The U-line Line Balancing Problem

Abstract

The traditional line balancing (LB) problem considers a production line in which stations are arranged consecutively in a line. A balance is determined by grouping tasks into stations while moving forward (or backward) through a precedence network. Recently many production lines are being arranged in a "U-line," as a consequence of the use of just-in-time production principles in many factories. In this paper the U-line LB problem is introduced and modelled, and solution procedures are developed. It more complex than the traditional LB problem because tasks can be grouped by moving forward, backward, or simultaneously in both directions, through the precedence network. We also show how solution techniques developed for the traditional LB problem can be adapted for use with the new problem. Some computational results for well-known problems from the literature are given.

Ant colony optimization for the single model U-type assembly line balancing problem

“…• T(S k ) denotes the station time, the total operation time of tasks assigned to station k, and must not exceed the cycle time: In UALBP, each task and any of its predecessors and/or successors can share the same station but it must be satisfied that, all predecessors and/or successors of a task j, performed at station k, have to be assigned to one of the stations 1,…, k. (Miltenburg and Wijngaard, 1994). In Figure 1.3 the optimal solution of UALBP-1 for c = 10, with 6 stations is given.…”

“…Standard test problems of Miltenburg and Wijngaard (1994) are solved using this model. Urban (1998) considers only the "larger" problems (21 or more tasks).…”

“…This is the reason why U-shaped layout allows for adapting to the changes in the circumstances more easily than the traditional layout. Miltenburg and Wijngaard (1994) note advantages of U-lines over straight lines as follows:…”

A survey of the literature on the multiple or parallel assembly line balancing problem

“…Miltenburg (1998) address the problem of balancing U-shaped lines in a multiple U-line facility. The U-line assembly line balancing problem (UALBP), which was introduced and modelled by Miltenburg and Wijngaard (1994), considers an assembly line arranged in an U-shape. Stations can be arranged so that during the same cycle two workpieces at different positions on the line can be handled.…”

“…A station which handles the same workpiece in two different cycles is called a crossover station. With a U-line, the number of required stations can be smaller than with a regular line (for more details on the UALBP see Miltenburg and Wijngaard, 1994;Nakade et al, 1997;Sparling and Miltenburg, 1998;Urban, 1998;Scholl and Klein, 1999;Miltenburg, 2000;Erel et al, 2001;Chiang and Urban, 2006;.…”