An efficient way of single and multiple containers loading by resizing the boxes

This thesis presents efficient ways of loading boxes into containers by resizing them. Two different problems are determined to apply the proposed method. First problem contains filling a single container with only one type of boxes. It is objected to pack maximum products in the container. In second one, customers give orders of different products and thus different boxes are tried to be filled efficiently in one or multiple containers in a fashion of blocks for purpose of minimizing the volume of the block areas and increasing the remained space for the next orders. Also a procedure and its sub-procedures and policies are defined to create more customer satisfaction. Two mathematical models are formed to solve the problems and three stages are defined in appliance of each. At first stage, the model is modified to the reduced form which has integer linear properties and applied to the current box sizes. Second stage uses the original model which has integer nonlinear properties and may not get global optimal solutions although operates in less time for the solution. Third stage contains reduced form of the model as the first stage. This time all candidates for box sizes are applied and global optimal solutions are found. At the end, a comparison for all stages and 2D visualizing of the solutions are given in order.