Scheduling step-deteriorating jobs to minimize the total completion time

2020 ◽  
Vol 144 ◽  
pp. 106329
Author(s):  
T.C.E. Cheng ◽  
Svetlana A. Kravchenko ◽  
Bertrand M.T. Lin
Keyword(s):  
Completion Time ◽  
Deteriorating Jobs ◽  
Total Completion Time

SCHEDULING WITH POSITION-BASED DETERIORATING JOBS AND MULTIPLE DETERIORATING RATE-MODIFYING ACTIVITIES

2014 ◽  
Vol 31 (01) ◽  
pp. 1450009 ◽  
Author(s):  
GUIYI WEI ◽  
YONG QIU ◽  
MIN JI
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Completion Time ◽  
Heuristic Algorithms ◽  
Deteriorating Jobs ◽  
Single Machine Scheduling ◽  
Integer Program ◽  
Total Completion Time ◽  
Unique Integer ◽  
Optimal Polynomial

In a recent paper, Ozturkoglu and Bulfin (Ozturkoglu, Y. and RL Bulfin (2011). A unique integer mathematical model for scheduling deteriorating jobs with rate-modifying activities on a single machine. The International Journal of Advanced Manufacturing Technology, 57, 753–762.) formulate a unique integer program to solve the single-machine scheduling for the objectives of minimizing makespan and total completion time. They also propose efficient heuristic algorithms for solving large size problems. However their heuristics are not optimal and so the NP-hardness of the considered problem is still open. In this note, we show that a more general problem can be optimally solved in polynomial time. We also provide optimal polynomial-time solution algorithm for the parallel-machine case to minimize total completion time.

SCHEDULING POSITION-BASED DETERIORATING JOBS WITH MULTIPLE RATE-MODIFYING ACTIVITIES AND PAST-SEQUENCE-DEPENDENT DELIVERY TIMES

2014 ◽  
Vol 31 (03) ◽  
pp. 1450018 ◽  
Author(s):  
KE CHEN ◽  
MIN JI ◽  
JIAOJIAO GE ◽  
GUIYI WEI
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Parallel Machines ◽  
Deteriorating Jobs ◽  
Planning Horizon ◽  
Parallel Machine ◽  
Total Completion Time ◽  
Delivery Time ◽  
Delivery Times ◽  
Sequence Dependent

In this paper, we consider a scheduling problem with position-based deteriorating jobs and past-sequence-dependent delivery times on a single machine or parallel machines. Each job's delivery time is dependent on its waiting time for processing. Because of the deteriorating effect, each machine will undergo multiple rate-modifying activities throughout the planning horizon to restore its processing rate. For the single-machine case, the objectives are to minimize the makespan and the total completion time. For the parallel-machine case, the objectives are to minimize the total completion time and the total machine load. We show that all these problems are solvable in polynomial time.

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