parseGoal {goalp}

Parses text describing goal programming problem.

Description

Given a character vector describing a series of linear equations, it parses them into an A numerical matrix describing the variables coefficient in the left hand size, a b numerical vector with values on the right hand size, and an m character vector indicating the relation between the left and right hand side (=, ==, <=, >=, <, >).

Usage

parseGoal(eqs)

Arguments

eqs

Character vector describing a set of linear equations. The vector can either contain a single element with one equation per line, or multiple elements, each with a single equation. Equations must be valid R expressions (see details).

Details

This function can only parse linear equations. All variables must be on the left-hand side, with only numeric values on the right-hand side. Equations must be valid R expressions. Examples of valid equations are the following:

• "3*x + 2*y = 16"

• "4*x - y = 3"

The following are not valid expressions:

• "3*x = 16 - 2*y"

• "4x + 1y = 5"

Signs = and == are considered equivalent, and the first will be replaced by the second after parsing.

Optionally, names, weights and lexicographic priorities can be provided for each goal (equation) using the following format: " Labour : 20*A + 12*B + 40*C = 1200 | 0.2 0.1 | 1# 2# Profit : 11*A + 16*B + 8*C = 1000 | 0.1 0.3 | 3# 4# Batteries: 4*A + 3*B + 6*C = 200 | 0.2 0.1 | 5# 6#" The name of the goal must be followed by a colon (:) or vertical bars (|). Then the goal. Then the weights associated to the negative deviation first (lack), and the positive deviation (excess) last, separated by an empty space. Finally, the lexicographic priorities for the negative (lack) and positive (excess) deviations can be provided as numbers, each followed by a hashtag (#), and separated by an space, in that order. Lower values imply a higher priority, and the same priority can be assigned to multiple deviations. Only the equation is mandatory. If the weights are omitted, all of them are assumed to be equal to one for equations with the = sign. If the equation is actually an inequality with >=, then the default positive (excess) deviation weight is zero. If <=, then the default negative (lack) deviation is zero. If the lexicographic priorities are omitted, all of them are assumed to be equal to one for equations, but for inequalities >= the positive (excess) deviation is given a priority of +Inf (i.e. it will never be minimised), and for inequalities <= the negative (lack) deviation is given a default priority of +Inf (i.e. it will never be minimised).

Value

List with five elements.

• A: Numeric matrix with the coefficients of the variables. One row per equation, one column per variable. Columns are named according to the variables they represent. Rows are named for each equation, if a name for them was provided.

• b: Numeric vector with the values on the right hand side of the equations.

• m: Character vector with as many elements as equations. Each element is one of =, ==, <=, >=, <, >.

• w: Numeric matrix with the weights associated to the deviations of each goal. Each row corresponds to a goal. The first column corresponds to the positive deviation (excess) and the second column to the negative deviation (lack).

• p: Numeric matrix with the lexicographic priority associated to each goal. Lower values represent higher priority. Each row corresponds to a goal. The first column corresponds to the positive deviation (excess) and the second column to the negative deviation (lack).