ABSTRACT
This work investigates a new multi-period vaccination planning problem that simultaneously optimizes the total travel distance of vaccination recipients (service level) and the operational cost. An optimal plan determines, for each period, which vaccination sites to open, how many vaccination stations to launch at each site, how to assign recipients from different locations to opened sites, and the replenishment quantity of each site. We formulate this new problem as a bi-objective mixed-integer linear program (MILP). We first propose a weighted-sum and an ϵ -constraint methods, which rely on solving many single-objective MILPs and thus lose efficiency for practical-sized instances. To this end, we further develop a tailored genetic algorithm where an improved assignment strategy and a new dynamic programming method are designed to obtain good feasible solutions. Results from a case study indicate that our methods reduce the operational cost and the total travel distance by up to 9.3% and 36.6%, respectively. Managerial implications suggest enlarging the service capacity of vaccination sites can help improve the performance of the vaccination program. The enhanced performance of our heuristic is due to the newly proposed assignment strategy and dynamic programming method. Our findings demonstrate that vaccination programs during pandemics can significantly benefit from formal methods, drastically improving service levels and decreasing operational costs.
ABSTRACT
Meta-analysis, a systematic statistical examination that combines the results of several independent studies, has the potential of obtaining problem- and implementation-independent knowledge and understanding of metaheuristic algorithms, but has not yet been applied in the domain of operations research. To illustrate the procedure, we carried out a meta-analysis of the adaptive layer in adaptive large neighborhood search (ALNS). Although ALNS has been widely used to solve a broad range of problems, it has not yet been established whether or not adaptiveness actually contributes to the performance of an ALNS algorithm. A total of 134 studies were identified through Google Scholar or personal e-mail correspondence with researchers in the domain, 63 of which fit a set of predefined eligibility criteria. The results for 25 different implementations of ALNS solving a variety of problems were collected and analyzed using a random effects model. This dataset contains a detailed comparison of ALNS with the non-adaptive variant per study and per instance, together with the meta-analysis summary results. The data enable to replicate the analysis, to evaluate the algorithms using other metrics, to revisit the importance of ALNS adaptive layer if results from more studies become available, or to simply consult the ready-to-use formulas in the summary file to carry out a meta-analysis of any research question. The individual studies, the meta-analysis and its results are described and interpreted in detail in Renata Turkes, Kenneth Sörensen, Lars Magnus Hvattum, Meta-analysis of Metaheuristics: Quantifying the Effect of Adaptiveness in Adaptive Large Neighborhood Search, in the European Journal of Operational Research.
ABSTRACT
In this paper, we compare different formulations of the multi-depot fleet size and mix vehicle routing problem (MDFSMVRP). This problem extends the multi-depot vehicle routing problem and the fleet size and mix vehicle routing problem, two logistics problems that have been extensively studied for many decades. This difficult vehicle routing problem combines complex assignment and routing decisions under the objective of minimizing fixed vehicle costs and variable routing costs. We first propose five distinct formulations to model the MDFSMVRP. We introduce a three-index formulation with an explicit vehicle index and a two-index formulation in which only vehicle types are identified. Other formulations are obtained by defining aggregated and disaggregated loading variables. The last formulation makes use of capacity-indexed variables. For each formulation, we summarize known and propose new valid inequalities, including symmetry breaking, lexicographic ordering, routing, and rounded capacity cuts. We then implement branch-and-cut and branch-and-bound algorithms for these formulations, and we fed them into a general purpose solver. We compare the bounds provided by the formulations on a commonly used set of instances in the MDFSMVRP literature, containing up to nine depots and 360 customers, and on newly generated instances. Our in-depth analysis of the five formulations shows which formulations tend to perform better on each type of instance. Moreover, our results have considerably improved available lower bounds on all instances and significantly improved quality of upper bounds that can be obtained by means of currently available methods.
