# Exact and heuristic algorithms for minimizing Tardy/Lost penalties on a single-machine scheduling problem

## Abstract

This paper addresses minimizing Tardy/Lost penalties with common due dates on a single machine. According to this penalty criterion, if tardiness of a job exceeds a predefined value, the job will be lost and penalized by a fixed value. The problem is formulated as an integer programming model, and a heuristic algorithm is constructed. Then, using the proposed dominance rules and lower bounds, we develop two dynamic programming algorithms as well as a branch and bound. Experimental results show that the heuristic algorithm has an average optimality gap less than 2 % in all problem sizes. Instances up to 250 jobs with low variety of process times are optimally solved and for high process time varieties, the algorithms solved all instances up to 75 jobs.

- Authors:

- University of Isfahan, Faculty of Engineering (Iran, Islamic Republic of)
- Isfahan University of Technology, Department of Industrial and Systems Engineering (Iran, Islamic Republic of)

- Publication Date:

- OSTI Identifier:
- 22769366

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 2; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; DYNAMIC PROGRAMMING; PROGRAMMING

### Citation Formats

```
Kianfar, K., E-mail: k.kianfar@eng.ui.ac.ir, Moslehi, G., and Nookabadi, A. S.
```*Exact and heuristic algorithms for minimizing Tardy/Lost penalties on a single-machine scheduling problem*. United States: N. p., 2018.
Web. doi:10.1007/S40314-016-0370-4.

```
Kianfar, K., E-mail: k.kianfar@eng.ui.ac.ir, Moslehi, G., & Nookabadi, A. S.
```*Exact and heuristic algorithms for minimizing Tardy/Lost penalties on a single-machine scheduling problem*. United States. doi:10.1007/S40314-016-0370-4.

```
Kianfar, K., E-mail: k.kianfar@eng.ui.ac.ir, Moslehi, G., and Nookabadi, A. S. Tue .
"Exact and heuristic algorithms for minimizing Tardy/Lost penalties on a single-machine scheduling problem". United States. doi:10.1007/S40314-016-0370-4.
```

```
@article{osti_22769366,
```

title = {Exact and heuristic algorithms for minimizing Tardy/Lost penalties on a single-machine scheduling problem},

author = {Kianfar, K., E-mail: k.kianfar@eng.ui.ac.ir and Moslehi, G. and Nookabadi, A. S.},

abstractNote = {This paper addresses minimizing Tardy/Lost penalties with common due dates on a single machine. According to this penalty criterion, if tardiness of a job exceeds a predefined value, the job will be lost and penalized by a fixed value. The problem is formulated as an integer programming model, and a heuristic algorithm is constructed. Then, using the proposed dominance rules and lower bounds, we develop two dynamic programming algorithms as well as a branch and bound. Experimental results show that the heuristic algorithm has an average optimality gap less than 2 % in all problem sizes. Instances up to 250 jobs with low variety of process times are optimally solved and for high process time varieties, the algorithms solved all instances up to 75 jobs.},

doi = {10.1007/S40314-016-0370-4},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 2,

volume = 37,

place = {United States},

year = {2018},

month = {5}

}