lpSolve (version 1.1.7)

lp.transport: Integer Programming for the Transportation Problem

Description

Interface to lp_solve linear/integer programming system specifically for solving transportation problems

Usage

lp.transport (cost.mat, row.signs, row.rhs, col.signs, col.rhs, presolve=0, compute.sens=0)

Arguments

cost.mat

Matrix of costs; ij-th element is the cost of transporting one item from source i to destination j.

row.signs

Vector of character strings giving the direction of the row constraints: each value should be one of "<," "<=","" "=","">," or ">=."

row.rhs

Vector of numeric values for the right-hand sides of the row constraints.

col.signs

Vector of character strings giving the direction of the column constraints: each value should be one of "<," "<=","" "=","">," or ">=."

col.rhs

Vector of numeric values for the right-hand sides of the column constraints.

presolve

Numeric: presolve? Default 0 (no); any non-zero value means "yes." Currently ignored.

compute.sens

Numeric: compute sensitivity? Default 0 (no); any non-zero value means "yes."

Value

• An lp object. See documentation for details.

Details

This is a particular integer programming problem. All the decision variables are assumed to be integers, and there is one constraint per row and one per column (and no others). This is assumed to be a minimization problem.

References

Example problem from Bronson (1981), Operations Research, Scahum's Outline Series, McGraw-Hill.

See Also

lp.assign, lp.transport

Examples

#
# Transportation problem, Bronson, problem 9.1, p. 86
#
# Set up cost matrix
#
costs <- matrix (10000, 8, 5); costs[4,1] <- costs[-4,5] <- 0
costs[1,2] <- costs[2,3] <- costs[3,4] <- 7; costs[1,3] <- costs[2,4] <- 7.7
costs[5,1] <- costs[7,3] <- 8; costs[1,4] <- 8.4; costs[6,2] <- 9
costs[8,4] <- 10; costs[4,2:4] <- c(.7, 1.4, 2.1)
#
# Set up constraint signs and right-hand sides.
#
row.signs <- rep ("<", 8)
row.rhs <- c(200, 300, 350, 200, 100, 50, 100, 150)
col.signs <- rep (">", 5)
col.rhs <- c(250, 100, 400, 500, 200)
#
# Run
#
lp.transport (costs, row.signs, row.rhs, col.signs, col.rhs)
Success: the objective function is 7790
lp.transport (costs, row.signs, row.rhs, col.signs, col.rhs)$solution
[,1] [,2] [,3] [,4] [,5]
[1,]    0  100    0  100    0
[2,]    0    0  300    0    0
[3,]    0    0    0  350    0
[4,]  200    0    0    0    0
[5,]   50    0    0    0   50
[6,]    0    0    0    0   50
[7,]    0    0  100    0    0
[8,]    0    0    0   50  100