Determining the optimal inventory holding time using mixed integer linear programming (MILP) in a forwarder company

Mixed Integer Linear Programming is an application of optimization in form of linear programming model with the requirement that the variables used are not all integers. This optimization method is used to determine the company's decision optimally by considering the constraints that exist in the company, including the problem of optimizing the storage time of goods at the forwarder company. Currently, forwarder companies do not have a standard time for storing goods because the period of inbound goods from suppliers is uncertain and not in one delivery process. Moreover, the forwarder company has a new branch and is attracting customers so it doesn't have any holding fee yet. This is a quantitative study that aims to determine the optimal time for storing goods while in the warehouse, knowing the inventory holding cost for a day, and minimizing the company's carrying cost. By using Mixed Integer Linear Programming, the optimal time for storing goods is 14 days with a daily inventory holding cost of IDR 113,832. In addition, the results of the application of the model are able to reduce carrying costs by IDR 2,344,948 or 8.6% from the initial condition.