Table 1.

Notations of the mathematical model.

Sets
T	set of cycle length, T = {1, 2,3, …, t} days
N	The set of medical institutions, N = {1, 2, 3… n}, 0 and n + 1 are vehicle parking points, N0 = N∪{0, n + 1}
V	Set of vehicles, V = {1,2,3 … v}
Parameters
cij	Distance from medical institution i to medical institution j, i, j∈N0
tij	Transportation time from medical institution i to medical institution j, i, j∈N0
sei	Service time for medical institution i, i ∈ N0, where se0 = sen+1 = 0
ei	The lower bound of time window for medical institution i
li	The upper bound of time window for medical institution i
ω 1	Unit fixed usage costs of vehicle
ω 2	Unit travel cost of vehicle
Ψ	Maximum value
Q	Maximum load capacity of medical waste recycling vehicles
$q_i$	Amount of medical waste generated by medical institution i in a cycle
Decision-making variables
$f_i$	The required recycling frequency of medical institution i in a cycle (The amount of waste that needs to be recycled each day within a cycle of medical institution i is qi/fi)
$x_{ijv}^t$	Binary variables: 1 if vehicle v arrives directly at medical institution j from medical institution i on day t; 0 otherwise
$y_{iv}^t$	Binary variables: 1 if vehicle v visits medical institution i on day t; 0 otherwise
$s_i^v$	Arrival time of vehicle v at medical institution i