We define the problem as follows:
- Objective: The objective is to minimize the vehicle fleet and the sum of travel time needed to supply all customers.
- Feasibility: A solution is feasible if all constraints of VRP are satisfied. Furthermore a vehicle may not return to the depot in the same day it departs. Over the M-day period, each customer must be visited at least once.
- Formulation: Minimize
the sum of the cost of all routes. Each customer has a known daily demand
that must be completely satisfied in only one visit by exactly one vehicle.
If the planning period M = 1, then PVRP becomes an instance of the classical
VRP. Each customer in PVRP must be visited k
times, where
.
In the classical model of PVRP, the daily demand of a customer is always
fixed. The PVRP can be seen as a problem of generating a group of routes
for each day so that the constraints involved are satisfied and the global
costs are minimized. PVRP can also be seen as a multi-level combinatorial
optimization problem: - In the first level, the
objective is to generate a group of feasible alternatives (combinations)
for each customer. For example, if the planning period has
days 
then the possible combinations are: 
;
; 
;
;
; 
;
and 
. If a customer requests
two visits, then this customer has the following visiting alternatives:
, 
, and
(or
the options: 3, 5 and 6 of the table below).