Flexible machine layout design for dynamic and uncertain production environments

Flexible manufacturing systems operate in a dynamic environment and face considerable uncertainty in production demands. The development of a flexible machine layout is a critical issue in creating a system that can respond effectively to these requirements. Unlike most existing methods for creating flexible layout designs, the procedure developed in this paper is not restricted to equal size machines. It optimizes the trade-offs between increased material handling costs as requirements change and machine rearrangement costs needed to adapt the layout to these changes. The proposed flexible machine layout design procedure formulates and solves a robust machine layout design problem over a rolling horizon planning time window. The formulation, details of the solution methodology, illustrative examples, and computational results are presented.     

Knapsack-based Algorithms for Designing Cellular Manufacturing Systems

In this paper, we use a 0–1 linear programming model for the machine assignment problem in cellular manufacturing. The formulated machine assignment problem considers many manufacturing factors such as machine utilization cost, cost of intercellular moves, part demand, and operating time capacity. The problem is shown to be NP-complete. Two designing algorithms are proposed to exploit the problem structure of the knapsack problem. Computational experience of the two algorithms is also reported.     

Iterative algorithms for part grouping and loading in cellular reconfigurable manufacturing systems

A reconfigurable manufacturing system (RMS), one of state-of-the-art manufacturing system technologies, is the one designed at the outset for rapid changes in its hardware and software components in order to quickly adjust its production capacity and functionality in response to market or system changes. In this study, we consider a cellular RMS with multiple reconfigurable machining cells (RMCs), each of which has numerical control machines, a setup station, and an automatic material handling and storage system. Each machine within the RMC has an automatic tool changer and a tool magazine of a limited capacity. Two important operational problems, part grouping and loading, are considered in this study. Part grouping is the problem of allocating parts to RMCs, and loading is the problem of allocating operations and their cutting tools to machines within the RMC. An integer programming model is suggested to represent the two problems at the same time for the objective of balancing the workloads assigned to machines. Then, due to the complexity of the problem, we suggest two iterative algorithms in which the two problems are solved repeatedly until a solution is obtained. Computational experiments were done on various test instances and the results are reported.     

Integrated production and material handling scheduling using mathematical programming and constraint programming

In this article, we propose an integrated formulation of the combined production and material handling scheduling problems. Traditionally, scheduling problems consider the production machines as the only constraining resource. This is however no longer true as material handling vehicles are becoming more and more valuable resources requiring important investments. Their operations should be optimized and above all synchronized with machine operations. In the problem addressed in this paper, a job shop context is considered. Machines and vehicles are both considered as constraining resources. The integrated scheduling problem is formulated as a mathematical programming model and as a constraint programming model which are compared for optimally solving a series of test problems. A commercial software (ILOG OPLStudio) was used for modeling and testing both models.     

A novel approach for considering layout problem in cellular manufacturing systems with alternative processing routings and subcontracting approach

In this paper a new integrated approach is presented for designing cellular manufacturing system and its inter- and intra-cell layouts. Various production factors such as part demands, alternative processing routings, operation sequences, processing times, capacity of machines, etc. are incorporated in the problem in order to extend its applicability. To increase the accuracy of the inter- and intra-cell layout design, the material handling cost is calculated in terms of the actual position of machines within the cells and regarding the dimensions of the machines and aisle distances. Also, a subcontracting approach is proposed to determine the production volume of parts within the CF and layout design process regarding the production, material handling and outsourcing costs and under demand and machine capacity constraints. To the best of our knowledge, this is the first study that addresses all these design features simultaneously. As the proposed problem is NP-hard, an efficient GA is employed to solve it. Finally, numerical examples adopted from the literature are used to verify the proposed approach.     

