Mathematical Model for Maritime Inventory Routing Problem with Multiple Time Windows

This paper considers a new variant of the maritime inventory routing problem which considers multiple time windows. The typical time windows that this problem considers that it may exist for certain ports which only permit a ship entering and leaving the ports within daytime due to both natural conditions and their facilities. A mathematical model formulated as mixed integer programming is developed for solving this kind of problem. The problem is to find how many products and how much of each products are carried by each ship from source ports which assumed have constant production rates to destination ports which assumed have constant consumptions rates without exceeding the production port storages and out of stocks in the consumption port storages during the planning horizon. The objective of the problem is to minimize the cost while satisfying a set of technical and physical constraints. The detailed modified variables and constraints from the ones exist in the literature are discussed. Then the model is tested with several test problems with different days of planning horizon as well as different number of ship visits at consumption ports during planning horizon. The experiment results solved using LINGO show that modeling multiple time windows can give higher objective functions in comparison to the ones of without time windows. Moreover, modeling multiple time windows significantly increases the computational time in comparison with the ones without multiple time windows. Keywords—mathematical model, maritime, inventory routing problem, multiple time windows