Multi-Depot Pickup and Delivery Problem with Resource Sharing

Table 2

Notations and description.

Set	Description
SD	Set of DCs, the total number of DCs is ND
SP	Set of PCs, the total number of PCs is NP
SF	Set of DCs and PCs, SF=SP ∪ SD
CD	Set of delivery customers
CP	Set of pickup customers
CU	Set of all customers, U=CD∪CP
V	Set of vehicles, the total number of vehicles is NV
B	Set of trucks, the total number of trucks is NB
Parameters
Qc^D	Delivery demand of customer c, c ∈ CD
Qc^P	Pickup demand of customer c, c ∈ CP
[Ec,Lc]	Service time window of customer or logistics facility c, c ∈ CU∪SF
dch	Travel distance between customer or facility c and customer h. c, h ∈ CU∪SF
tch	Travel time of a vehicle driving from customer or facility c to customer h. c, h ∈ CU∪SF
PE	Waiting penalty coefficient of arriving earliness (unit: dollars/unit time)
PL	Tardiness penalty coefficient of arriving delay (unit: dollars/unit time)
W	Number of working periods in a year
T	Number of working days in a working period
	Maximum travel time of vehicle v, v ∈ V
Tb	Maximum travel time of truck b, b ∈ B
	Fuel consumption rate of vehicle per km (unit: gallon/miles)
fb	Fuel consumption rate of truck b per km (unit: gallon/miles)
	Gasoline price (unit: dollars/gallon)
Pb	Gasoline price (unit: dollars/gallon)
	Capacity of vehicle v, v ∈ V
Cb	Capacity of truck b, b ∈ B
Cf	Capacity of facility f, f ∈ SF
	Annual maintenance cost of vehicle v, v ∈ V
Mb	Annual maintenance cost of truck b, b ∈ B
If	Annual fixed cost of facility f, f ∈ SF
	The total service route number of vehicle ,  ∈ V
Gvfk	The departure time of vehicle from facility f in the kth service route. ∈ V, f ∈ SF, k ∈
Avck	The arriving time of vehicle at customer or facility c in the kth service route,  ∈ V, c ∈ CU∪SF, k ∈
Qof	The number of transported goods from facility o to f, o, f ∈ SF
Variables
xvcfk	= 1 if customer c is served by vehicle departing from DC or PC f in the kth service route of vehicle ; otherwise, xvcfk = 0,  ∈ V, c ∈ CU, f ∈ SF,k ∈
xcof	xcod = 1 if the facility providing logistics service for customer c is changed from facility o to f; otherwise, xcod = 0, c ∈ CU,o, f ∈ SF
xvch	= 1 if vehicle travels directly from facility or customer c to h; otherwise, xvch = 0,  ∈ V, c,h ∈ SF∪CU.
xbof	xbof = 1, if the goods transported from facility o to f is carried by truck k; otherwise, xbof = 0, b ∈ B, o, f ∈ SF
xbowf	xbowf = 1, if truck k departs from facility o and travels directly from facility to f; otherwise, xbowf = 0, b ∈ B, o,, f ∈ SF
zf	zf = 1 if facility f agrees to share resource, otherwise, zf = 0, f ∈ SF.