Each day qi tons of freight arrive by sea10 in Japan bound for in-country regions i = 1,

c, 50.

These goods may arrive at any of the major ports j = 1,

c, 17, but the internal transportation cost per ton ci,j varies by port and destination.

The government plans a capital investment program in port facilities to pick daily tonnage processing capacities at each port j that minimize these internal transportation costs plus associated port maintenance costs, plus delay costs from freight passing through each port. Port j maintenance costs can be expressed aj1capacity j2bj, where aj and bj are known constants. Delay cost at j can be estimated by d/[(capacity j) − (traffic through j)], where d is the delay cost per ton per day. Formulate an NLP model to optimize the ports using the decision variables 1i = 1,

c, 50; j = 1,

c, 172 xi,j ! tons shipped through port j for i xj ! total tons shipped through port j yj ! capacity of port j