A location problem on unicyclic networks: Balanced case

Move based heuristics for the unidirectional loop network layout problem

“…The system is balanced. Adjacent locations are unit distance apart (since the system is balanced, the distance between machines is of no importance, as proved in Bozer andRim, 1989, andKiran, Unal andKarabati, 1992). Process plans and the number of units to be produced for each part type are given, so that pairwise part flows between machine pairs can be calculated.…”

“…For problems of size up to 10, we computed the exact value of the problem by enumeration. For larger sized problems, we used the LP relaxation of the IP model of Kiran, Unal and Karabati ( 1992). The LP relaxation yields a lower bound on the optimal value.…”

“…We remark that the nonequal spaced ULNLP with Q conserved (balanced) Jlow matrix (i.e. for each station, the total material flow into a station is the same as the total outflow from that station) is equivalent to the equal spaced ULNLP (Bozer and Rim, 1989;Kiran, Unal and Karabati, 1992). Hence, the conserved flow version of the non-equal spaced ULNLP is also polynomially solvable if Bozer and Rim's result is true.…”

“…( I ) minimization of the sum of flows times distances per unit time (Bozer and Rim, 1989, Kiran and Karabati, 1988, and Kiran, Unal and Karabati, 1992. (2) minimization of the total number of parts that cross the LUL station per unit time (Afentakis, 1989, andKouvelis andKim, 1992).…”

“…Hence, the conserved flow version of the non-equal spaced ULNLP is also polynomially solvable if Bozer and Rim's result is true. Kiran, Unal and Karabati ( 1992) report that integer solutions are obtained from the LP relaxation of their formulation of the conserved flow problem. However, their test runs are restricted to problems with up to six stations.…”