Exact algorithms for the multi-compartment vehicle routing problem with flexible compartment sizes

The multi-compartment vehicle routing problem with flexible compartment sizes is a variant of the classical in which customers demand different product types and capacity can be separated into compartments each dedicated to specific type. size not fixed beforehand but number limited. We consider two variants for dividing capacity: On one hand discretely divided on other continuously. objective minimize total distance all routes such that customer demands are met capacities respected. Modifying branch-and-cut algorithm based three-index formulation discrete from literature, we introduce an exact solution approach tailored continuous variant. Moreover, propose approaches, namely two-index branch-price-and-cut route-indexed formulation, tackle both small adaptions combined effective two-stage approach. Extensive computational tests have been conducted compare algorithms. For variant, solve instances up 50 optimality several previously open now solved proven optimality. analyze cost savings using continuously instead sizes.