S. Belmokhtar

Integer programming models for logical layout design of modular machining lines

The preliminary design or reconfiguration of modular manufacturing lines is addressed. The modules are multi-spindle units. Each unit executes a subset of operations. The set of all available spindle units and their costs are known. The problem is to select the right spindle units and to arrange them into linear workstations. The objective is to design such a line respecting technological constraints and minimizing the investment cost. In this paper, some efficient formulations of linear integer programming (IP) models and specific techniques to reduce the calculation time are proposed. Experiments were carried out which highlight the performance of the models.

A New Exact Solution Algorithm for the Job Shop Problem with Sequence-Dependent Setup Times

We propose a new solution approach for the Job Shop Problem with Sequence Dependent Setup Times (SDST-JSP). The problem consists in scheduling jobs, each job being a set of elementary operations to be processed on different machines. The objective pursued is to minimize the completion time of the set of operations. We investigate a relaxation of the problem related to the traveling salesman problem with time windows (TSPTW). Our approach is based on a Branch and Bound procedure, including constraint propagation and using this relaxation. It compares favorably over the best available approaches from the literature on a set of benchmark instances.

Balancing of Transfer Lines with Simultaneously Activated Spindles

Abstract A balancing problem for transfer lines with parallel spindles is investigated. All spindle heads of the same workstation are activated simultaneously. The relations of the necessity of executing some operations at the same workstation, the possibility of combining the spindles at the same workstation as well as precedence constraints are given. The problem is to choose spindle heads from a given set and allocate them to workstations in such a way that i) all the operations are performed, ii) all constraints are satisfied, iii) the cycle time is provided, and iv) the line cost is minimal. The proposed method for solving the problem is based on its formulation as a mixed integer problem (MIP).

Reconfigurable transfer lines cost optimization - a linear programming approach

The transfer lines dealt with in this paper are equipped with multifunctional spindle heads, capable to realize several operations in the same time (in parallel) on the same work-piece. Each such multifunctional spindle head is called a block and is fully described by its set of operations, operating time and cost. The reconfigurability concerns here the possibility of realizing a family of products with the same equipment. The blocks and the product family features are supposed known. The problem is to assign the blocks to workstations such as to minimize the total cost of the line and to meet a set of time and technological constraints for the whole product family. This problem is formulated as a linear program (LP) and solved by using the Cplex ILOG optimization software. An example is provided to illustrate the steps of the proposed solving method

Modular Machining Line Design and Reconfiguration: Some Optimization Methods

Automated flow-oriented machining lines are typically encountered in the mechanical industry (Groover, 1987; Hitomi, 1996; Dashchenko, 2003). They are also called transfer (or paced) lines, being preferred mainly for the mass production, as they increase the production rate and minimize the cost of machining parts (Hutchinson, 1976). They consist of a linear sequence of multi-spindle machines (workstations), without buffers in between, arranged along a conveyor belt (transfer system). Each workstation is equipped with several spindle heads, each of these latter being composed of several tools. Each tool executes one or several (for the case of a combined cutting tool) operations. A block of operations is defined by the set of the operations executed simultaneously by one spindle head. When all blocks of a workstation have been accomplished, the workstation cycle time is terminated. The cycle time of the line is the longest workstation cycle time; its inverse is the line’s production rate. A machining line designed to produce a single product type is called dedicated line; its optimal structure, once found and implemented, is intended for a long exploitation time and needs high investments. The main drawback of such a system is its rigid structure which does not permit any conversion in case of change in product type. Thus, to react to changes effectively an alternative is to design the system from the outset for all the product types intended to be produced. Research has been conducted to an integrated approach of transfer lines design in the context of flexibility (Zhang et al., 2002). This is the most important aspect which characterizes the potential of a system for reconfiguration (Koren et al., 1999). The chapter deals with the designing of modular reconfigurable transfer lines, where a set of standard spindle heads are used to

OPTIMIZING MODULAR MACHINING LINE DESIGN PROBLEM

Abstract A generalization of modular transfer line designing problem is addressed. The problem is defined as a selection of a subset of modules from a given set and their arrangement into several stations respecting the technological and cycle time constraints. The objective is to minimize the line cost defined by the cost of the established stations and their modules. An approach based on mixed integer programming is proposed to tackle the problem. Experimental computations are reported to highlight the capacities of the model..