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MDVSP k k p p k k p K k p k p k ip K k p k p k p k k k ip k k p k j ij i i ij i i p K k x K k n x N i x a x c K k n N i p a p c K k K N j i t d s t A j i A K N j i j i d N i s N i t N K k k k min depot at vehicles of number available : otherwise 0 ; task covers path if 1 path of cost : depot to and from paths of set : , for , if) , (arcs; of set : , for ,(More)
Column generation is often used to solve problems involving set-partitioning constraints, such as vehicle-routing and crew-scheduling problems. When these constraints are in large numbers and the columns have on average more than 8–12 nonzero elements, column generation often becomes inefficient because solving the master problem requires very long solution(More)
Column generation has become a powerful tool in solving large scale integer programs. We argue that most of the often reported compatibility issues between pricing oracle and branching rules disappear when branching decisions are based on the reduction of the variables of the oracle's domain. This can be generalized to branching on variables of a so-called(More)
The problem considered involves finding the minimum cost path, with cost and time being two independent quantities that govern the shortest path. In this problem, each arc is associated with a cost of traversing the arc as well as the time required to traverse it and each node is associated with a lower bound and an upper bound on the time of departure from(More)