scholarly journals Single-Machine Scheduling to Minimize Total Completion Time and Tardiness with Two Competing Agents

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Wen-Chiung Lee ◽  
Yau-Ren Shiau ◽  
Yu-Hsiang Chung ◽  
Lawson Ding
Keyword(s):  
Simulated Annealing ◽  
Branch And Bound ◽  
Single Machine ◽  
Completion Time ◽  
Heuristic Algorithms ◽  
Single Machine Scheduling ◽  
Total Completion Time ◽  
Optimal Sequence ◽  
Tardy Jobs ◽  
Annealing Algorithms

We consider a single-machine two-agent problem where the objective is to minimize a weighted combination of the total completion time and the total tardiness of jobs from the first agent given that no tardy jobs are allowed for the second agent. A branch-and-bound algorithm is developed to derive the optimal sequence and two simulated annealing heuristic algorithms are proposed to search for the near-optimal solutions. Computational experiments are also conducted to evaluate the proposed branch-and-bound and simulated annealing algorithms.

scholarly journals A Single-Machine Two-Agent Scheduling Problem by a Branch-and-Bound and Three Simulated Annealing Algorithms

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Shangchia Liu ◽  
Wen-Hsiang Wu ◽  
Chao-Chung Kang ◽  
Win-Chin Lin ◽  
Zhenmin Cheng
Keyword(s):  
Simulated Annealing ◽  
Branch And Bound ◽  
Single Machine ◽  
Completion Time ◽  
Optimal Solution ◽  
Total Completion Time ◽  
Practical Applications ◽  
Processing Resource ◽  
Agent Scheduling ◽  
Annealing Algorithms

In the field of distributed decision making, different agents share a common processing resource, and each agent wants to minimize a cost function depending on its jobs only. These issues arise in different application contexts, including real-time systems, integrated service networks, industrial districts, and telecommunication systems. Motivated by its importance on practical applications, we consider two-agent scheduling on a single machine where the objective is to minimize the total completion time of the jobs of the first agent with the restriction that an upper bound is allowed the total completion time of the jobs for the second agent. For solving the proposed problem, a branch-and-bound and three simulated annealing algorithms are developed for the optimal solution, respectively. In addition, the extensive computational experiments are also conducted to test the performance of the algorithms.

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 Minimizing the Number of Tardy Jobs on a Single Machine with an Availability Constraint

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Ehsan Molaee ◽  
Ghasem Moslehi
Keyword(s):  
Branch And Bound ◽  
Single Machine ◽  
Planning Horizon ◽  
Single Machine Scheduling ◽  
Upper And Lower Bounds ◽  
Scheduling Problems ◽  
Bearing Witness ◽  
Number Of Tardy Jobs ◽  
Problem Instances ◽  
Tardy Jobs

Most scheduling problems are based on the assumption that machines work continuously during the planning horizon. This assumption is not true in many production environments because the machine may not be available during one or more periods such as during breakdowns or maintenance operations. In this paper, the problem of the single machine scheduling with one unavailability period and nonresumable jobs with the aim of minimizing the number of tardy jobs is studied. A number of theorems are proved and a heuristic procedure is developed to solve the problem. A branch-and-bound approach is also presented which includes upper and lower bounds and efficient dominance rules. Computational results for 2680 problem instances show that the branch-and-bound approach is capable of solving 98.7% of the instances optimally, bearing witness to the efficiency of the proposed procedure. Our results also indicate that the proposed approaches are more efficient when compared to other methods.

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.

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