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Cargo Loading Problem
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| Organization: | University of Western Ontario |
| Department: | Department of Statistical and Actuarial Sciences |
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0210-104
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1999-04-27
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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.
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Integer programming, Dynamic programming, constrained optimization, Knapsack problem, Capital Budgeting
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| cargo.m (2.5 KB) - Mathematica package to solve the cargo loading problem | | cargo.nb (15.3 KB) - Mathematica notebook; essay about the problem and documention for cargo.m |
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