Minimizing the total completion time in single-machine scheduling with step-deteriorating jobs

2005 ◽  
Vol 32 (3) ◽  
pp. 521-536 ◽  
Author(s):  
A.A.K. Jeng ◽  
B.M.T. Lin
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Deteriorating Jobs ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Total Completion Time

SINGLE MACHINE SCHEDULING WITH LINEAR DETERIORATING JOBS UNDER PREDICTIVE DISRUPTION

2011 ◽  
Vol 28 (03) ◽  
pp. 419-429 ◽  
Author(s):  
CHUAN-LI ZHAO ◽  
HENG-YONG TANG
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Optimal Schedule ◽  
Deteriorating Jobs ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Total Completion Time ◽  
Weighted Sum ◽  
Scheduling Problems ◽  
Original Objective

This paper considers single machine scheduling problems with linear deteriorating jobs under predictive disruption. In this model, the actual processing time of a job is a increasing linear function of its starting time; and machine is subject to an availability constraint. We assume that an optimal schedule can be obtained by using some algorithms if machine is available at all time. Because of the machine disruption, the original schedule may become infeasible or too far from optimal. We want to create the new schedule that takes into account both the original objective function and a measure of deviation from the original schedule. We consider two versions of the problem. In the first one, the objective is weighted sum of total completion time and total tardiness while in the second one, the objective is weighted sum of total completion time and total earliness. We first prove some properties of the optimal schedule then dynamic programming algorithms are proposed, respectively.

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.

scholarly journals The Optimality Region for a Single-Machine Scheduling Problem with Bounded Durations of the Jobs and the Total Completion Time Objective

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 382 ◽  
Author(s):  
Yuri N. Sotskov ◽  
Natalja G. Egorova
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Optimal Schedule ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Total Completion Time ◽  
Scheduling Problem ◽  
Lower And Upper Bounds ◽  
The Given ◽  
Optimality Region

We study a single-machine scheduling problem to minimize the total completion time of the given set of jobs, which have to be processed without job preemptions. The lower and upper bounds on the job duration is the only information that is available before scheduling. Exact values of the job durations remain unknown until the completion of the jobs. We use the optimality region for the job permutation as an optimality measure of the optimal schedule. We investigate properties of the optimality region and derive O ( n ) -algorithm for calculating a quasi-perimeter of the optimality set (i.e., the sum of lengths of the optimality segments for n given jobs). We develop a fast algorithm for finding a job permutation having the largest quasi-perimeter of the optimality set. The computational results in constructing such permutations show that they are close to the optimal ones, which can be constructed for the factual durations of all given jobs.

Sign in / Sign up

Export Citation Format

Share Document