Olga Guschinskaya

A heuristic multi-start decomposition approach for optimal design of serial machining lines

We study an optimal design problem for serial machining lines. Such lines consist of a sequence of stations. At every station, the operations to manufacture a product are grouped into blocks. The operations within each block are performed simultaneously by the same spindle head and the blocks of the same station are executed sequentially. The inclusion and exclusion constraints for combining operations into blocks and stations as well as the precedence constraints on the set of operations are given. The problem is to group the operations into blocks and stations minimizing the total line cost. A feasible solution must respect the given cycle time and all given constraints. In this paper, a heuristic multi-start decomposition approach is proposed. It utilizes a decomposition of the initial problem into several sub-problems on the basis of a heuristic solution. Then each obtained sub-problem is solved by an exact algorithm. This procedure is repeated many times, each time it starts with a new heuristic solution. Computational tests show that the proposed approach outperforms simple heuristic algorithms for large-scale problems.

A MIP approach for balancing transfer line with complex industrial constraints

This paper deals with a novel line balancing problem for flexible transfer lines composed of identical CNC machines. The studied lines are paced and serial, i.e. a part to be machined passes through a sequence of workstations. At least one CNC machine is installed at each workstation. The objective is to assign a given set of operations required for the machining of the part to a sequence of workstations while minimizing the total number of machines used. This problem is subject to precedence, exclusion and inclusion constraints. In addition, accessibility has to be considered. Moreover, the workstation workload depends on the sequence in which the operations are assigned because of setup times related to the change and displacement of tools, rotation of the part, etc. It is a novel line balancing problem, and we highlight its particularities by reviewing the close problems existing in the literature. Then, a mathematical model as a mixed-integer program is suggested. A procedure for computing ranges for variables is given. Experimental computations with ILOG Cplex are reported.

An evaluation of constructive heuristic methods for solving the alternative subgraphs assembly line balancing problem

This paper evaluates a set of constructive heuristic methods developed to solve the novel Alternative Subgraphs Assembly Line Balancing Problem (ASALBP), which considers variants for different parts of a production or manufacturing process. Each variant is represented by a precedence subgraph that defines the tasks to be performed and their processing times. The proposed methods use priority rules and random choice to select the assembly subgraphs and to assign the tasks to the stations in order to minimize the number of required workstations. The methods are evaluated by a computational experiment based on medium- and large-scale benchmark problems.

Balancing large-scale machining lines with multi-spindle heads using decomposition

The paper deals with optimal logical layout design for a type of machining lines. Such lines are made of many machine-tools (workstations) located in sequence. On each workstation there are several multi-spindle heads. A spindle head does not execute one operation but a block of machining operations simultaneously. The problem studied in this paper consists of finding the best partition of the set of all operations to be executed on the line into blocks and workstations. The objective is to minimize the number of blocks and workstations. An optimal decision must satisfy a desired productivity rate (cycle time) and precedence and compatibility constraints for machining operations. A heuristic approach based on decomposition of a Mixed Integer Programming (MIP) model is developed. Two ways of forming sub-problems are proposed. One treats the obtained subsets independently. The second aggregates the solution of the previous subproblems. Results of their computational evaluation are reported.

Minimizing makespan for multi-spindle head machines with a mobile table

This paper presents a novel application of operational research techniques in Manufacturing. This concerns scheduling of multi-spindle head machines with a mobile table to minimize the makespan. We show that this problem can be formulated as scheduling for a single max-batch processing machine with inclusion, exclusion and precedence constraints between jobs. What makes this study unique from others in literature is that the batch processing time can exceed that of the longest job in the batch. The job compatibility and the batch time depend on the batch content, i.e. which jobs constitute the batch. This problem is transformed into finding the constrained shortest path in a specially constructed digraph. Dominance properties are developed to decrease the digraphs size. An industrial example is presented to illustrate the effectiveness of the proposed techniques.

MIP-based GRASP and Genetic Algorithm for Balancing Transfer Lines

Abstract In this chapter, we consider a problem of balancing transfer lines with multi-spindle machines. The problem has a number of distinct features in comparison with the well-studied assembly line balancing problem, such as parameterized operation times, non-strict precedence constraints, and parallel operations execution. We propose a mixed-integer programming (MIP)-based greedy randomized adaptive search procedure (GRASP) and a genetic algorithm (GA) for this problem using a MIP formulation. Both algorithms are implemented in GAMS using the CPLEX MIP solver and compared to problem-specific heuristics on randomly generated instances of different types. The results of computational experiments indicate that on large-scale problem instances the proposed methods have an advantage over the methods from literature for finding high quality solutions. The MIP-based recombination operator that arranges the elements of parent solutions in the best possible way is shown to be useful in the GA.

Heuristic Methods to Solve the Alternative Subgraphs Assembly Line Balancing Problem

This paper studies the performance of a group of heuristic methods developed to solve the alternative subgraphs assembly line balancing problem. This problem implies selecting an assembly subgraph for each subassembly that allows alternatives and assigning the tasks to the workstations, simultaneously. A computational experiment is carried out to analyse and compare the efficiency of the proposed procedures considering medium and large scale problems. Test results are reported.

Conception de systèmes de fabrication : prototype d'un logiciel d'aide à la décision

In this paper we present a prototype of decision aid system for the logical layout design of unit-head machines with rotary table. User can add and modify characteristics of the part to be machined, the constraints related to the design of spindle heads and working positions, as well as precedence constraints related to operations. The goal of this software tool is to minimize the total number of working positions and spindle heads, while reaching a given cycle time and satisfying the above constraints. The proposed method to solve the problem is based on its reduction to a constrained shortest path problem.

A comparative evaluation of exact and heuristic methods for transfer line balancing problem

Ten best exact and heuristic methods for Transfer Line Balancing Problem (TLBP) are compared in a computational experiment. The TLBP deals with the optimization of design solutions for serial machining lines. Such lines consist of a sequence of unit head machines. The operations are grouped into blocks at every station. These blocks are executed sequentially and the operations within each block are performed simultaneously by the same multi-spindle head. The objective is to assign the operations to blocks and the blocks to stations minimizing the total number of station and spindle heads. The challenge is to minimize the line cost and time for line design. Experimental results are presented. They help to choose the best optimization method for each situation.

Qualitative stability analysis of an optimal balance for an assembly line with fixed stations number

We focus on one of the simple assembly line balancing problems known as SALBP-2 which consists in assigning a set of elementary operations V = {1, 2, … , n} to the m linearly ordered stations with respect to the precedence constraints and aims in minimizing the line cycle time c. The processing times of operations tj , j ∈ V may vary during the life cycle of assembly line for manual operations (represented by set Ṽ ) and be fixed for automated operations (set V ∖ Ṽ ). The goal of this paper is to derive necessary and sufficient condition (so-called qualitative analysis) of the stability of an optimal balance found for a given vector of operations times t = (t1, t2, … , tn) with regard to possible independent perturbations of the processing times of the operations from set .