# Case Study: The Winstone Aggregates Problem

## Problem Description

Winstone Aggregates NZ is New Zealand's largest aggregate company. They operate 12 hard rock quarries throughout New Zealand along with Sand Plants, Gravel and Shingle Plants and a Scoria Pit. The aggregates produced by Winstones are used in the construction of roads and buildings. In 1997 Winstone Aggregates approached the Department of Engineering Science (University of Auckland) to help with strategic planning for the closure of the Lunn Ave Quarry in Mt Wellington.

The original model devised by Department of Engineering Science researchers was written in GAMS (General Algebraic Modeling language), and solved using MINOS.

Winstones take Sand, Scoria, Basalt and Greywacke from their quarries and mix these to produce several different types of aggregate:

• Coarse
• Fines
• LowBase
• HighBase
• Sand
• Scalpings
• Scoria
• Sealchips

The amount of each raw material available is limited as the Resource Consent Act controls the extraction of the raw materials from the quarries.

Raw materials may also undergo intermediate processing, e.g., rocks extracted as large boulders must be crushed and then "screened" at the processing plant, before being "mixed" into aggregates.

Winstone Aggregates wants to maximise the profit it receives to determine the best use of its raw materials, but it has to consider factors such as

• the demand for different aggregates varies during the year;
• stockpiling product costs money, i.e., the holding cost;
• each aggregate is made according to a recipe that defines how it is produced from the raw materials;
• transportation costs from quarries to customer must be incorporated.

For this case study, we will consider a smaller problem from Winstone Aggregates. They have extracted 40 tonnes of Scoria and 20 tonnes of Greywacke. They can use these raw materials to produce Fines, HighBase and Coarse aggregates. The recipe and sale price for the aggregates is given in Table 1.

Table 1 Aggregate recipes and prices

 Recipe (per tonne) Scoria (tonnes) Greywacke (tonnes) Sale Price (\$/tonne) Fines 0.6 0.9 70 HighBase 0.5 0.7 60 Coarse 1.2 0.3 40

Winstones want to find the best production plan for their supply of raw materials.