A Logic-Based Benders Approach to Home Healthcare Delivery

Heching, Aliza; Hooker, John; Kimura, Ryo

doi:10.1287/trsc.2018.0830

Cited by 60 publications

(30 citation statements)

References 33 publications

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“…LBBD-MIP-OC denotes the LBBD method with sub-problems solved via MIP and optimality cut (26). LBBD-TS-GC means the LBBD method with sub-problems solved via TS and greedy assignment cut (27). LBBD-MIP-GC and LBBD-TS-OC have similar meanings.…”

Section: Computational Resultsmentioning

confidence: 99%

“…The constraint enforces the set of jobs assigned to the machine with the largest portion in the objective value that must remove a job in the next iteration. Although we considered the cut mentioned in Tadumadze et al [47] to change the set of jobs assigned to every machine by removing a job, the numerical test reports that it does not perform better than the greedy cut (27). We want to point out that constraint (27) does not warrant an optimal solution as it does not consider the impact on the objective function value by removing a job from other machines, which potentially can lead to a better job-to-machine assignment.…”

Section: Proposition 2 Constraint (26) Is a Valid Benders Optimality Cutmentioning

confidence: 99%

“…Although we considered the cut mentioned in Tadumadze et al [47] to change the set of jobs assigned to every machine by removing a job, the numerical test reports that it does not perform better than the greedy cut (27). We want to point out that constraint (27) does not warrant an optimal solution as it does not consider the impact on the objective function value by removing a job from other machines, which potentially can lead to a better job-to-machine assignment. This suboptimality of the GC will be illustrated in the computing experiments in "Computational results".…”

Section: Proposition 2 Constraint (26) Is a Valid Benders Optimality Cutmentioning

confidence: 99%

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Decomposition approaches for parallel machine scheduling of step-deteriorating jobs to minimize total tardiness and energy consumption

Guo

Wang

et al. 2021

Complex Intell. Syst.

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In this paper, an identical parallel machine scheduling problem with step-deteriorating jobs is considered to minimize the weighted sum of tardiness cost and extra energy consumption cost. In particular, the actual processing time of a job is assumed to be a step function of its starting time and its deteriorating threshold. When the starting time of a job is later than its deteriorating threshold, the job faces two choices: (1) maintaining its status in holding equipment and being processed with a base processing time and (2) consuming an extra penalty time to finish its processing. The two work patterns need different amounts of energy consumption. To implement energy-efficient scheduling, the selection of the pre-processing patterns must be carefully considered. In this paper, a mixed integer linear programming (MILP) model is proposed to minimize the total tardiness cost and the extra energy cost. Decomposition approaches based on logic-based Benders decomposition (LBBD) are developed by reformulating the studied problem into a master problem and some independent sub-problems. The master problem is relaxed by only making assignment decisions. The sub-problems are to find optimal schedules in the job-to-machine assignments given by the master problem. Moreover, MILP and heuristic based on Tabu search are used to solve the sub-problems. To evaluate the performance of our methods, three groups of test instances were generated inspired by both real-world applications and benchmarks from the literature. The computational results demonstrate that the proposed decomposition approaches can compute competitive schedules for medium- and large-size problems in terms of solution quality. In particular, the LBBD with Tabu search performs the best among the suggested four methods.

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Section: Computational Resultsmentioning

confidence: 99%

Section: Proposition 2 Constraint (26) Is a Valid Benders Optimality Cutmentioning

confidence: 99%

Section: Proposition 2 Constraint (26) Is a Valid Benders Optimality Cutmentioning

confidence: 99%

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Decomposition approaches for parallel machine scheduling of step-deteriorating jobs to minimize total tardiness and energy consumption

Guo

Wang

et al. 2021

Complex Intell. Syst.

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“…We optimize the MP using a mathematical programming model (solved via CPLEX) and SPs using both mathematical (solved via CPLEX) and constraint (solved via CPOptimizer) programming model, and note that IP/CP decomposition methods are by far more popular than IP/IP decompositions (Fazel‐Zarandi and Beck 2012, Heching et al. 2019, Ku and Beck 2016, Ku et al. 2014, Roshanaei et al.…”

Section: Decomposition Alternatives: An Overviewmentioning

confidence: 99%

“…Such a disconnect between the variables that the MP optimizes and those of SPs has been resolved by the concept of SP relaxation (Heching et al. 2019, Hooker 2007). (Remark 4 defines SP relaxation.)…”

Section: Decomposition Alternatives: An Overviewmentioning

confidence: 99%

Increased Surgical Capacity without Additional Resources: Generalized Operating Room Planning and Scheduling

Naderi

Roshanaei

Begen

et al. 2021

Production and Operations Management

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We study a generalized operating room planning and scheduling (GORPS) problem at the Toronto General Hospital (TGH) in Ontario, Canada. GORPS allocates elective patients and resources (i.e., operating rooms, surgeons, anesthetists) to days, assigns resources to patients, and sequences patients in each day. We consider patients’ due‐date, resource eligibility, heterogeneous performances of resources, downstream unit requirements, and lag times between resources. The goal is to create a weekly surgery schedule that minimizes fixed‐ and over‐time costs. We model GORPS using mixed‐integer and constraint programming models. To efficiently and effectively solve these models, we develop new‘ multi‐featured logic‐based Benders decomposition approaches. Using data from TGH, we demonstrate that our best algorithm solves GORPS with an average optimality gap of 2.71% which allows us to provide our practical recommendations. First, we can increase daily OR utilization to reach 80%—25% higher than the status quo in TGH. Second, we do not require to optimize for the daily selection of anesthetists—this finding allows for the development of effective dominance rules that significantly mitigate intractability. Third, solving GORPS without downstream capacities (like many papers in literature) makes GORPS easier to solve, but such OR schedules are only feasible in 24% of instances. Finally, with existing ORs’ safety capacities, TGH can manage 40% increase in its surgical volumes. We provide recommendations on how TGH must adjust its downstream capacities for varying levels of surgical volume increases (e.g., current urgent need for more capacity due to the current Covid‐19 pandemic).

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Towards a Prototype for the Strategic Recomputing of Schedules in Home Care Services

Martinez¹,

Mascolo²,

Espinouse³

et al. 2022

Healthcare Systems

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A Logic-Based Benders Approach to Home Healthcare Delivery

Cited by 60 publications

References 33 publications

Decomposition approaches for parallel machine scheduling of step-deteriorating jobs to minimize total tardiness and energy consumption

Decomposition approaches for parallel machine scheduling of step-deteriorating jobs to minimize total tardiness and energy consumption

Increased Surgical Capacity without Additional Resources: Generalized Operating Room Planning and Scheduling

Towards a Prototype for the Strategic Recomputing of Schedules in Home Care Services

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