NTS is a Swiss intermodal operator located in Lausanne. When a customer has to transport goods between origin and destination, NTS supplies him with one or more empty containers into which the goods can be loaded. After arriving at the destination. goods are unloaded and empty containers must be transported to the new customer pickup point. Therefore, NTS management needs to reallocate empty containers periodically (every week). What the company focuses on is that empty container transportation activities are very expensive (the cost is almost 35% of total operational costs). In May 2023, some 20 empty containers must be reallocated between terminals in Amsterdam, Berlin, Munich, Paris, Milan, Barcelona and Madrid. The number of empty containers available or requested at various terminals is reported. together with transportation costs (in euros/container) are shown in Figure 1.

Figure 1. Cross flow of goods distribution

Determine how to solve the problem with cost minimization goal transportation

NOTE: The "+" (Supply) and "-" (demand) Arrow quantity nodes describe the flow of materials and costs.

Thank you.