A major challenges in modeling vehicle routing problems is the formulation of constraints that prevent short-cycles (roundtrips not including the depot node 0). Beside the con straints you know from the lecture slides there are several different ideas for the formu lation of short-cycle-prevention constraints. In the following, we investigate the Miller Tucker-Zemlin-contraints for the prevention of short-cycles. In this context, we use the following symbols N number of customer locations that require a visit (Attention: the depot hus the number of) . K: number of available vehicles binary decision variable, which is equal to 1 if and only if vehicle & drives directly from node i to node j Ma non-negative and continuous decision variable for the combination of customer location i and vehicle k. It indicates the position of node i in the visiting sequence decided for vehicle k My+N SN-1 vije (1.....N) Vk (1K) Assume that we have a vehicle routing problem with exactly one vehicle (K-1). (1) Figure 2: Locations of a vehicle routing problems (to be served by one vehicle) (a) Draw a least distance round trip through all five nodes into Fig. The travel distances correspondig to the distances in the figure. (4 points)