Model and Algorithm for Container Allocation Problem with Random Freight Demands in Synchromodal Transportation

Table 1

List of notations.

Symbol	Description
(1) Index sets
	Set of freight types .
	Set of destinations .
	Set of transportation modes .
	Set of scenarios .
	Set of freight transported by mode .
(2) Random data
	Demands for transportation of freight type to destination under scenario .
	Penalty per unit shortage in supplied capacity for freight type transported by mode to destination under scenario .
	Penalty per unit overage in supplied capacity for freight type transported by mode to destination under scenario .
(3) Deterministic parameters
	Profit for carrying a unit freight of type to destination by transportation mode .
	Requested bottom supply of capacity for transportation mode to destination .
	Amount of available container capacity at the origin .
(4) Decision variables
	Container capacity for transportation mode of freight type to destination , which will be supplied for shipping cargoes in a planning horizon. In this paper, we assume that the unit of capacity is TEU (i.e., twenty-foot equivalent unit).
	Amount of shortage capacity for freight type transported by mode to destination under scenario .
	Amount of overage in capacity for freight type transported by mode to destination under scenario .
	Binary variable: that is, , transportation mode to destination will be operated; , otherwise.