The development of the inventory model started when Harris introduced the classic inventory model. It was firstly published by Wilson using the optimization method. He derived a mathematical equation model to obtain economic order quantities. Later, this model is known as the classic Economic Order Quantity (EOQ) or Wilson Model. The classic inventory EOQ model has some limitations. The model assumed that order items do not have physical changes during a planning period. This assumption becomes the weakness of the classical EOQ inventory model. Many items have material changes during a planning period, such as amelioration, deterioration, and growth. This research proposed a new mathematical model. The model relaxes three implicit assumptions of the classical EOQ: (1) the ordered items do not grow; (2) unlimited capacity; and (3) unlimited budget. A solution procedure to solve the model was developed and illustrated with a numerical example. A numerical example was performed to compare the result between the reference model and the new model. The number of ordered items per cycle time increased by 7%, and cycle time increased by 28%. It increased because the proposed model tends to choose large purchased quantities to get a cheap price. It caused the number of ordered items per cycle time to be larger and the cycle time to be smaller than the reference model. This research also provided sensitivity analysis. It showed the response of decision variables to some changes in input parameters.

This study discusses the problem of determining which container port should be developed within an existing network and when this should be carried out. A case study of Indonesia’s port network is presented, where several new ports are to be improved to ensure smooth interisland transportation flows of goods. The effects of the investment on economic consequences and increased network connectivity are assessed. When improving the ports, we consider that the available budget limits the investment. The network connectivity is evaluated by considering the number of reachable ports from the developed ports or transportation time required from other ports within the same port cluster. Based on our knowledge, our study is the first one that discusses the investment problem in multiple container ports under single management, as well as its effects regarding the increase in container flows. The problem is introduced and three mathematical models are proposed and used to solve a real problem. The results show that different models have different improved aspects of container transportation flows—e.g., a balanced improvement of the whole port network (Model 2) and appropriate investment priority for port clusters (Model 3).