Case Study: The Brewery Logistics Problem

Submitted: 2 Apr 2008

Operations Research Topics: LinearProgramming, IntegerProgramming

Application Areas: Logistics

Problem Description

A boutique brewery has two warehouses from which it distributes beer to five carefully chosen bars. At the start of every week, each bar sends an order to the brewery’s head office for so many crates of beer, which is then dispatched from the appropriate warehouse to the bar. The brewery would like to have an interactive computer program which they can run week by week to tell them which warehouse should supply which bar so as to minimize the costs of the whole operation.

For example, suppose that at the start of a given week the brewery has 1000 cases at warehouse A, and 4000 cases at warehouse B, and that the bars require 500, 900, 1800, 200, and 700 cases respectively.

The transportation costs are given in Table 1.

Table 1 Transportation costs from warehouses to bars

Cost ($/crate)	Warehouse A	Warehouse B
Bar 1	2	3
Bar 2	4	1
Bar 3	5	3
Bar 4	2	2
Bar 5	1	3

Which warehouse should supply which bar?

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Problem Formulation

Since crates of beer are being shipped from the warehouses to the bars, this problem is a bipartite network and can be modelled as a transportation problem.

The supply nodes are the warehouses, the demand nodes are the bars

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