Measurement of loading and operations flexibility in flexible manufacturing systems: An information-theoretic approach

An information-theoretic approach is applied for measuring the flexibility in flexible manufacturing systems (FMSs). The general relation between flexibility and entropy is discussed. The entropy for a Markovian process is obtained and then applied to closed queueing network models of FMSs to discuss loading flexibility which arises from the power to regulate the frequency of the visit of a part to different work stations. The concept of operations entropy as a measure of operations flexibility, which arises from the power to choose the work station and the corresponding operations, is introduced. The operations entropy has been decomposed into entropies within and between operations and entropies within and between groups of operations. This measure has been used to determine the next operation to be performed on a part by using the principle of least reduction of flexibility.The present paper is an improved version of the paper On measurement of flexibility in flexible manufacturing systems: An information-theoretic approach, presented at the II ORSA/TIMS Special Conference on Flexible Manufacturing Systems, held at Ann Arbor in August 1986.     

柔性制造系统的载荷模型和对偶分解算法

本文研究柔性制造系统最优排序问题的载荷模型，通过优化系统的最优利用率并考虑系统各机器的工作平衡，本文给出了载荷问题三个新的优化模型，这些模型形成具有０－１变量和一般整型变量的大规模整数规划问题，根据分解理论，考虑到问题的变量特性，这些大规模问题可被分解成若干维数较低的子问题求解，文章还给出了一个对偶分解算法。     

Queueing models for a flexible machining station Part II: The method of Coxian phases

A work station of a flexible manufacturing system (fms) is modeled as a multi-server queue with finite waiting room. The interarrival/service time distributions have squared coefficients of variations not less than 0.5 and are modeled as Coxian laws of two phases. A recursive scheme is developed to calculate the equilibrium queue length distribution. The model, together with the diffusion approximation model of Part I, can be used to aid the design of fms work stations.     

A Petri Net based algorithm for minimizing total tardiness in flexible manufacturing systems

Petri Nets have been extensively used for modeling and simulating of the dynamics of flexible manufacturing systems. Petri Nets can capture features such as parallel machines, alternative routings, batch sizes, multiplicity of resources, to name but a few. However, Petri Nets have not been very popular for scheduling in manufacturing due to the Petri Net “state explosion” combined with the NP-hard nature of many of such problems. A promising approach for scheduling consists of generating only portions of the Petri Net state space with heuristic search methods. Thus far, most of this scheduling work with Petri Nets has been oriented to minimize makespan. The problem of minimizing total tardiness and other due date-related criteria has received little attention. In this paper, we extend the Beam A^* Search algorithm presented in a previous work with capability to handle the total tardiness criterion. Computational tests were conducted on Petri Net models of both flexible job shop and flexible manufacturing systems. The results suggest that the Petri Net approach is also valid to minimize due date related criteria in flexible systems.     

An interactive approach to bicriterion loading of a flexible assembly system

This paper presents integer programming formulations and an interactive solution procedure for a bicriterion loading problem in a flexible assembly system. The system is made up of a set of assembly stations linked with an automated material handling system. In the system, several different product types can be assembled simultaneously. The problem objective is to assign assembly tasks and products to stations with limited working space, so as to balance the station workloads and to minimize station-to-station product transfer time, subject to precedence relations among the tasks for a mix of product types. The solution procedure proposed is based on the weighting method and the interactive search for a set of weights which would produce the most preferred nondominated solution. Numerical examples are included to illustrate possible applications of the interactive approach for various problem formulations proposed.     

Exact solution procedures for the balanced unidirectional cyclic layout problem

In this paper, we consider the balanced unidirectional cyclic layout problem (BUCLP) arising in the determination of workstation locations around a closed loop conveyor system, in the allocation of cutting tools on the sites around a turret, in the positioning of stations around a unidirectional single loop AGV path. BUCLP is known to be NP-Complete. One important property of this problem is the balanced material flow assumption where the material flow is conserved at every workstation. We first develop a branch-and-bound procedure by using the special material flow property of the problem. Then, we propose a dynamic programming algorithm, which provides optimum solutions for instances with up to 20 workstations due to memory limitations. The branch and bound procedure can solve problems with up to 50 workstations.     

Covering and connectivity constraints in loop-based formulation of material flow network design in facility layout

The shortest loop covering at least one edge of each workcenter in a manufacturing facility layout is an instance of the generalized traveling salesman problem. The optimal solution to this problem is a promising design for non-vehicle-based material handling, typical of most types of conveyors and power-and-free systems, where the length of the path is the main driver of the total investment costs. The loop formulation is usually embedded within a larger problem of the concurrent design of the loop and the input/output stations for vehicle-based material handling typical of automatically guided vehicles and autonomous delivery robots. In these systems, it is not the length, but the total flow of the loaded and empty vehicles that drives the objective function. It has been shown that the shortest loop provides an effective heuristic scheme to achieve prosperous and robust solutions for the concurrent design of the loop and input/output stations. We review and compare covering constraints formulations, provide new insight into connectivity constraints, improve the model formulation and its solution procedure, and report computational results.     

