Longer dwelling time in a port cause cost inefficiency and uncertainty in ship scheduling. Due to higher port charge, unnecessary queue in a port should be avoided since it will reduce ship utilization and increase operation cost. In the context of industrial shipping, the lateness of a trip of a ship may also cause inventory stock out in the destination ports. These risks will be disadvantages for the supplier since he is also responsible to manage the inventory of commodity in the depot of buyers. The supplier will be charged penalty cost for the lateness under the agreement of Vendor Managed Inventory (VMI). The model which combines transportation and inventory decisions in literature is called Inventory Routing Problem (IRP). In this research, we modify the basic model of IRP for ship scheduling to include some decisions dynamically made to response the information of dwelling time received during the journey: speed of ships and rerouting. We called the proposed model Dynamic-Inventory Ship Routing Problem (D-ISRP). We develop a mixed-integer non-linear program (MINLP) to solve this problem. The objective is to minimize the total cost while avoiding the inventory stock out. The total cost consists of sail bunker consumption cost, port bunker consumption cost, ship operational cost, port charge, loading/unloading cost, and penalty cost for late delivery. Since the proposed model is an NP-hard problem thus a heuristic model is preferred. Specifically, we design a new efficient heuristic algorithm based on the model of interaction theory. The algorithm determines the ship schedule based on the interaction coefficient of ships and ports. The matrices of interaction coefficient of ships and ports is determined by considering the ability of ships to supply port's demand and vice versa. In order to examine the behavior of the model, we conduct some numerical experiments. Our experiments concluded that the proposed algorithm has a high reliability to solve the D-ISRP problem in efficient computational time. We also conduct some experiments to compare between the decisions of speed reduction and rerouting in anticipating updated dwelling time information.

Original languageEnglish
Pages (from-to)344-351
Number of pages8
JournalProcedia Manufacturing
Publication statusPublished - 2015


  • Dwelling time
  • interaction theory
  • inventory ship routing problem
  • mixed-integer non-linear program
  • vendor managed inventory


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