Job Sequencing with One Common and Multiple Secondary Resources: A Problem Motivated from Particle Therapy for Cancer Treatment

Int Trans Operational Res

2018

The particle therapy patient scheduling problem (PTPSP) arises in modern cancer treatment facilities that provide particle therapy. It consists of scheduling a set of therapies within a planning horizon of several months. A particularity of PTSP compared with classical radiotherapy scheduling is that therapies need not only be assigned to days but also scheduled within each day to account for the more complicated operational scenario. In an earlier work, we introduced this novel problem setting and provided first algorithms including an iterated greedy (IG) metaheuristic. In this work, we consider an important extension to the PTPSP emerging from practice in which the therapies should be provided on treatment days roughly at the same time. To be more specific, the variation between the starting times of the therapies' individual treatments should not exceed the given limits, and needs otherwise to be minimized. This additional constraint implies that the sequencing parts within each day can no longer be treated independently. To tackle this variant of PTPSP, we revise our previous IG and exchange its main components: the part of the applied construction heuristic for scheduling within the days and the local search algorithm. The resulting metaheuristic provides promising results for the proposed extension of the PTPSP and further enhances the existing approach for the original problem.

Section: Related Worksupporting

confidence: 54%

“…() and Horn et al. () deal with strongly simplified variants of the time assignment part for a single day. Motivated by the fact that irradiation times are known exactly beforehand, Riedler et al.…”

Section: Related Workmentioning

confidence: 99%

Particle therapy patient scheduling with limited starting time variations of daily treatments

Maschler

Int Trans Operational Res

2018

“…This work is an extension of our preliminary conference article [12], where we already proved that the JSOCMSR is NP-hard and provided a basic lower bound for the makespan. We also presented the construction heuristic and the anytime A * algorithm there, however, with only a simple greedy-based diving.…”

Section: Contribution Of This Workmentioning

confidence: 83%

“…Our already mentioned preliminary work on the JSOCMSR [12] considered, besides the construction heuristic and the simple anytime A * approach, three different MIP models for the JSOCMSR problem: (1) a time-indexed based formulation, (2) a position-based formulation and (3) a disjunctive MIP model. All three variants were clearly outperformed by our anytime A * approach.…”

Section: Related Workmentioning

confidence: 99%

Job sequencing with one common and multiple secondary resources: An A⁎/Beam Search based anytime algorithm

Horn

Artificial Intelligence

Blum

2019

Self Cite

We consider a sequencing problem that arises, for example, in the context of scheduling patients in particle therapy facilities for cancer treatment. A set of non-preemptive jobs needs to be scheduled, where each job requires two resources: (1) a common resource that is shared by all jobs and (2) a secondary resource, which is shared with only a subset of the other jobs. While the common resource is only required for a part of the job's processing time, the secondary resource is required for the whole duration. The objective is to minimize the makespan. First we show that the tackled problem is NP-hard and provide three different lower bounds for the makespan. These lower bounds are then exploited in a greedy construction heuristic and a novel exact anytime A * algorithm, which uses an advanced diving mechanism based on Beam Search and Local Search to find good heuristic solutions early. For comparison we also provide a basic Constraint Programming model solved with the ILOG CP optimizer. An extensive experimental evaluation on two types of problem instances shows that the approach works even for large instances with up to 2000 jobs extremely well. It typically yields either optimal solutions or solutions with an optimality gap of less than 1%.

“…Hence, we write Z (π) for the total prize of the normalized solution given by the ordering π of jobs. Above problem variant extends the job sequencing with one common and multiple secondary resources (JSOCMSR) problem originally proposed by Horn et al (2017) by the considered time windows and the maximization of the scheduled jobs' prizes. In Horn et al's JSOCMSR, the objective is to minimize the makespan.…”

Section: The Problemmentioning

confidence: 99%

Multivalued decision diagrams for prize-collecting job sequencing with one common and multiple secondary resources

Maschler

2019

Ann Oper Res

Multivalued decision diagrams (MDD) are a powerful tool for approaching combinatorial optimization problems. Relatively compact relaxed and restricted MDDs are applied to obtain dual bounds and heuristic solutions and provide opportunities for new branching schemes. We consider a prize-collecting sequencing problem in which a subset of given jobs has to be found that is schedulable and yields maximum total prize. The primary aim of this work is to study different methods for creating relaxed MDDs for this problem. To this end, we adopt and extend the two main MDD compilation approaches found in the literature: top down construction and incremental refinement. In a series of computational experiments these methods are compared. The results indicate that for our problem the incremental refinement method produces MDDs with stronger bounds. Moreover, heuristic solutions are derived by compiling restricted MDDs and by applying a general variable neighborhood search (GVNS). Here we observe that the top down construction of restricted MDDs is able to yield better solutions as the GVNS on small to medium-sized instances.