TY - JOUR

T1 - The just-in-time scheduling problem in a flow-shop scheduling system

AU - Shabtay, Dvir

N1 - Funding Information:
Partial support by the Paul Ivanier Center for Robotics and Production Management, Ben-Gurion University of the Negev is gratefully acknowledged.

PY - 2012/2/1

Y1 - 2012/2/1

N2 - We study the problem of maximizing the weighted number of just-in-time (JIT) jobs in a flow-shop scheduling system under four different scenarios. The first scenario is where the flow-shop includes only two machines and all the jobs have the same gain for being completed JIT. For this scenario, we provide an O(n3) time optimization algorithm which is faster than the best known algorithm in the literature. The second scenario is where the job processing times are machine-independent. For this scenario, the scheduling system is commonly referred to as a proportionate flow-shop. We show that in this case, the problem of maximizing the weighted number of JIT jobs is NP-hard in the ordinary sense for any arbitrary number of machines. Moreover, we provide a fully polynomial time approximation scheme (FPTAS) for its solution and a polynomial time algorithm to solve the special case for which all the jobs have the same gain for being completed JIT. The third scenario is where a set of identical jobs is to be produced for different customers. For this scenario, we provide an O(n3) time optimization algorithm which is independent of the number of machines. We also show that the time complexity can be reduced to O(n log n) if all the jobs have the same gain for being completed JIT. In the last scenario, we study the JIT scheduling problem on m machines with a no-wait restriction and provide an O(mn2) time optimization algorithm.

AB - We study the problem of maximizing the weighted number of just-in-time (JIT) jobs in a flow-shop scheduling system under four different scenarios. The first scenario is where the flow-shop includes only two machines and all the jobs have the same gain for being completed JIT. For this scenario, we provide an O(n3) time optimization algorithm which is faster than the best known algorithm in the literature. The second scenario is where the job processing times are machine-independent. For this scenario, the scheduling system is commonly referred to as a proportionate flow-shop. We show that in this case, the problem of maximizing the weighted number of JIT jobs is NP-hard in the ordinary sense for any arbitrary number of machines. Moreover, we provide a fully polynomial time approximation scheme (FPTAS) for its solution and a polynomial time algorithm to solve the special case for which all the jobs have the same gain for being completed JIT. The third scenario is where a set of identical jobs is to be produced for different customers. For this scenario, we provide an O(n3) time optimization algorithm which is independent of the number of machines. We also show that the time complexity can be reduced to O(n log n) if all the jobs have the same gain for being completed JIT. In the last scenario, we study the JIT scheduling problem on m machines with a no-wait restriction and provide an O(mn2) time optimization algorithm.

KW - Complexity

KW - Flow-shop

KW - Just-in-time scheduling

KW - No-wait restriction

KW - Pseudo-polynomial time algorithm

UR - http://www.scopus.com/inward/record.url?scp=80053928362&partnerID=8YFLogxK

U2 - 10.1016/j.ejor.2011.07.053

DO - 10.1016/j.ejor.2011.07.053

M3 - Article

AN - SCOPUS:80053928362

VL - 216

SP - 521

EP - 532

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 3

ER -