Optimizing Central Kitchen Deliveries with a Practical VRP Model

Many chain restaurants rely on a central kitchen that prepares food in bulk and distributes it to multiple outlets. The challenge is to transport food efficiently and economically.

This article introduces the classic Vehicle Routing Problem (VRP) and presents its mathematical model with a case study.

VRP Model

The VRP is a combinatorial optimization problem that requires designing optimal routes for a fleet of vehicles departing from a depot to serve a set of customers and return to the depot, minimizing total distance or cost while respecting vehicle capacity.

Decision Variables

x_{ij} : binary variable, equals 1 if a vehicle travels from node i to node j, otherwise 0.

y_{i} : binary variable, equals 1 if a vehicle serves node i, otherwise 0.

d_{ij} : travel distance from node i to node j.

q_{i} : demand of node i.

Q : maximum load capacity of a vehicle.

Node 0 represents the depot.

Objective Function

The goal is to minimize the total travel distance of all vehicles.

Constraints

Service constraint: each customer is served by exactly one vehicle.

Vehicle capacity constraint: the total load on each vehicle cannot exceed its maximum capacity.

Route continuity constraint: if a vehicle serves a customer, it must arrive from a previous node and depart to the next node.

Depot start/end constraint: each vehicle's route must start and end at the depot.

Binary and non‑negativity constraints.

Example: a central kitchen with three trucks (each 1000 kg capacity) serving ten distribution points with demands ranging from 100 kg to 300 kg. Applying linear programming or heuristic algorithms can solve this VRP, optimizing routes, reducing costs, and improving efficiency.

The key of VRP is to transform complex daily transportation tasks into a mathematical problem that can be effectively solved with modern optimization techniques, though real‑world data may require model refinements such as traffic conditions, driver work hours, and operating costs.