A large scale machine loading problem in flexible assembly

Flexible manufacturing is characterized by versatile work stations with minimum change over times and a versatile material handling system. The loading problem in flexible manufacturing is to assign tools, material, operations and jobs to work stations in order to minimize the total number of job-to-work station assignments. In this paper, we describe a special case of the general loading problem applied to flexible assembly and develop a discrete optimization model. We then discuss approaches for obtaining good heuristic solutions and present results for a large scale study.     

Estimating Stochastically Ordered Survival Functions via Geometric Programming

Many procedures have been proposed to compute nonparametric maximum likelihood estimators (NPMLEs) of survival functions under stochastic ordering constraints. However, each of them is only applicable to a specific type of stochastic ordering constraint and censoring, and is often hard to implement. In this article, we describe a general and flexible method based on geometric programming for computing the NPMLEs from right- or interval-censored data. To this end, we show that the monotonicity properties of the likelihood function and the stochastic ordering constraints considered in the literature allow us to reformulate the estimation problem as a geometric program (GP), a special type of mathematical optimization problem, which can be transformed to a convex optimization problem, and then solved globally and efficiently. We apply this GP-based method to real data examples to illustrate its generality in handling different types of ordering constraints and censoring. We also conduct simulation studies to examine its numerical performance for various sample sizes. Supplemental materials including technical details, computer code, and data files are available online.     

Detailed layout planning for irregularly-shaped machines with transportation path design

In order to obtain a competitive level of productivity in a manufacturing system, efficient machine or department arrangements and appropriate transportation path structures are of considerable importance. By defining a production system’s basic structure and material flows, the layout determines its operational performance over the long term. However, most approaches proposed in the literature provide only a block layout, which neglects important operational details. By contrast, in this paper, we introduce approaches to planning layouts at a more detailed level. Hence, this present paper introduces an integrated approach which allows a more detailed layout planning by simultaneously determining machine arrangement and transportation paths. Facilities to be arranged as well as the entire layout may have irregular shapes and sizes. By assigning specific attributes to certain layout subareas, application-dependent barriers within the layout, like existing walls or columns, can be incorporated. We introduce a new mathematical layout model and develop several improvement procedures. An analysis of the computational experiments shows that more elaborate heuristics using variable neighborhoods can generate promising layout configurations.     

Forming and scheduling jobs with capacitated containers in semiconductor manufacturing: Single machine problem

We study a scheduling problem motivated by the challenges observed in the newest semiconductor manufacturing wafer fabrication facilities. As wafers are larger and heavier in these wafer fabs, it is becoming more common to use specialized material handling containers that carry multiple orders coming from different customers and to schedule the containers as jobs in the fab. The system performance is a function of the completion times of orders, which ultimately depend on both (1) how the orders are assigned to such containers (“job formation”), and (2) how the containers are scheduled in the fab (“job scheduling”). The overall problem is to find the best way to form and schedule the jobs subject to complicating constraints, including the restrictions on the number of containers that can be used at one time and on the number of wafers the containers can carry. We focus on the single machine job formation and scheduling problem with the total completion time objective. We show that this problem is quite different from conventional parallel and serial batching scenarios and prove that the uncapacitated special case is polynomially solvable and the capacitated case is strongly NP-hard. We use a dynamic programming algorithm to solve the uncapacitated problem, which not only provides tight lower bounds for the capacitated problem, but also becomes a basis for a heuristic approach for the capacitated problem. The computational results show that this approach is very effective, leading to small optimality gaps that get even smaller as the problems become larger.     

Reducing work-in-process movement for multiple products in one-dimensional layout problems

This research describes a method to assign M machines, which are served by a material handling transporter, to M equidistant locations along a track, so that the distance traveled by a given set of jobs is minimized. Traditionally, this problem (commonly known as a machine location problem) has been modeled as a quadratic assignment problem (QAP), which is NP-hard, thus motivating the need for efficient procedures to solve instances with several machines. In this paper we develop a branching heuristic to obtain sub-optimum solutions to the problem; a lower bound on the optimum solution has also been presented. Results obtained from the heuristics are compared with results obtained from other heuristics with similar objectives. It is observed that the results are promising, and justify the usage of developed methods.     

