Case Study: The Forestry (Logistics) Problem

Submitted: 3 Apr 2008

Operations Research Topics: LinearProgramming, IntegerProgramming, NetworkOptimisation, TransportationProblem

Application Areas: Logistics

Contents

Problem Description

Adapted from a real-world problem

A paper company own a number of mills that produce paper with different processes, e.g., the thermo-mechanical process (see Figure 1), the cold caustic soda process, etc. They procure raw materials for each of their processing machines from a number of different suppliers.

Figure 1 Thermo-mechanical Processing Machine

tmp.jpg

Their suppliers consist of 3 forestry operations: Kaingaroa, NSW and Taupo. They also own a recycling plant where they receive waste paper.

They own mills at Kawerau (NZ), Boyer (Tasmania) and Albury (NSW). The following table summarises the processing machines at each mill:

Mill Thermo-Mechanical Process (TMP) Refiner-Mechanical Process (RMP) Stone Groundwood Process (SGW) Cold Caustic Soda Process (CCS) Recycled Fibre Process (RCF)
Kawerau yes yes yes no no
Boyer yes no no yes no
Albury yes no no no yes

The paper company purchases three types of raw materials: woodchips, pulp logs and waste paper. The thermo-mechanical, refiner-mechanical and cold caustic soda processes use woodchips, the stone groundwood process uses pulp logs and the recycled fibre process uses waste paper. The requirements (in tonnes) for their different machines are given below:

Mill Thermo-Mechanical Process (TMP) Refiner-Mechanical Process (RMP) Stone Groundwood Process (SGW) Cold Caustic Soda Process (CCS) Recycled Fibre Process (RCF)
Kawerau 10 15 52 - -
Boyer 15 - - 10 -
Albury 20 - - - 22

The supplies of the various raw material is given in the following table:

tonnes Woodchips Pulp Logs Waste Paper
Kaingaroa 20 20 0
NSW 23 17 0
Taupo 19 22 0
Recycling Plant 0 0 24

The transportation cost of the raw materials is given in the following table:

$100/tonne of material Kawerau Boyer Albury
Kaingaroa 4 10 8
NSW 12 6 3
Taupo 5 10 7
Recycling Plant 7 11 10

Note that pulp logs can be "chipped" into woodchips at the suppliers at a cost of $250/tonne and that waste paper can be "compacted" into woodchips at the recycling plant at a cost of $600/tonne. Any excess waste paper that is not used must be disposed of at a cost of $150/tonne.

Tree Chipper

The paper company want to know how to supply their mills at minimum cost. They also want to know how much "streamlining" their processes (i.e., reduce the amount of raw materials they use) will reduce their overall transportation costs.

For more detail see Supply Chain Optimisation in the Paper Industry, Philpott and Everett

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