# Semilinear programming: applications and implementation

## Abstract

Semilinear programming is a method of solving optimization problems with linear constraints where the non-negativity restrictions on the variables are dropped and the objective function coefficients can take on different values depending on whether the variable is positive or negative. The simplex method for linear programming is modified in this thesis to solve general semilinear and piecewise linear programs efficiently without having to transform them into equivalent standard linear programs. Several models in widely different areas of optimization such as production smoothing, facility locations, goal programming and L/sub 1/ estimation are presented first to demonstrate the compact formulation that arises when such problems are formulated as semilinear programs. A code SLP is constructed using the semilinear programming techniques. Problems in aggregate planning and L/sub 1/ estimation are solved using SLP and equivalent linear programs using a linear programming simplex code. Comparisons of CPU times and number iterations indicate SLP to be far superior. The semilinear programming techniques are extended to piecewise linear programming in the implementation of the code PLP. Piecewise linear models in aggregate planning are solved using PLP and equivalent standard linear programs using a simple upper bounded linear programming code SUBLP.

- Authors:

- Publication Date:

- Research Org.:
- Carnegie-Mellon Univ., Pittsburgh, PA (USA)

- OSTI Identifier:
- 5423805

- Resource Type:
- Thesis/Dissertation

- Resource Relation:
- Other Information: Thesis (Ph. D.)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; LINEAR PROGRAMMING; OPTIMIZATION; COMPUTER CODES; IMPLEMENTATION; PROGRAMMING; 990200* - Mathematics & Computers

### Citation Formats

```
Mohan, S.
```*Semilinear programming: applications and implementation*. United States: N. p., 1984.
Web.

```
Mohan, S.
```*Semilinear programming: applications and implementation*. United States.

```
Mohan, S. Sun .
"Semilinear programming: applications and implementation". United States.
```

```
@article{osti_5423805,
```

title = {Semilinear programming: applications and implementation},

author = {Mohan, S},

abstractNote = {Semilinear programming is a method of solving optimization problems with linear constraints where the non-negativity restrictions on the variables are dropped and the objective function coefficients can take on different values depending on whether the variable is positive or negative. The simplex method for linear programming is modified in this thesis to solve general semilinear and piecewise linear programs efficiently without having to transform them into equivalent standard linear programs. Several models in widely different areas of optimization such as production smoothing, facility locations, goal programming and L/sub 1/ estimation are presented first to demonstrate the compact formulation that arises when such problems are formulated as semilinear programs. A code SLP is constructed using the semilinear programming techniques. Problems in aggregate planning and L/sub 1/ estimation are solved using SLP and equivalent linear programs using a linear programming simplex code. Comparisons of CPU times and number iterations indicate SLP to be far superior. The semilinear programming techniques are extended to piecewise linear programming in the implementation of the code PLP. Piecewise linear models in aggregate planning are solved using PLP and equivalent standard linear programs using a simple upper bounded linear programming code SUBLP.},

doi = {},

url = {https://www.osti.gov/biblio/5423805},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1984},

month = {1}

}