The offshore wind farm array cable layout problem: a planar open vehicle routing problem

In an offshore wind farm (OWF), the turbines are connected to a transformer by cable routes that cannot cross each other. Finding the minimum cost array cable layout thus amounts to a vehicle routing problem with the additional constraints that the routes must be embedded in the plane. For this problem, both exact and heuristic methods are of interest. We optimize cable layouts for real-world OWFs by a hop-indexed integer programming formulation, and develop a heuristic for computing layouts based on the Clarke and Wright savings heuristic for vehicle routing. Our heuristic computes layouts on average only 2% more expensive than the optimal layout. Finally, we present two problem extensions arising from real-world OWF cable layouts, and adapt the integer programming formulation to one of them. The thus obtained optimal layouts are up to 13% cheaper than the actually installed layouts.     

Exploiting process plan flexibility in production scheduling: A multi-objective approach

When solving a product/process design problem, we must exploit the available degrees of freedom to cope with a variety of issues. Alternative process plans can be generated for a given product, and choosing one of them has implications on manufacturing functions downstream, including planning/scheduling. Flexible process plans can be exploited in real time to react to machine failures, but they are also relevant for off-line scheduling. On the one hand, we should select a process plan in order to avoid creating bottleneck machines, which would deteriorate the schedule quality; on the other one we should aim at minimizing costs. Assessing the tradeoff between these possibly conflicting objectives is difficult; actually, it is a multi-objective problem, for which available scheduling packages offer little support. Since coping with a multi-objective scheduling problem with flexible process plans by an exact optimization algorithm is out of the question, we propose a hierarchical approach, based on a decomposition into a machine loading and a scheduling sub-problem. The aim of machine loading is to generate a set of efficient (non-dominated) solutions with respect to the load balancing and cost objectives, leaving to the user the task of selecting a compromise solution. Solving the machine loading sub-problem essentially amounts to selecting a process plan for each job and to routing jobs to the machines; then a schedule must be determined. In this paper we deal only with the machine loading sub-problem, as many scheduling methods are already available for the problem with fixed process plans. The machine loading problem is formulated as a bicriterion integer programming model, and two different heuristics are proposed, one based on surrogate duality theory and one based on a genetic descent algorithm. The heuristics are tested on a set of benchmark problems.     

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.     

The effect of material flow and workload on the performance of machine location heuristics

Depending on the problem structure and routing strategies a machine location problem plays an important role in controlling the material flow of work-in-process in discrete product manufacturing environment. In this paper we investigate the effect of material flow and workload on the performance of heuristics for solving an important design problem for job routing and material flow in a manufacturing system. In this research we first develop a model for workload or traffic intensity between machines in a shop floor and then identify different structures of the problems, especially the data. This measure is then used to evaluate the effect of workload on efficiency of the heuristics to solve machine location problems. Some concluding remarks are made on to the effect of the workload or the traffic intensity of materials within the machine cell on the performance of some known heuristics. Conclusions are also made on the performance measures such as makespan, transporter utilization and machine utilization, depending on the problem and data structures.     

Layout design for flexible manufacturing systems considering single-loop directional flow patterns

To achieve high productivity in a flexible manufacturing system (FMS), an efficient layout arrangement and material flow path design are important due to the large percentage of product cost that is related to material handling. The layout design problem addressed in this paper has departments with fixed shapes and pick-up/drop-off points. It is an open-field type layout with single-loop directed flow path. A two-step heuristic is proposed to solve the problem. It first solves a traditional block layout with directed-loop flow path to minimize material handling costs by using a combined spacefilling curve and simulated annealing algorithm. The second step of the proposed methodology uses the resulting flow sequence and relative positioning information from the first step as input to solve the detailed FMS layout, which includes the spatial coordinates and orientation of each FMS cell. This detailed FMS layout problem is formulated and solved as a mixed integer program. Empirical illustrations show promising results for the proposed methodology in solving real-world type problems.     

