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Péter Györgyi - One of the best experts on this subject based on the ideXlab platform.
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New complexity and approximability results for minimizing the total weighted completion time on a single machine subject to Non-Renewable Resource constraints
arXiv: Optimization and Control, 2020Co-Authors: Péter Györgyi, Tamás KisAbstract:In this paper we consider single machine scheduling problems with additional Non-Renewable Resource constraints. Examples for Non-Renewable Resources include raw materials, energy, or money. Usually they have an initial stock and replenishments arrive over time at a-priori known time points and quantities. The jobs have some requirements from the Resources and a job can only be started if the available quantity from each of the required Resources exceeds the requirements of the job. Upon starting a job, it consumes its requirements which decreases the available quantities of the respective Non-Renewable Resources. There is a broad theoretical and practical background for this class of problems. Most of the literature concentrate on the makespan, and the maximum lateness objectives. This paper focuses on the total weighted completion time objective for which the list of the approximation algorithms is very short. In this paper we extend that list by considering new special cases and obtain new complexity results and approximation algorithms. We show that even if there is only a single Non-Renewable Resource, and each job has unit weight and requires only one unit from the Resource, the problem is still NP-hard, however, in our construction we need a high-multiplicity encoding of the jobs in the input. We also propose an FPTAS for a variant in which the jobs have arbitrary weights, and the number of supply time points is bounded by a constant. Finally, we prove some non-trivial approximation guarantees for simple greedy algorithms for some further variants of the problem.
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Minimizing total weighted completion time on a single machine subject to Non-Renewable Resource constraints
Journal of Scheduling, 2019Co-Authors: Péter Györgyi, Tamás KisAbstract:In this paper, we describe new complexity results and approximation algorithms for single-machine scheduling problems with Non-Renewable Resource constraints and the total weighted completion time objective. This problem is hardly studied in the literature. Beyond some complexity results, only a fully polynomial-time approximation scheme (FPTAS) is known for a special case. In this paper, we discuss some polynomially solvable special cases and also show that under very strong assumptions, such as the processing time, the Resource consumption and the weight is the same for each job; minimizing the total weighted completion time is still NP-hard. In addition, we also propose a 2-approximation algorithm for this variant and a polynomial-time approximation scheme (PTAS) for the case when the processing time equals the weight for each job, while the Resource consumptions are arbitrary.
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A PTAS for a Resource scheduling problem with arbitrary number of parallel machines
Operations Research Letters, 2017Co-Authors: Péter GyörgyiAbstract:In this paper we study a parallel machine scheduling problem with Non-Renewable Resource constraints. That is, besides the jobs and machines, there is a common Non-Renewable Resource consumed by the jobs, which has an initial stock and some additional supplies over time. Unlike in most previous results, the number of machines is part of the input. We describe a polynomial time approximation scheme for minimizing the makespan.
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Approximation schemes for single machine scheduling with Non-Renewable Resource constraints
Journal of Scheduling, 2013Co-Authors: Péter Györgyi, Tamás KisAbstract:In this paper we discuss exact and approximation algorithms for scheduling a single machine with additional Non-Renewable Resource constraints. Given the initial stock levels of some Non-Renewable Resources (e.g., raw materials, fuel, money), and time points along with replenishment quantities, a set of Resource consuming jobs has to be scheduled on the machine such that there are enough Resources for starting each job, and the makespan is minimized. We show that the problem admits a pseudo-polynomial time algorithm when the number of replenishments is not part of the input, and also present an FPTAS when there is only a single Resource, and it is replenished only once. We also describe a PTAS for the problem with a constant number of replenishments.
Tamás Kis - One of the best experts on this subject based on the ideXlab platform.
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New complexity and approximability results for minimizing the total weighted completion time on a single machine subject to Non-Renewable Resource constraints
arXiv: Optimization and Control, 2020Co-Authors: Péter Györgyi, Tamás KisAbstract:In this paper we consider single machine scheduling problems with additional Non-Renewable Resource constraints. Examples for Non-Renewable Resources include raw materials, energy, or money. Usually they have an initial stock and replenishments arrive over time at a-priori known time points and quantities. The jobs have some requirements from the Resources and a job can only be started if the available quantity from each of the required Resources exceeds the requirements of the job. Upon starting a job, it consumes its requirements which decreases the available quantities of the respective Non-Renewable Resources. There is a broad theoretical and practical background for this class of problems. Most of the literature concentrate on the makespan, and the maximum lateness objectives. This paper focuses on the total weighted completion time objective for which the list of the approximation algorithms is very short. In this paper we extend that list by considering new special cases and obtain new complexity results and approximation algorithms. We show that even if there is only a single Non-Renewable Resource, and each job has unit weight and requires only one unit from the Resource, the problem is still NP-hard, however, in our construction we need a high-multiplicity encoding of the jobs in the input. We also propose an FPTAS for a variant in which the jobs have arbitrary weights, and the number of supply time points is bounded by a constant. Finally, we prove some non-trivial approximation guarantees for simple greedy algorithms for some further variants of the problem.
