Vehicle Routing Problem with Transshipment: Mathematical Model and Algorithm

Table 1

Research gap.

Problem	Variant	Problem specific	Linehaul depot to D	Backhaul P to depot	Transshipment P to D
Many-to-many PDP	MVSPDP	Each item is not specific to P and D nodes			Unpaired
1-to-many-to-1 PDP (aka. VRPPD)	VRPB	Visit D nodes before P nodes	✓	✓
	VRPMPD	Any orders of P and D	✓	✓
	VRPSPD	Simultaneous P and D at each node	✓	✓
	SVRPDSP	P is selected only when profitable	✓	Selective
	VRPDDP	Customer node may be visited twice	✓	✓
	VRPTT	Transshipments to transfer loads b/w vehicles at transship points		✓
1-to-1 PDP	DARP	Each item is specific to a pair of P and D node			Paired
	PDPTTW	Transshipments between vehicles allowed at transshipment points			Paired
IRPT		A mix of inv. management and VRP with transshipment location	✓		Not in VRP
LRIPT		A mix of location, inventory, and VRP with transshipment location
This paper	VRPT	A mix of 1-to-many-to-1 PDP (regular demand) and 1-to-1 PDP (transshipment demand)	✓		Paired
	VRPOT		✓	✓	Optional

Note. D denotes delivery node and P denotes pickup node.