E. Application Domains and Software
• Mixed integer programs can be used to formulate just about any discrete optimization problem. They are heavily used in practice for solving problems in transportation and
manufacturing: airline crew scheduling, vehicle routing, production planning, etc. Michael Tricks
Operations Research Page contains pointers to many web sites on operations
research in general, including math programming, specific methods, and specific problems or problem areas. The following are good journals to look at for technical papers applying
integer programming: Operations Research
, Mathematical Programming
Series A and B, and
SIAM Journal on Optimization .
• Commercial code includes IBMs Optimization Subroutine Library OSL
, CPLEX
, and XPRESS-MP by
Dash . The University of Karlsruhe has a list of
23 commerical solvers , with
some comparison information. Compass Modeling Solutions
, provides an AMPL ATT
Mathematical Programming Language interface to some commercial solvers. There are
other modeling languages, sometimes provided with the MIP package http:www.cs.sandia.govoptsurveymip.html
IV. Problem description A. Harvest areas
• A district is divided into harvest areas. Annual planning starts with a list of areas, identified as suitable for harvest during the next 1.5-2 years. Each harvest area is unique with its own
properties. It varies in size and in available volumes of assortments, and areas require between 1 and 20 days of work to harvest. The operations are either final felling or thinning.
• The production time depends on the average size of the trees and the equipment of the harvest team. Each area is also connected to a particular road or road group. Table 1 gives
typical data for five areas in the case study. The name of the areas, the number of standard hours to harvest the area, the average tree diameter, and quantities of the different
assortments are given.
• The accessibility profile code implies a certain annual profile of the accessibility, i.e., a certain grade of accessibility for each month. Areas with accessibility profile 5 correspond to
areas with soft ground, and areas with accessibility profile 1 correspond to areas with high accessibility, possible to harvest during thawing. There is generally a shortage of areas with
a good accessibility profile.
Table 1. Information used for five harvest areas.
B. Harvest teams
• There are a number of teams working full time in a district. A harvest team consists of a harvester, a forwarder, and two working groups with two people in each. The harvester fells,
Universitas Sumatera Utara
Kategori