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Minimizing total weighted completion time on a single machine subject to Non-Renewable Resource constraints
Journal of Scheduling, 2019Co-Authors: Péter Györgyi, Tamás KisAbstract:In this paper, we describe new complexity results and approximation algorithms for single-machine scheduling problems with Non-Renewable Resource constraints and the total weighted completion time objective. This problem is hardly studied in the literature. Beyond some complexity results, only a fully polynomial-time approximation scheme (FPTAS) is known for a special case. In this paper, we discuss some polynomially solvable special cases and also show that under very strong assumptions, such as the processing time, the Resource consumption and the weight is the same for each job; minimizing the total weighted completion time is still NP-hard. In addition, we also propose a 2-approximation algorithm for this variant and a polynomial-time approximation scheme (PTAS) for the case when the processing time equals the weight for each job, while the Resource consumptions are arbitrary.
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Approximation schemes for single machine scheduling with Non-Renewable Resource constraints
Journal of Scheduling, 2013Co-Authors: Péter Györgyi, Tamás KisAbstract:In this paper we discuss exact and approximation algorithms for scheduling a single machine with additional Non-Renewable Resource constraints. Given the initial stock levels of some Non-Renewable Resources (e.g., raw materials, fuel, money), and time points along with replenishment quantities, a set of Resource consuming jobs has to be scheduled on the machine such that there are enough Resources for starting each job, and the makespan is minimized. We show that the problem admits a pseudo-polynomial time algorithm when the number of replenishments is not part of the input, and also present an FPTAS when there is only a single Resource, and it is replenished only once. We also describe a PTAS for the problem with a constant number of replenishments.
Sébastien Rouillon - One of the best experts on this subject based on the ideXlab platform.
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A simple characterization of the optimal extraction policy of a Non-Renewable Resource when extraction cost is stock-independent
Energy Economics, 2013Co-Authors: Sébastien RouillonAbstract:Abstract This note provides a simple characterization of the optimal extraction of a Non-Renewable Resource. The proposed formula determines the solution in its feedback form. It is shown to hold for a large class of models, as long as the utility is stock-independent.
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A Simple Characterization of the Optimal Extraction Policy of a Non-Renewable Resource When Extraction Cost is Stock-Independent
2013Co-Authors: Sébastien RouillonAbstract:This note provides a simple characterization of the optimal extraction of a Non-Renewable Resource. The proposed formula determines the solution in its feedback form. It is shown to hold for a large class of models, as long as the utility is stock-independent. (This abstract was borrowed from another version of this item.)
Marina Tsygankova - One of the best experts on this subject based on the ideXlab platform.
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Short run effects of bleaker prospects for oligopolistic producers of a Non-Renewable Resource
The Energy Journal, 2016Co-Authors: Kristine Grimsrud, Knut Einar Rosendahl, Halvor Briseid Storrøsten, Marina TsygankovaAbstract:In a Non-Renewable Resource market with imperfect competition, both the Resource rent and the current market influence large Resource owners' optimal supply. New information regarding future market conditions that affect the Resource rent will consequently impact current supply. Bleaker demand prospects tend to accelerate Resource extraction. We show, however, that it may slow down early extraction by producers with sufficiently large reserves and thus small Resource rents. The reason is that the supply from such producers is driven more by current market considerations than concern about Resource scarcity. As producers with relatively smaller reserves accelerate their supply in response to bleaker demand prospects, producers with sufficiently large reserves will reduce their current supply. The surge in shale gas production will reduce residual demand facing suppliers to the European gas market. We demonstrate the effects of this in a numerical model. Most gas producers accelerate their supply while Russia reduces its supply slightly and thus loses market shares even before the additional gas enters the market.
