#### Date of Award

1999

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Engineering Science (Interdepartmental Program)

#### First Advisor

Bhaba R. Sarker

#### Abstract

Jobs (parts) and machines are usually grouped into part-families and machine-cells in a flexible, cellular manufacturing system to minimize the flows of all work-in-processes (WIP). As a result of this grouping, some parts may need processing on some machines that are not in their own cells. The parts requiring machines in other cells are called 'exceptional parts,' and the corresponding machines are called ' bottleneck machines.' Usually, there are two ways to deal with this inter-cell flow problem: using a material handling system to move the exceptional parts among the cells or duplicating the bottleneck machine(s) for the corresponding exceptional part(s). The objective of this research is to minimize the total costs of these inter-cell flows. A two-phase procedure, machine-cell location (MCL) and duplication of bottleneck machines (DBM), is presented in this research to achieve this goal. The MCL problem covers both one-dimensional layout and two-dimensional layout, especially dealing with one-dimensional equidistant (1DE), one-dimensional non-equidistant (1DNE) and two-dimensional non-equidistant (2DNE) machine-cell location problems. All versions of the MCL problem fall under the general class of quadratic assignment problem (QAP) which is NP-hard and it is difficult to solve a large problem optimally. The DBM problem, which arises as a natural extension to the MCL problem, may be classified as an integer linear programming (ILP) problem and a solution to it may provide an alternative way to reduce the total inter-cell flow costs. The 1DE problem is solved first by using a simple depth-first heuristic (SDH) which is later modified to a directional decomposition heuristic (DDH) for a better quality of solution. The directional decomposition of inter-cell flow, the core foundation of the DDH algorithm, is then extended to the one-dimensional non-equidistant (1DNE) and the two-dimensional non-equidistant (2DNE) problems. This leads to the development of the modified directional decomposition heuristic (MDDH) and the quadra-directional decomposition heuristic (QDDH), respectively. Based on the solutions to various facets of the MCL problem, a binary ILP model is proposed for solving the DBM problem optimally. Empirical tests show that heuristic DDH and its extensions, MDDH and QDDH, are more efficient than most other comparable heuristics.

#### Recommended Citation

Yu, Junfang, "Machine -Cell Location Problems for Multiproduct Flowlines." (1999). *LSU Historical Dissertations and Theses*. 7136.

https://digitalcommons.lsu.edu/gradschool_disstheses/7136

#### ISBN

9780599636521

#### Pages

369