A hybrid simulated annealing for solving an extended model of dynamic cellular manufacturing system

This paper develops a mixed-integer programming model to design the cellular manufacturing systems (CMSs) under dynamic environment. In dynamic environment, the product mix and part demand change under a multi-period planning horizon. Thus, the best designed cells for one period may not be efficient for subsequent periods and reconfiguration of cells is required. Reconfiguration may involve adding, removing or relocating machines; it may also involve a change in processing rout of part types from a period to another. The advantages of the proposed model are as follows: considering the batch inter/intra-cell material handling by assuming the sequence of operations, considering alternative process plans for part types, and considering machine replication. The main constraints are maximal cell size and machine time-capacity. The objective is to minimize the sum of the machine constant and variable costs, inter- and intra-cell material handling, and reconfiguration costs. An efficient hybrid meta-heuristic based on mean field annealing (MFA) and simulated annealing (SA) so-called MFA–SA is used to solve the proposed model. In this case, MFA technique is applied to generate a good initial solution for SA. The obtained results show that the quality of the solutions obtained by MFA–SA is better than classical SA, especially for large-sized problems.     

Approaches to Machine Load Balancing in Flexible Manufacturing Systems

The load balancing problem for a flexible manufacturing system concerns the allocation of operations to machines and of tools to magazines with limited capacity, while seeking to balance the workload on all machines. Previous attempts to tackle this problem have used integer programming and a specialized branch and bound procedure has been developed. A modified integer programming approach is proposed here. The problem has certain features which can be used advantageously for an approximate solution technique. The approximation technique is described and computational results presented. Extensions to the problem of pooling machines are also considered.     

Auxiliary tool allocation in flexible manufacturing systems

This paper analyses a new approach to the machine loading problem arising in flexible manufacturing systems (FMSs). This approach allows the operations to be assigned to machines assuming that machines have access to all the tools required for their operations. This exploits the flexibility of the FMS completely. Next an allocation of tools to machines is determined which satisfies the tool requirements for each machine and minimizes the total number of tools. Thus this approach minimizes the unnecessary tool duplications in the system and maximizes the tool utilization. The problem is modeled as an integer linear program (ILP). We notice that the main problem has a block diagonal structure which is decomposable by relaxing a set of linking constraints. Each separated sub-problem represents a problem of allocation of a single type of tools. We develop a branch-and-bound based exact solution procedure and three heuristic procedures to solve the sub-problems. Our lower bounding approach uses Lanrangean relaxation. The solutions to the Lagrangean relaxation are further used to determine the branching sequences and to develop heuristic approaches. Since finding even a feasible solution to the main problem is NP-hard, we develop only enumerative procedures to solve the main problem. Finally, these solution procedures are tested on randomly generated test problems.     

The wafer probing scheduling problem (WPSP)

The wafer probing scheduling problem (WPSP) is a variation of the parallel-machine scheduling problem, which has many real-world applications, particularly, in the integrated circuit (IC) manufacturing industry. In the wafer probing factories, the jobs are clustered by their product types, which must be processed on groups of identical parallel machines and be completed before the due dates. Further, the job processing time depends on the product type, and the machine setup time is sequence dependent on the orders of jobs processed. Since the wafer probing scheduling problem involves constraints on job clusters, job-cluster dependent processing time, due dates, machine capacity, and sequence dependent setup time, it is more difficult to solve than the classical parallel-machine scheduling problem. In this paper, we formulate the WPSP as an integer programming problem. We also transform the WPSP into the vehicle routing problem with time windows (VRPTW), a well-known network routing problem which has been investigated extensively. An illustrative example is given to demonstrate the proposed transformation. Based on the provided transformation, we present three efficient algorithms to solve the WPSP near-optimally.     

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。