PAMDO – Optimized Density for Wood Supply Planning
Developed and implemented in 2004, PAMDO is a planning support tool for wood supply at the pulp mill in Barra do Riacho – ES belonging to Aracruz Celulose S.A. The problem was represented using a Mixed Integer Programming Model through the ILOG CPLEX Component Libraries.
At the Barra do Riacho – ES mill, the crop harvest is usually done mechanically, through the use of harvesters. In areas that this is not possible, the trees are cut down manually. The tree rows are cut down sequentially, so as to reduce the distance covered by the workers and reduce the risk of accidents. The logs are then transported and stacked throughout the roads by forwarders.
The transport logistics for supplying wood at the pulp mills (mills A, B and C), as well as its stocking in the courtyard and supplying for the chip production lines are done by the Wood Transport Control Center. The transport is monitored through an entry invoice, which concentrates all licencing and obligations relative to the process, also acting as a control document for the mill.
The wood loading for third party trucks, at the field, is done through the use of cranes. BR 101 (Brazilian federal highway) is the main means of transportation, connecting the regional units to the mill. Throughout the highway, there is a network of voluntaries that monitor the transportation, reporting improper driving conditions and security issues along the way.
The wood supply process aims to guarantee the supply of several plants at Barra do Riacho, according to a security stock policy (logs and chips) that minimizes the probability of downtime due to lack of material. Besides this, it seeks to guarantee a minimal gap between harvest and transportation, allowing the wood to effectively dry, minimizing the humidity transport and, consequently, the transportation freight.
The wood quality has a direct influence in the production process and the final pulp quality. Its influential characteristics include basic density, the levels of lignin and ash, amongst others. In general, higher density wood is more productive because it results in greater quantity of dry material – generating more material volume for the pulp digesters. On the other hand, higher density wood needs more cooking time, which reduces its productivity.
The several wood plantations available for transport have different densities. The range of possible densities interferes with the control of the pulp extraction process, in the digesters, through the use of chemicals from white liquor (a mixture of sodium hydroxide and sodium sulfide). If the process is configured for higher density wood, the lower density ones will be over cooked. On the other hand, if the process is prepared according to lower density wood, the higher density wood won’t be correctly processed.
In 2003, the Planning and Forest Control Management at Barra do Riacho hired UniSoma to study alternative policies for wood supply that could provide higher quality pulp. Due to the need of maintaining a high supply level for the production lines, without intense courtyard movement, it was quickly perceived that the study had to cover the transport planning activities, integrated to the production lines supply.
In a period of 4 months, UniSoma developed a wood transport and supply planning prototype system. Written in AIMMS, and based on a Mixed Integer Programming Model, the system was able to point out, for scenarios provided by Aracruz, transport and production lines supplying plans that, considering technical-operational constraints of the problem, allowed a significant reduction in wood density variation through time at each mill.
In a second phase, Aracruz decided to develop a system based on the prototype elaborated during the first study phase. Because of information technology standards, this system should use a mathematical programming component library already licensed, at the time, by Aracruz: the ILOG CPLEX Component Libraries. Accustomed to working with AIMMS Software, UniSoma was challenged to develop the system through this new tool.
PAMDO is a three layers system. The first layer is the graphical user interface (GUI), which allows users to interact with the mathematical model; intermediate layer, which translates the several input scenarios into a mathematical programming model format. The mathematical solver is the last system layer and consists of an algorithm that searches for several solutions for the instances created in the intermediate layer.
PAMDO’s graphical user interface (GUI) was developed in Borland Delphi 7.0. Through it, several external procedures involving Aracruz’s corporate data base are executed to import information regarding the plantations. The mathematical model was developed through the ILOG Concert Technology (part of ILOG CPLEX Component Libraries), a set of high level methods for constructing mathematical programming models. The mathematical solvers used are Linear Programming and Mixed Integer Programming from CPLEX Callable Library, a set of routines used to solve the mathematical programming models, also a part of ILOG CPLEX Component Libraries.
In PAMDO, the various planning scenarios can be stored in XML files. This functionality allows the recovery of not only the solution plans, but the hypothesis that where considered in the generation of the plan.
The mathematical model contemplates several problem conditions, such as:
- the need to supply mills;
- the need for specific quality and wood origin;
- maximum consumption of wood with unknown density;
- minimum and maximum wood use with bark at mills;
- the transport windows for several plantations;
- the maximum density variation between consecutive weeks;
Most constraints are treated as soft constraints, to facilitate the obtaining of feasible solutions. Still, there constraint violations, or lack of violation, are controlled through the use of penalized constraints, controlled by the planner.
The optimization criteria aims to find solutions that minimize (a) the variation of density from week to week, (b) partial wood transportation and (c) the sum of the slack variables, with their respective penalizations.
The solution with minimized density variation through time, can be interpreted as a dynamic specialization policy for production lines, in opposition to a static and predefined alternative many times used in other pulp production mills.
Optimized solution generated by the prototype where compared to real transportation and supply plans, indicating a reduction of up to 70% in the amplitude of variation in density in the various mills and through the planned periods.
To access a technical capability certification relative to the project, click here (Portuguese).
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