Complexity of single machine scheduling subject to nonnegative inventory constraints

Briskorn, Dirk; Choi, Byung-Cheon; Lee, Kangbok; Leung, Joseph Y.-T.; Pinedo, Michael

doi:10.1016/j.ejor.2010.05.036

Cited by 45 publications

(45 citation statements)

References 19 publications

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“…Constraints (2) express that the jobs assigned to the first ℓ supply periods cannot consume more resource(s) than the total supply over the first ℓ supply periods. Constraints (3) ensure that each job has to be assigned to exactly one supply period.…”

Section: Problem 1|rm Ddc|c Maxmentioning

confidence: 99%

“…In a more general setting, jobs may consume as well as produce non-renewable resources. In [2], Briskorn et al study the complexity of several variants, while Briskorn et al [3] devise a branch-andbound method for minimizing the weighted sum of job completion times on a single machine. However, none of these papers propose approximation schemes for NPhard special cases of single machine scheduling subject to non-renewable resource constraints for the makespan objective.…”

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confidence: 99%

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Approximation schemes for single machine scheduling with non-renewable resource constraints

Györgyi

Kis

2013

J Sched

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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.

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Section: Problem 1|rm Ddc|c Maxmentioning

confidence: 99%

mentioning

confidence: 99%

Approximation schemes for single machine scheduling with non-renewable resource constraints

Györgyi

Kis

2013

J Sched

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“…Some numerical results complement the theoretical findings. This line of work has been taken up by Briskorn et al [2], where several variants are studied, and either an NP-hardness proof is presented, or a polynomial time algorithm is devised. In [3], an exact branch-and-bound based method is developed and numerical results are provided for the general problem with 5 to 20 jobs.…”

Section: Related Workmentioning

confidence: 99%

Scheduling of inventory releasing jobs to minimize a regular objective function of delivery times

Drótos

Kis

2012

J Sched

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In this note we provide new complexity and algorithmic results for scheduling inventory releasing jobs, a new class of single machine scheduling problems proposed recently by Boysen et al. We focus on tardiness related criteria, while known results are concerned with inventory levels between fixed delivery points. Our interest is motivated by the fact that deciding whether a feasible schedule exists is NP-hard in the strong sense, provided that all delivery deadlines are fixed, and there are no restrictions on the amount of products released by the jobs, nor on the job processing times. We will establish NP-hardness results, or provide polynomial or pseudo-polynomial time algorithms for various special cases, and describe a fully polynomial approximation scheme for one of the variants with the maximum tardiness criterion.

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“…Different truck scheduling procedures which vary, e.g., with regard to the number of dock doors, the objective function applied, whether or not transportation times inside the terminal are considered and whether or not commodities are interchangeable between outbound trucks, are presented by Boysen [1], Boysen et al [3], Briskorn et al [4], Chen and Lee [6], Chen and Song [7], Miao et al [17] as well as Yu and Egbelu [23]. However, all of these papers concur in their assumption on the organization of outbound trucks' departures.…”

Section: Introductionmentioning

confidence: 99%

“…Since max {C i | i ∈ I} < d 6 outbound truck 6 is provided non-tardily by all inbound trucks. Summarizing, we have U(S) = {(2, 1), (3, 1), (4, 1), (4, 2), (5, 1), (5, 2), (5, 3), (6, 1), (6,2), (6,3), (6,4), (6,5), (7,1), (8,1), (8,2), (9, 1), (9, 2), (9, 3), (11,1), (12,1), (12,2), (13,1), (13,2), (13,3), (14,1), (14,2), (14,3), (14,4) …”

Section: Formal Problem Descriptionmentioning

confidence: 99%

Truck scheduling in cross-docking terminals with fixed outbound departures

2012

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At a cross docking terminal, inbound shipments are directly transshipped across the terminal to designated outbound trucks, so that delays and inventories are kept as low as possible. We consider an operational truck scheduling problem, where a dock door and a start time has to be assigned to each inbound truck. A set of outbound trucks is scheduled beforehand and, therefore, departure times are fixed. If a shipment is not unloaded, transshipped to the outbound gate and loaded onto the designated outbound truck before its departure we consider the shipments's value as lost profit. The objective is to minimize total lost profit. The paper at hand formalizes the resulting truck scheduling problem. We settle its computational complexity and develop heuristics in order to tackle the problem. We show the efficiency of these heuristics by means of a computational study. Last but not least, a case study is presented.

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Complexity of single machine scheduling subject to nonnegative inventory constraints

Cited by 45 publications

References 19 publications

Approximation schemes for single machine scheduling with non-renewable resource constraints

Approximation schemes for single machine scheduling with non-renewable resource constraints

Scheduling of inventory releasing jobs to minimize a regular objective function of delivery times

Truck scheduling in cross-docking terminals with fixed outbound departures

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