V + k M f k x k – j . p(38)(two) Cop
V + k M f k x k – j . p(38)(2) Cop (operating cost) The operating price is associated to the total operating time as well as other factors. The total operating time expense is calculated as shown in the formula: Cop =k iV jV k M xij cij .(39)(three) C pwt (passenger waiting cost) Passenger waiting cost refers for the waiting time cost triggered by time window limitations when passengers are waiting for follow-up passengers to get around the vehicle, which focus on the viewpoint of passengers. The total price of passenger waiting time is calculated as follows: k k C pwt = kK iV jV c p xij yi Wjk . (40) (four) Cvwt (vehicle waiting expense) Automobile waiting time expense refers to the time cost brought on by time window limitations, which concentrate around the perspective of vehicles. The total cost of automobile waiting time is calculated as shown inside the formula: C pwt = (5) Service excellent penaltyunsatis Cqua = C unsatis + Cdelivery + Cdt pickupkK iV cwk Wik .(41)(42)In order to measure the service high-quality, we define 3 top quality indexes. Analysis shows that most passengers favor the car to arrive in the mid-point in the pickup time window and also the low limit in the delivery time window [29]. C unsatis indicates the pickupunsatis time gap involving the expected pickup time and the actual ones, Cdelivery indicates the time gap among the anticipated delivery time along with the actual ones. Cdt may be the distinction in between direct travel time and actual travel time which caused by important detouring distance.C unsatis = GSK2646264 site pickupi N k Kei + + li + – Dik iV x k – i , p 2 ei- – Dik- iV x k – i , pp(43) (44) (45)unsatis Cdelivery =i N k KCdt =i N k Ktserve i – ti,i+n iV x k – i . pEquations (2)four) may be the equilibrium constraint. Equation (five) guarantees every single section of each service unit is assigned to precisely 1 vehicle. Equations (six) and (7) ensures only if the car passes IEM-1460 In stock certain section on the service unit, can the demand be served. Equation (8) ensures the continuity of service with transfers. Equation (9) guarantees the starting point of every single car is corresponded for the beginning station it belongs to. Equation (10) guarantees each automobile only goes back to on the list of returning stations. Equation (11) ensures the total number of autos returned to every station is larger than the minimum value. Equation (12) guarantees automobiles is not going to visit a very same transfer point repeatedly in one service procedure. Equations (13)16) ensures the condition for the occurrence of transferring: only if automobile k and automobile l passes transfer point t within a similar service process, can they exchange passengers in transfer point t, and only if demand n has been picked up by car k, can it be transferred from car k to automobile l. Equations (17) and (18) definesInformation 2021, 12,8 ofthe arrival time of each and every node. Equation (19) ensures the transfer waiting time of passengers is shorter than twp. Equation (20) guarantees the transfer waiting time of cars is shorter kl k l than twc. Equations (21) and (22) guarantees if wti = 1, Dik+ Dt and Dt Dik- , which defined the time sequence with the procedure of transferring. Equations (23) and (24) furtherly define the sequence of arrival. Equations (25) and (26) is automobile loading constraint which define how car pickup and deliver shoppers when devoid of passing transfer points. Equations (27) and (28) define how vehicle pickup and provide shoppers when it comes to transfer. Equations (29) and (30) define the maximum operating time and maximum travelling distance of each v.