Exact lexicographic scheduling and approximate rescheduling

Letsios, Dimitrios; Mistry, Miten; Misener, Ruth

doi:10.1016/j.ejor.2020.08.032

Cited by 9 publications

(21 citation statements)

References 39 publications

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“…A common way of measuring solution robustness of a given discrete optimization problem instance is by comparing the final solution objective value after uncertainty realization with the solution objective value that we could have achieved if we had a crystal ball that accurately predicts the future. From this perspective, we recently proposed a two-stage robust scheduling approach for P||C max , based on lexicographic optimization (Letsios et al 2021). If processing times are perturbed by a (1 + ) factor, the lexicographic optimization approach yields schedules a factor (2 + O( )) far from achievable optima with perfect knowledge.…”

Section: Related Workmentioning

confidence: 99%

“…Because Royal Mail delivery scheduling is subject to uncertainty, Sect. 6 exploits machine augmentation and lexicographic optimization for P||C max under uncertainty (Letsios et al 2021;Skutella and Verschae 2016) to construct a two-stage robust optimization approach for the BJSP under uncertainty. We measure robustness based on the resource augmentation required for the final solution feasibility.…”

Section: Paper Organization and Contributionsmentioning

confidence: 99%

“…This section proposes a two-stage robust optimization approach for BJSP under uncertainty based on lexicographic optimization. We recently proposed a variant of this approach for two-stage robust P||C max (Letsios et al 2021). Because job start times are irrevocable in the Royal Mail context, we adapt the P||C max approach to BJSP, using resource augmentation.…”

Section: Dealing With Uncertaintymentioning

confidence: 99%

“…That is, new machines are added once the uncertainty is realized. The robustness of a solution is measured by the level of resource augmentation, i.e., number of machines required for the final solution feasibility (instead of the actual makespan objective value we adopt in Letsios et al 2021 with a different recovery strategy). Section 6.1 formally describes our uncertainty setting, including the uncertainty set structure and investigated robustness measure.…”

Section: Dealing With Uncertaintymentioning

confidence: 99%

“…. , T m }, where T i corresponds to the i-th greatest machine completion time (Letsios et al 2021). That is, we minimize T 1 and, among all schedules minimizing T 1 , we select a schedule minimizing T 2 , then T 3 etc.…”

Section: Exact Lexopt Scheduling With Machine Augmentation (Stage 1)mentioning

confidence: 99%

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Approximate and robust bounded job start scheduling for Royal Mail delivery offices

Letsios

Bradley²,

Suraj

et al. 2021

J Sched

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Motivated by mail delivery scheduling problems arising in Royal Mail, we study a generalization of the fundamental makespan scheduling $$P||C_{\max }$$ P | | C max problem which we call the bounded job start scheduling problem. Given a set of jobs, each specified by an integer processing time $$p_j$$ p j , that have to be executed non-preemptively by a set of m parallel identical machines, the objective is to compute a minimum makespan schedule subject to an upper bound $$g\le m$$ g ≤ m on the number of jobs that may simultaneously begin per unit of time. With perfect input knowledge, we show that Longest Processing Time First (LPT) algorithm is tightly 2-approximate. After proving that the problem is strongly $${\mathcal {N}}{\mathcal {P}}$$ N P -hard even when $$g=1$$ g = 1 , we elaborate on improving the 2-approximation ratio for this case. We distinguish the classes of long and short instances satisfying $$p_j\ge m$$ p j ≥ m and $$p_j<m$$ p j < m , respectively, for each job j. We show that LPT is 5/3-approximate for the former and optimal for the latter. Then, we explore the idea of scheduling long jobs in parallel with short jobs to obtain tightly satisfied packing and bounded job start constraints. For a broad family of instances excluding degenerate instances with many very long jobs, we derive a 1.985-approximation ratio. For general instances, we require machine augmentation to obtain better than 2-approximate schedules. In the presence of uncertain job processing times, we exploit machine augmentation and lexicographic optimization, which is useful for $$P||C_{\max }$$ P | | C max under uncertainty, to propose a two-stage robust optimization approach for bounded job start scheduling under uncertainty aiming in a low number of used machines. Given a collection of schedules of makespan $$\le D$$ ≤ D , this approach allows distinguishing which are the more robust. We substantiate both the heuristics and our recovery approach numerically using Royal Mail data. We show that for the Royal Mail application, machine augmentation, i.e., short-term van rental, is especially relevant.

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Section: Related Workmentioning

confidence: 99%

Section: Paper Organization and Contributionsmentioning

confidence: 99%

Section: Dealing With Uncertaintymentioning

confidence: 99%

Section: Dealing With Uncertaintymentioning

confidence: 99%

Section: Exact Lexopt Scheduling With Machine Augmentation (Stage 1)mentioning

confidence: 99%

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