Wieslaw Kubiak - Academia.edu (original) (raw)
Papers by Wieslaw Kubiak
arXiv (Cornell University), Jul 16, 2021
Springer eBooks, Oct 31, 2021
Springer eBooks, Oct 31, 2021
Springer eBooks, Oct 31, 2021
Springer eBooks, Oct 31, 2021
International Journal of Operational Research, 2022
arXiv (Cornell University), Jul 20, 2018
We study shared processor scheduling of multiprocessor weighted jobs where each job can be execut... more We study shared processor scheduling of multiprocessor weighted jobs where each job can be executed on its private processor and simultaneously on possibly many processors shared by all jobs in order to reduce their completion times due to processing time overlap. Each of m shared processors may charge different fee but otherwise the processors are identical. The total weighted overlap of all jobs is to be maximized. This problem is key to subcontractor scheduling in extended enterprises and supply chains, and divisible load scheduling in computing. We prove that, quite surprisingly, synchronized schedules that complete each job using shared processors at the same time on its private and shared processors include optimal schedules. We show that optimal α-private schedules that require each job to use its private processor for at least α = 1/2 + 1/(4(m + 1)) of the time required by the job guarantee more than an α fraction of the total weighted overlap of the optimal schedules. This gives an α-approximation algorithm that runs in strongly polynomial time for the problem, and improves the 1/2-approximation reported recently in the literature to 5/8-approximation for a single shared processor problem. The computational complexity of the problem, both single and multi-shared processor, remains open. We show however an LP-based optimal algorithm for antithetical instances where for any pair of jobs j and i, if the processing time of j is smaller than or equal to the processing time of i, then the weight of j is greater than or equal to the weight of i.
Foundations of Computing and Decision Sciences, 2007
Zeszyty Naukowe. Automatyka / Politechnika Śląska, 2008
European Journal of Operational Research, Apr 1, 2020
We study shared processor scheduling of multiprocessor weighted jobs where each job can be execut... more We study shared processor scheduling of multiprocessor weighted jobs where each job can be executed on its private processor and simultaneously on possibly many processors shared by all jobs in order to reduce their completion times due to processing time overlap. Each of m shared processors may charge different fee but otherwise the processors are identical. The total weighted overlap of all jobs is to be maximized. This problem is key to subcontractor scheduling in extended enterprises and supply chains, and divisible load scheduling in computing. We prove that, quite surprisingly, synchronized schedules that complete each job using shared processors at the same time on its private and shared processors include optimal schedules. We show that optimal α-private schedules that require each job to use its private processor for at least α = 1/2 + 1/(4(m + 1)) of the time required by the job guarantee more than an α fraction of the total weighted overlap of the optimal schedules. This gives an α-approximation algorithm that runs in strongly polynomial time for the problem, and improves the 1/2-approximation reported recently in the literature to 5/8-approximation for a single shared processor problem. The computational complexity of the problem, both single and multi-shared processor, remains open. We show however an LP-based optimal algorithm for antithetical instances where for any pair of jobs j and i, if the processing time of j is smaller than or equal to the processing time of i, then the weight of j is greater than or equal to the weight of i.
International Series in Operations Research & Management Science, 2021
Infor, Aug 1, 2001
Аннотация The balanced schedule problem in mixed-model, JIT manufacturing is examined. Solving th... more Аннотация The balanced schedule problem in mixed-model, JIT manufacturing is examined. Solving this problem is the cornerstone of production in any JIT facility. Although very efficient procedures have been demonstrated for the single-level problems, nobody ...
Springer eBooks, Oct 31, 2021
Springer eBooks, Dec 18, 2008
International Journal of Sustainable Economy, 2020
Coronavirus disease (COVID-19) and the Saudi Arabia-Russia Oil Price War have created economic ca... more Coronavirus disease (COVID-19) and the Saudi Arabia-Russia Oil Price War have created economic catastrophe. This crippled the US sustainable petroleum supply chain (SPSC), which is created in response to government policies, as a solution to global warming and achieving energy independency. Government and investors are striving to rescue the SPSC from bankruptcy. This motivated us to investigate creating a robust SPSC. Thus we extended the risk neutral study performed by Ghahremanlou and Kubiak (2020a) for regular economic conditions. To that end, we propose a risk averse approach by applying conditional value-at-risk (CVaR) and developing a two-stage stochastic programming model. We conduct a case study in Nebraska and provide investment decisions that can withstand economic crises. Our results show that for the survival of the SPSC, government must at least consider 2.151 $/gal tax credit for US cellulosic bioethanol blended with gasoline, and push the blend wall to at least 15%.
Discrete Applied Mathematics, Aug 1, 2021
Abstract The University timetabling is a generalization of the well-known class-teacher timetabli... more Abstract The University timetabling is a generalization of the well-known class-teacher timetabling model, where in addition to lectures given by a single teacher to a single class, there are some lectures given by a single teacher to a group of classes simultaneously. One looks for a minimum number of periods in which to complete all lectures without conflicts. The problem is NP-hard in the strong sense even if the number of groups is three, but it is polynomially solvable for two groups. In the latter case, it has been conjectured that the minimum number of periods in which to complete all lectures without conflicts equals ⌈ T ⌉ , where T is the optimal value of an L P -relaxation. The L P -relaxation permits fractions of periods in feasible solutions. We prove this conjecture in this paper.