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Short Run Effects of Bleaker Prospects for Oligopolistic Producers of a Non-Renewable Resource
2014Co-Authors: Kristine Grimsrud, Knut Einar Rosendahl, Halvor Briseid Storrøsten, Marina TsygankovaAbstract:In a Non-Renewable Resource market with imperfect competition, both the Resource rent and current prices influence a large Resource owner’s optimal supply. New information regarding future market conditions that affect the Resource rent will consequently impact current supply. Bleaker demand prospects tend to accelerate Resource extraction. A more pessimistic outlook for future demand may, however, slow down the early Resource extraction of producers with sufficiently large Resource stocks and thus more limited Resource rent, because the supply from these producers is driven more by current market considerations than by changes in the Resource rent. As producers with relatively smaller Resource stocks accelerate their supply in response to bleaker demand prospects, producers with sufficiently large Resource stocks will reduce their current supply. A numerical model of the European gas market illustrates that the effect of the shale gas revolution is an accelerated supply by most gas producers, but a reduced supply by Russia who loses market shares even before the additional gas enters the market.
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Short run effects of bleaker prospects for oligopolistic producers of a Non-Renewable Resource
2014Co-Authors: Kristine Grimsrud, Knut Einar Rosendahl, Halvor Briseid Storrøsten, Marina TsygankovaAbstract:In a Non-Renewable Resource market with imperfect competition, the Resource owners' supply is governed both by current demand and by the Resource rent. New information regarding future market conditions will typically affect the Resource rent and hence current supply. Bleaker prospects will tend to accelerate extraction. We show, however, that for Resource owners with substantial Resource stocks, a more pessimistic outlook may in fact slow down early extraction. The explanation is that for players with extensive Resource stocks, the Resource rent is limited and supply is more driven by current market considerations. As players with less Resources accelerate their supply, it may be optimal for the large Resource owners to cut back on their supply. We illustrate this in the case of the European gas market, finding that the shale gas revolution may lead to an accelerated supply by most gas producers, but a postponement of Russian gas extraction.
John R. Boyce - One of the best experts on this subject based on the ideXlab platform.
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Non-Renewable Resource Stackelberg games
Resource and Energy Economics, 2014Co-Authors: Rui Wan, John R. BoyceAbstract:The market structure for many mineral industries can be described as oligopoly with potential for Stackelberg leadership. This paper derives and analyzes dynamically consistent extraction equilibria in a two-period discrete-time "Truly" Stackelberg (TS) model of Non-Renewable Resource extraction, where firms move sequentially within each period and where both the leader and follower have market power. We show how the leader may be able to manipulate extraction patterns by exploiting Resource constraints. Whether the leader wants to speed up its own production relative to the Cournot-Nash (CN) equilibrium depends on the shape of its iso-profit curve, which is affected by the two firms' relative stock endowments and relative production costs. If the leader extracts faster, then the follower extracts slower, but in aggregate the industry extracts faster. Unlike static Stackelberg games, the follower does not necessarily have a second mover disadvantage.
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Exploration can cause falling Non-Renewable Resource prices
Energy Economics, 2003Co-Authors: John R. BoyceAbstract:Abstract This note shows that when marginal exploration costs are increasing in the rate of exploration that it is possible to observe Non-Renewable Resource prices falling over a portion of the extraction profile. Thus, while the model of Pindyck (J. Polit. Econ. 86 (1978) 841) was based on an incorrect specification of the aggregate extraction cost function, its general conclusion that exploration can cause falling Non-Renewable Resource prices is upheld. This result is in contrast to Mendelsohn and Swierzbinski (Int. Econ. Rev. 30 (1989) 175), who assumed that marginal extraction costs were constant.
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Exploration can cause falling Non-Renewable Resource prices
Energy Economics, 2003Co-Authors: John R. BoyceAbstract:Abstract This note shows that when marginal exploration costs are increasing in the rate of exploration that it is possible to observe Non-Renewable Resource prices falling over a portion of the extraction profile. Thus, while the model of Pindyck (J. Polit. Econ. 86 (1978) 841) was based on an incorrect specification of the aggregate extraction cost function, its general conclusion that exploration can cause falling Non-Renewable Resource prices is upheld. This result is in contrast to Mendelsohn and Swierzbinski (Int. Econ. Rev. 30 (1989) 175), who assumed that marginal extraction costs were constant.