheduling up to 200 jobs on 40 machines within 10 min.     

A Look-Ahead Routing Procedure for Machine Selection in a Highly Informative Manufacturing System

Many dispatching rules have been developed for the on-line control of product flow in a job shop. The introduction of a highly informative manufacturing system (HIMS) has added a new requirement to a classical job-shop control problem: the selection of machines by parts of different types. An HIMS can keep a great deal of information on the status of the system, such as information on what is scheduled in the near future with great accuracy, which can be used for shop floor control. For example, the knowledge of the time when the next parts arrive at the machines can be used for better routing. This article tests the effect of the use of this knowledge for part routing on the part's flow time and tardiness under a look-ahead routing procedure (LARP). LARP assigns a new part to a machine so that the assignment minimizes the flow time or tardiness of the current part and the next N parts arriving after the current part. A test shows that the reduction of part flow time is up to 11% and the reduction of tardiness is up to 21% for the cases with this procedure.     

Tool addition strategies for flexible manufacturing systems

The allocation of tools to machines determines potential part routes in flexible manufacturing systems. Given production requirements and a minimum feasible set of tools, the decision of how to fill vacant slots in tool magazines to maximize routing flexibility is shown to be a minimum cost network flow problem for the cases when routing flexibility is a function of the average workload per tool aggregated over tool types, or of the number of possible routes through the system. A linear programming model is then used to plan a set of routes for each part type so as to minimize either the material handling requirement or the maximum workload on any machine. The impact of these tool addition strategies on the material handling and workload equalization is investigated and computational results presented. The advantage of the overall approach is computational simplicity at each step and the ability to react to dynamic changes.     

Component Partitioning Under Demand and Capacity Uncertainty in Printed Circuit Board Assembly

This paper considers the problem of configuring a printed circuit board (PCB) assembly line experiencing uncertainty in demand and capacity. The PCB assembly process involves a single line of automatic placement machines, a variety of board types, and a number of component types. The line is set up only once, at the beginning of a production cycle, to eliminate setups between board types. Using this strategy, the line therefore can assemble all different types of PCBs without feeder changes. The problem then becomes to partition component types to the different machines in the hope of processing all boards quickly with a good workload balance. In this paper, the board demands and machine breakdowns are random but follow some probability distribution, which can be predicted from past observations of the system. We formulate this problem as a stochastic mixed-integer programming formulation with the objective of minimizing the expected makespan for assembling all PCBs during a production cycle. The results obtained indicate significant improvement over the existing methods. We hope that this research will provide more PCB assembly facilities with models and techniques to hedge against variable forecasts and capacity plans     

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.     

A study of nurse scheduling in Japan

Scheduling nurses to staff shifts is a major problem in hospitals. The necessity of maintaining a certain level of service and skill in the makeup of every shift, while balancing the workload among the nurses involved, is incredibly difficult. It is often impossible to develop a schedule which satisfies all the requirements despite the time and resources spent in the effort. This paper summarizes all our published research on nurse scheduling to date. The difficulties realized by our two investigations in Japan are shown first, together with a resulting scheduling problem. The nurse scheduling model based on the results is then described. In this model, all constraints are divided into two essentially different types; that which maintains a certain level of skill for each shift ('shift constraints') and that which concerns the workload for each nurse ('nurse constraints'). By classifying the constraints in this manner, we can determine what is affected by a specific constraint when the constraint is not satisfied. We developed efficient algorithms while taking advantage of the structure of this model. Finally, it is shown that our algorithm can solve this problem for a 2-shift system efficiently.     

A Genetic Algorithm Approach to the Scheduling of FMSs with Multiple Routes

Usually, most of the typical job shop scheduling approaches deal with the processing sequence of parts in a fixed routing condition. In this paper, we suggest a genetic algorithm (GA) to solve the job-sequencing problem for a production shop that is characterized by flexible routing and flexible machines. This means that all parts, of all part types, can be processed through alternative routings. Also, there can be several machines for each machine type. To solve these general scheduling problems, a genetic algorithm approach is proposed and the concepts of virtual and real operations are introduced. Chromosome coding and genetic operators of GAs are defined during the problem solving. A minimum weighted tardiness objective function is used to define code fitness, which is used for selecting species and producing a new generation of codes. Finally, several experimental results are given.     

A flexible crane scheduling methodology for container terminals

In this paper, we propose a flexible neighbourhood search strategy for quay crane scheduling problems based on the framework of tabu search (TS) algorithm. In the literature, the container workload of a ship is partitioned into a number of fixed jobs to deal with the complexity of the problem. In this paper, we propose flexible jobs which are dynamically changed by TS throughout the search process to eliminate the impact of fixed jobs on the generated schedules. Alternative job sequences are investigated for quay cranes and a new quay crane dispatching policy is developed to generate schedules. Computational experiments conducted with problem instances available in the literature showed that our algorithm is capable of generating quality schedules for quay crane handling operations at reasonable times.     

Sequencing of Parts in Robotic Cells

This paper considers scheduling problems in robotic cells that produce a set of part types on several machines served by one robot. We study the problem of sequencing parts of different types in a cell to minimize the production cycle time when the sequence of the robot moves is given. This problem is NP-hard for most of the one-unit robot move cycles in a robotic cell with more than two machines and producing more than two part types. We first give a mathematical formulation to the problem, and then propose a branch-and-bound algorithm to solve it. The bounding scheme of this algorithm is based on relaxing, for all of the machines except two, the constraints that a machine should be occupied by a part for a period at least as long as the processing time of the part. The lower bound obtained in this way is tight. This relaxation allows us to overcome the complexity of the problem. The lower bound can be computed using the algorithm of Gilmore and Gomory. Computational experiments on part sequencing problems in three-machine robotic cells are given.     

A note on productivity gains in flexible robotic cells

Flexible robotic cells combine the capabilities of robotic flow shops with those of flexible manufacturing systems. In an m-machine flexible cell, each part visits each machine in the same order. However, the m operations can be performed in any order, and each machine can be configured to perform any operation. We derive the maximum percentage increase in throughput that can be achieved by changing the assignment of operations to machines and then keeping that assignment constant throughout a lot's processing. We find that no increase can be gained in two-machine cells, and that the gain in three- and four-machine cells each is at most 14 \(\frac{2}{7}\)%.     

An inexact algorithm for part input sequencing and scheduling with side constraints in FMS

Consider a flexible manufacturing system that produces parts of several types. The FMS consists of several groups of pooled, identical machines, a materials handling system, and a set of nonconsumable resources. Each type of part has its own unique sequence in the execution of the operations. An inexact algorithm is presented that sequences and schedules the input of the parts in the FMS by considering constraints such as machine availabilities and other resources in the machine groups, the availability of the transport units, and so on. Primarily, the goal of the algorithm is to minimize makespan and, secondarily, to minimize turnaround time. Several strategies are discussed, and the results are reported. A real-life problem is described.     

Exact methods for the robotic cell problem

This paper investigates an exact method for the Robotic Cell Problem. We present a branch-and-bound algorithm which is the first exact procedure specifically designed with regard to this complex flow shop scheduling variant. Also, we propose a new mathematical programming model as well as new lower bounds. Furthermore, we describe an effective genetic algorithm that includes, as a mutation operator, a local search procedure. We report the results of a computational study that provides evidence that medium-sized instances, with up to 176 operations, can be optimally solved. Also, we found that the new proposed lower bounds outperform lower bounds from the literature. Finally, we show, that the genetic algorithm delivers good solutions while requiring short CPU times.