Springer eBooks, Oct 31, 2021
Springer eBooks, Oct 31, 2021
Springer eBooks, Oct 31, 2021
Springer eBooks, Oct 31, 2021
arXiv (Cornell University), Jul 16, 2021
Springer eBooks, Oct 31, 2021
Springer eBooks, Oct 31, 2021
Springer eBooks, Oct 31, 2021
Springer eBooks, Oct 31, 2021
International Journal of Operational Research, 2022
arXiv (Cornell University), Jul 20, 2018
We study shared processor scheduling of multiprocessor weighted jobs where each job can be execut... more We study shared processor scheduling of multiprocessor weighted jobs where each job can be executed on its private processor and simultaneously on possibly many processors shared by all jobs in order to reduce their completion times due to processing time overlap. Each of m shared processors may charge different fee but otherwise the processors are identical. The total weighted overlap of all jobs is to be maximized. This problem is key to subcontractor scheduling in extended enterprises and supply chains, and divisible load scheduling in computing. We prove that, quite surprisingly, synchronized schedules that complete each job using shared processors at the same time on its private and shared processors include optimal schedules. We show that optimal α-private schedules that require each job to use its private processor for at least α = 1/2 + 1/(4(m + 1)) of the time required by the job guarantee more than an α fraction of the total weighted overlap of the optimal schedules. This gives an α-approximation algorithm that runs in strongly polynomial time for the problem, and improves the 1/2-approximation reported recently in the literature to 5/8-approximation for a single shared processor problem. The computational complexity of the problem, both single and multi-shared processor, remains open. We show however an LP-based optimal algorithm for antithetical instances where for any pair of jobs j and i, if the processing time of j is smaller than or equal to the processing time of i, then the weight of j is greater than or equal to the weight of i.
Foundations of Computing and Decision Sciences, 2007
Zeszyty Naukowe. Automatyka / Politechnika Śląska, 2008
European Journal of Operational Research, Apr 1, 2020
We study shared processor scheduling of multiprocessor weighted jobs where each job can be execut... more We study shared processor scheduling of multiprocessor weighted jobs where each job can be executed on its private processor and simultaneously on possibly many processors shared by all jobs in order to reduce their completion times due to processing time overlap. Each of m shared processors may charge different fee but otherwise the processors are identical. The total weighted overlap of all jobs is to be maximized. This problem is key to subcontractor scheduling in extended enterprises and supply chains, and divisible load scheduling in computing. We prove that, quite surprisingly, synchronized schedules that complete each job using shared processors at the same time on its private and shared processors include optimal schedules. We show that optimal α-private schedules that require each job to use its private processor for at least α = 1/2 + 1/(4(m + 1)) of the time required by the job guarantee more than an α fraction of the total weighted overlap of the optimal schedules. This gives an α-approximation algorithm that runs in strongly polynomial time for the problem, and improves the 1/2-approximation reported recently in the literature to 5/8-approximation for a single shared processor problem. The computational complexity of the problem, both single and multi-shared processor, remains open. We show however an LP-based optimal algorithm for antithetical instances where for any pair of jobs j and i, if the processing time of j is smaller than or equal to the processing time of i, then the weight of j is greater than or equal to the weight of i.
International Series in Operations Research & Management Science, 2021
Infor, Aug 1, 2001
Аннотация The balanced schedule problem in mixed-model, JIT manufacturing is examined. Solving th... more Аннотация The balanced schedule problem in mixed-model, JIT manufacturing is examined. Solving this problem is the cornerstone of production in any JIT facility. Although very efficient procedures have been demonstrated for the single-level problems, nobody ...
Springer eBooks, Oct 31, 2021
Springer eBooks, Dec 18, 2008
International Journal of Sustainable Economy, 2020
Coronavirus disease (COVID-19) and the Saudi Arabia-Russia Oil Price War have created economic ca... more Coronavirus disease (COVID-19) and the Saudi Arabia-Russia Oil Price War have created economic catastrophe. This crippled the US sustainable petroleum supply chain (SPSC), which is created in response to government policies, as a solution to global warming and achieving energy independency. Government and investors are striving to rescue the SPSC from bankruptcy. This motivated us to investigate creating a robust SPSC. Thus we extended the risk neutral study performed by Ghahremanlou and Kubiak (2020a) for regular economic conditions. To that end, we propose a risk averse approach by applying conditional value-at-risk (CVaR) and developing a two-stage stochastic programming model. We conduct a case study in Nebraska and provide investment decisions that can withstand economic crises. Our results show that for the survival of the SPSC, government must at least consider 2.151 $/gal tax credit for US cellulosic bioethanol blended with gasoline, and push the blend wall to at least 15%.
Discrete Applied Mathematics, Aug 1, 2021
Abstract The University timetabling is a generalization of the well-known class-teacher timetabli... more Abstract The University timetabling is a generalization of the well-known class-teacher timetabling model, where in addition to lectures given by a single teacher to a single class, there are some lectures given by a single teacher to a group of classes simultaneously. One looks for a minimum number of periods in which to complete all lectures without conflicts. The problem is NP-hard in the strong sense even if the number of groups is three, but it is polynomially solvable for two groups. In the latter case, it has been conjectured that the minimum number of periods in which to complete all lectures without conflicts equals ⌈ T ⌉ , where T is the optimal value of an L P -relaxation. The L P -relaxation permits fractions of periods in feasible solutions. We prove this conjecture in this paper.
Springer eBooks, Oct 31, 2021
Springer eBooks, Oct 31, 2021
Springer eBooks, Oct 31, 2021
Springer eBooks, Oct 31, 2021