Sequence Jobs and Assign Due Dates with Uncertain Processing Times and Quadratic Penalty Functions

Author(s):  
Yu Xia ◽  
Bintong Chen ◽  
Jinfeng Yue
2021 ◽  
Vol 58 ◽  
pp. 291-305
Author(s):  
Chin-Chia Wu ◽  
Danyu Bai ◽  
Xingong Zhang ◽  
Shuenn-Ren Cheng ◽  
Jia-Cheng Lin ◽  
...  

2020 ◽  
Vol 37 (01) ◽  
pp. 1950032
Author(s):  
Myoung-Ju Park ◽  
Byung-Cheon Choi ◽  
Yunhong Min ◽  
Kyung Min Kim

We consider a two-machine flow shop scheduling with two properties. The first is that each due date is assigned for a specific position different from the traditional definition of due dates, and the second is that a consistent pattern exists in the processing times within each job and each machine. The objective is to minimize maximum tardiness, total tardiness, or total number of tardy jobs. We prove the strong NP-hardness and inapproximability, and investigate some polynomially solvable cases. Finally, we develop heuristics and verify their performances through numerical experiments.


Author(s):  
Alexander A. Lazarev ◽  
Nikolay Pravdivets

In this chapter, we consider the single machine scheduling problem with given release dates, processing times, and due dates with two objective functions. The first one is to minimize the maximum lateness, that is, maximum difference between each job due date and its actual completion time. The second one is to minimize the maximum completion time, that is, to complete all the jobs as soon as possible. The problem is NP-hard in the strong sense. We provide a polynomial time algorithm for constructing a Pareto-optimal set of schedules on criteria of maximum lateness and maximum completion time, that is, problem 1 ∣ r j ∣ L max , C max , for the subcase of the problem: d 1 ≤ d 2 ≤ … ≤ d n ; d 1 − r 1 − p 1 ≥ d 2 − r 2 − p 2 ≥ … ≥ d n − r n − p n .


2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yuncheng Luo

In this paper, we investigate a static stochastic single machine JIT scheduling problem in which the jobs’ processing times are stochastically independent and follow geometric distributions whose mean is provided, due dates are geometrically distributed with a common mean, and both the unit penalty of earliness/tardiness and the fixed penalty of earliness/tardiness are deterministic and different. The objective is to minimize the expected total penalties for quadratic earliness, quadratic tardiness, and early and tardy jobs. We prove that the optimal schedule to minimize this problem is V-shaped with respect to the ratio of mean processing time to unit tardiness penalty under the specific condition. Also, we show a special case and two theorems related to this JIT scheduling problem under specific situations where the optimal solutions exist. Finally, based on the V-shaped characteristic, a dynamic programming algorithm is designed to achieve an optimal V-shaped schedule in pseudopolynomial time.


2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Hamiden Abd El-Wahed Khalifa ◽  
Sultan S. Alodhaibi ◽  
Pavan Kumar

This paper deals with constrained multistage machines flow-shop (FS) scheduling model in which processing times, job weights, and break-down machine time are characterized by fuzzy numbers that are piecewise as well as quadratic in nature. Avoiding to convert the model into its crisp, the closed interval approximation for the piecewise quadratic fuzzy numbers is incorporated. The suggested method leads a noncrossing optimal sequence to the considered problem and minimizes the total elapsed time under fuzziness. The proposed approach helps the decision maker to search for applicable solution related to real-world problems and minimizes the total fuzzy elapsed time. A numerical example is provided for the illustration of the suggested methodology.


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