Problem: Soft Fruit Spreads Distribution and Routing

A soft fruit spreads (jam, marmalade, fruit preserves) wholesaler located in the South of London distributes to 60 restaurant (retailers) mainly located in London. The spreads are packaged in quantities of 20 glass jars of 300ml each. A retailer can only order in packs of 20 glass jars. A homogeneous fleet of 9 vans deliver the soft fruit spreads from the distribution centre (wholesaler) to the retailers. Each retailer has a specific quantity of demand for the soft fruit spreads, and each van has a limited capacity for carrying 100 packs of these soft fruit spreads. The vans depart from the distribution centre to service the retailers with known locations and demands, and then return to the distribution centre. The locations of the retailers are expressed using (x, y) coordinates on the Euclidean plane. The coordinates of the locations and the demands are described in the file “Soft_Fruit_Spreads_Distribution-Routing.xls” on Moodle.

The main objective is to assign the vans to routes to deliver the soft fruit spreads to the retailers to minimise the total distance travelled by the vans, subject to the following hard constraints:

• Each van departs from and returns to the distribution centre.

• Each retailer is visited exactly once by a single van.

• Each van has a limited capacity of 100 packs.

• The total load on any van associated with a given route must not exceed the capacity of the van.

• The number of vans available at the distribution centre is 9.

1. Formulate mathematically the optimisation model of the Soft Fruit Spreads Distribution and Routing problem to minimise the total distance travelled by the vans. Describe clearly in detail your optimisation model: fitness function, decision variables, and constraints. Provide any references in the literature you have used.