A survey on problems and methods in generalized assembly line balancing

Assembly lines are traditional and still attractive means of mass and large-scale series production. Since the early times of Henry Ford several developments took place which changed assembly lines from strictly paced and straight single-model lines to more flexible systems including, among others, lines with parallel work stations or tasks, customer-oriented mixed-model and multi-model lines, U-shaped lines as well as unpaced lines with intermediate buffers.In any case, an important decision problem, called assembly line balancing problem, arises and has to be solved when (re-) configuring an assembly line. It consists of distributing the total workload for manufacturing any unit of the product to be assembled among the work stations along the line.Assembly line balancing research has traditionally focused on the simple assembly line balancing problem (SALBP) which has some restricting assumptions. Recently, a lot of research work has been done in order to describe and solve more realistic generalized problems (GALBP). In this paper, we survey the developments in GALBP research.     

Flowshop Scheduling of Robotic Cells with Job-dependent Transportation and Set-up Effects

A flexible manufacturing cell consisting of two machining centres, several automated storage/retrieval stations, and a mobile transporting robot is considered. The problem is to schedule jobs on machines so as to minimize the makespan, with the effects of transportation and set-ups to be taken into account. The problem is studied with the aid of a graph model, and an exact algorithm of cubic complexity is derived based on the Gilmore–Gomory algorithm for the travelling salesman problem.     

Column generation approaches to ship scheduling with flexible cargo sizes

We present a Dantzig–Wolfe procedure for the ship scheduling problem with flexible cargo sizes. This problem is similar to the well-known pickup and delivery problem with time windows, but the cargo sizes are defined by intervals instead of by fixed values. The flexible cargo sizes have consequences for the times used in the ports because both the loading and unloading times depend on the cargo sizes. We found it computationally hard to find exact solutions to the subproblems, so our method does not guarantee to find the optimum over all solutions. To be able to say something about how good our solution is, we generate a bound on the difference between the true optimal objective and the objective in our solution. We have compared our method with an a priori column generation approach, and our computational experiments on real world cases show that our Dantzig–Wolfe approach is faster than the a priori generation of columns, and we are able to deal with larger or more loosely constrained instances. By using the techniques introduced in this paper, a more extensive set of real world cases can be solved either to optimality or within a small deviation from optimality.     

Hierarchical Stochastic Production Planning with Delay Interaction

This paper explores the problem of hierarchical stochastic production planning (HSPP) for flexible automated workshops (FAWs), each consisting of a number of flexible manufacturing systems (FMSs). The objective is to devise a production plan which tells each FMS how many parts to produce and when to produce them so as to simultaneously minimize the amount of work in progress, maximize the machine utilization, and satisfy demands for finished products over a finite horizon of N time periods. Here, the problem formulation includes not only uncertainty in demand, capacities, and material supply (which is standard in the literature), but also uncertainties in processing times, rework, and waste products. It considers also multiple products and multiple time periods. This is in contrast to most work which looks at either a single periods or at an infinite horizon. The delay interaction aspect arises from taking into account the transportation of parts between FMSs. Apparently, any job which requires processing on more than one FMS cannot be transported directly from one FMS to the next. Instead, a semifinished product completed in one period must be put into shop storage until some future time period at which it can be transported to the next FMS for further processing. Herein, a stochastic interaction/prediction algorithm is developed by using standard calculus of variations techniques. By means of the software package developed, many HSPP examples have been studied, showing that the algorithm is very effective.     

Optimal and Heuristic Procedures for Row Layout Problems in Automated Manufacturing Systems

In many automated manufacturing environments, particularly flowlines and flexible manufacturing systems (FMSs), machines are arranged along a straight material handling track with a material handling device moving jobs from one machine to aother. These layouts are referred to as row machine layouts. In this paper we study the Row Layout Problem (RLP) under the design objective of minimizing the total backtracking distance of the material handling device, which is a NP-complete problem. We propose the use of a dynamic programming algorithm for its solution. Special cases of the problem, usually encountered in flexible manufacturing cells and which can be solved with polynomial procedures, are also discussed. For the equidistant case (i.e., successive candidate locations are in equal distances), we formulate the problem as an integer linear program. The use of standard mathematical programming codes can efficiently solve this formulation. Two effective heuristic procedures, which explore simple ideas based on local optimality conditions, are also presented. Extensive computational results demonstrate the effectiveness of such heuristics.     

Hybrid approaches to optimize mixed-model assembly lines in low-volume manufacturing

In this paper, a production planning problem for mixed-model assembly lines in low-volume manufacturing as can be found in aircraft manufacturing is considered. This type of manufacturing is labor-intensive. Low-volume production of huge-sized jobs, i.e. airplanes, is typical. Balancing labor costs and inventory holding costs assuming a given job sequence is the purpose of this paper. Therefore, worker assignments to each station and start times and processing times for each job on each station are determined. Two different mathematical models are proposed. The first formulation is a time-indexed linear formulation that allows for a flexible allocation of workers to periods and stations while the second one has a non-linear objective function and allows only for a fixed assignment of workers to stations. It is proven that the second formulation leads to a linear program with continuous decision variables if the values of the decision variables that determine the number of workers assigned to a station are given, while the first formulation contains even in this situation binary decision variables. Heuristics that hybridize the mathematical formulations with variable neighborhood search techniques are proposed. Computational experiments on randomly generated problem instances and on real-world instances demonstrate the high performance of the heuristics.     

