To optimize on the supply chain operation, researchers developed solutions for the vehicle routing problem (VLP) and also the container loading problem (CLP). It is impossible to optimize the routing process only and fail to optimize the CLP process. Likewise is impossible to develop solutions for CLP without developing VLP solutions. This paper suggests the use of an integrated approach to solve the routing problem.
Several methods have been put across by different mathematician to help tackle the routing and packing problems. Some of these methods include the formulation of mathematical models, the use of algorithms as well as the integration of the two methods. This paper suggests the use of an integrated vehicle routing and container packing problem with the use of generic algorithms.
G= (VA) which represents the complete graph with V representing the nodes and A representing the arc set, the vertex set V is described by V= and 0 represent the depot and represent the nodes. K represents the number of available vehicles. The vehicles are defined by their length, width and height. These dimensions are defined as HK, MK, WK,LK which represent the height , weight, width and length of the vehicle. the cost of vehicles to travel from point i to j is given by Cijk, the traveling time for the vehicle from the point i to j is given by tijk, the service time of vehicle K at node i
is given by Sik, the cargo type is represented by, the length of the cargo is represented by lp, while the cargo width is represented by wp. The weight of the cargo is given by mp. The time taken to load cargo to the track is given by tdpk, while the time taken to unload the cargo is given by tupk. The demand for the cargo at a given node (n) is represented by Dp(i). The number of cargo delivered by vehicle K is given by.
Setting the constrains
Clients; the model assumes that the clients are distributed within a given geographical area. Some clients are near the deport while others are situated away.
Deport: the model assumes that there is one deport to serve these clients
Vehicles; the vehicles are the same, that is they are homogenous
Vehicle capacity; the capacity constrains for the vehicle are given by weight that the vehicle can carry and the volume of the vehicle. The volume of the vehicle is defined by setting (length by width by height of the vehicle). The correct definition involves defining