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Cargo Loading Problem
Author

A. Ian McLeod
Organization: University of Western Ontario
Department: Department of Statistical and Actuarial Sciences
URL: http://www.stats.uwo.ca/faculty/aim/
Old MathSource #

0210-104
Revision date

1999-04-27
Description

The cargo loading problem is a special type of integer programming or optimization problem which can easily be solved by dynamic programming. The problem is explained in detail in this notebook and the use of a companion Mathematica package for solving this problem is illustrated. Some amusing timings with APL on computers of yesterday are made.

This problem is formulated mathematically as the maximization of a linear function subject to a single linear constraint (<=). The coefficients in the objective function and constraint are all assumed to be real positive numbers. The decision variables obey the nonnegativity condition and are integer valued. An additional constraint that can be imposed is that each decision variable is less than or equal to some prescribed number. The problem may be formulated as an integer programming problem: maximize v x subject to x>=0 and w x <= k and x <= q.
Subject

*Applied Mathematics > Optimization
Keywords

Integer programming, Dynamic programming, constrained optimization, Knapsack problem, Capital Budgeting
Downloads Download Wolfram CDF Player

Download
cargo.m (2.5 KB) - Mathematica package to solve the cargo loading problem
Download
cargo.nb (15.3 KB) - Mathematica notebook; essay about the problem and documention for cargo.m