Analysis of a finite capacity assembly system

Consider a finite capacity automatic assembly system consisting of a set of tandem work stations linked by a material handling system. Each work station consists of a set of machines and a local preprocessed inventory. The material handling system consists of a set of continuous line conveyors. Each conveyor has a beginning and an end with a specified length, velocity and capacity. The performance of the above manufacturing system is analyzed based on a mixed queuing network model, in the steady state. A methodology is presented for controlling blocking of the manufacturing system such that the probability of finding either a work station or a conveyor blocked will be sufficiently close to zero. Finally, numerical results are provided and the concluding remarks are discussed.     

Machine-part cell formation using biclustering

Cellular manufacturing is the cornerstone of many modern flexible manufacturing techniques, taking advantage of the similarities between parts in order to decrease the complexity of the design and manufacturing life cycle. Part-Machine Grouping (PMG) problem is the key step in cellular manufacturing aiming at grouping parts with similar processing requirements or similar design features into part families and by grouping machines into cells associated to these families. The PMG problem is NP-complete and the different proposed techniques for solving it are based on heuristics. In this paper, a new approach for solving the PMG problem is proposed which is based on biclustering. Biclustering is a methodology where rows and columns of an input data matrix are clustered simultaneously. A bicluster is defined as a submatrix spanned by both a subset of rows and a subset of columns. Although biclustering has been almost exclusively applied to DNA microarray analysis, we present that biclustering can be successfully applied to the PMG problem. We also present empirical results to demonstrate the efficiency and accuracy of the proposed technique with respect to related ones for various formations of the problem.     

Optimal workforce assignment to operations of a paced assembly line

We study a paced assembly line intended for manufacturing different products. Workers with identical skills perform non-preemptable operations whose assignment to stations is known. Operations assigned to the same station are executed sequentially, and they should follow the given precedence relations. Operations assigned to different stations can be performed in parallel. The operation’s processing time depends on the number of workers performing this operation. The problem consists in assigning workers to operations such that the maximal number of workers employed simultaneously in the assembly line is minimized, the line cycle time is not exceeded and the box constraints specifying the possible number of workers for each operation are not violated. We show that the general problem is NP-hard in the strong sense, develop conventional and randomized heuristics, propose a reduction to a series of feasibility problems, present a MILP model for the feasibility problem, show relation of the feasibility problem to multi-mode project scheduling and multiprocessor scheduling, establish computational complexity of several special cases based on this relation and provide computer experiments with real and simulated data.     

A lexicographic approach to bi-objective loading of a flexible assembly system

The paper presents a bi-objective integer program and an approximative lexicographic approach for a bicriterion loading and routing problem in a flexible assembly system. The problem objective is to determine an allocation of tasks among the assembly stations for a set of products so as to balance station workloads and minimize total interstation transfer time. In the approach proposed, first the station workloads are balanced using a linear relaxation-based heuristic and then assembly routes are selected based on a network flow model. An illustrative example is provided and some results of computational experiments are reported.     

Exact and heuristic procedures for the material handling circular flow path design problem

In this study we develop optimization, decomposition, and heuristic procedures to design a unidirectional loop flow pattern along with the pickup and delivery station locations for unit load automated material handling vehicles. The layout of the facility is fixed, the edges on the boundary of the manufacturing cells are candidates to form the unidirectional loop flow path, and a set of nodes located at an intermediate point on each edge are candidates for pickup and delivery stations of the cell formed by those edges. The objective is to minimize the total loaded and empty vehicle trip distances. The empty vehicle dispatching policy underlying the model is the shortest trip distance first. A binary integer programming model describes the problem of determining the flow path and locations of the pickup and delivery stations in which we then provide a decomposition procedure based on a loop enumeration strategy coupled with a streamlined integer linear programming model. It is shown that only a small proportion of all loops have to be enumerated to reach an optimum. Therefore a truncated version of this algorithm should yield a good heuristic. Finally we propose a neighbourhood search heuristic method and report on its performance.     

Optimal allocation of work in assembly lines for lots with homogenous learning

This paper deals with the problem of allocating work to the stations of an assembly line to minimize the makespan of a lot of products with a low overall demand. There is no buffer permitted in between the stations, and the line operates under homogeneous learning (i.e., under the same learning rate for all stations). We show that in the presence of learning, the optimal makespan requires imbalanced allocation of work to stations. The level of savings in the optimal makespan value due to the imbalanced loading of work over the balanced loading case are demonstrated as a function of the value of the learning constant, number of stations on the line as well as lot size. These savings can be quite significant under the case of low overall demand.