The Clarke and Wright savings algor

The Clarke and Wright savings algorithm is one of the most known heuristic for VRP. It was developed on [Clarke and Wright 1964] and it applies to problems for which the number of vehicles is not fixed (it is a decision variable), and it works equally well for both directed and undirected problems. When two routes ${(0,...,i,0)}$ and ${(0,j,...,0)}$ can feasibly be merged into a single route ${(0,...,i,j,...,0)}$, a distance saving ${s_{ij}=c_{i0}+c_{0j}-c_{ij}}$ is generated. The algorithm works at follows (the first step is equal in both parallel and sequential versions):

The Clarke and Wright savings algorithm is one of the most known heuristic for VRP. It was developed on [Clarke and Wright 1964] and it applies to problems for which the number of vehicles is not fixed (it is a decision variable), and it works equally well for both directed and undirected problems. When two routes $ {(0, ..., i, 0)} $ and $ {(0, j, ..., 0)} $ can feasibly be merged into a single route $ {(0, ..., i, j, ... , 0)} $, a distance saving $ {s_ {ij} = c_ {i0} + c_ {0j} -c_ {ij}} $ is generated. The algorithm works at follows (the first step is equal in both parallel and sequential versions):.

The Clarke and Wright savings algorithm is one of the most known heuristic for VRP. It was developed on [Clarke and Wright. 1964] and it applies to problems for which the number of vehicles is not fixed (it is a decision variable), and it works. Equally well for both directed and undirected problems. When two routes {$(,,, 0... I 0)} $and {$(0 J,,,... 0)} $can feasibly be. Merged into a single route {$(0,,,,... I, J... 0)} $, a distance saving {$s _ {ij} = C _} + {{I0 C _ 0j} - C _ {ij}} $is generated. The algorithm. Works at follows (the first step is equal in both parallel and sequential versions):