Abstract
This paper deals with an interval programming approach for an operational transportation problem, arising in a typical agricultural cooperative during the crop harvest time. More specifically, an interval programming model with uncertain coefficients occurred in the right-hand side and the objective function is developed for a single-period multi-trip planning of a heterogeneous fleet of vehicles, while satisfying the stochastic seed storage requests, represented as interval numbers. The proposed single-period interval programming model is conceived and implemented for a real life agricultural cooperative case study.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aissi, H., Bazgan, C., Vanderpooten, D.: Min-max and min-max regret versions of combinatorial optimization problems: A survey. European Journal of Operational Research 197(2), 427–438 (2009)
Ahumada, O., Villalobos, J.: Application of planning models in the agri-food s upply chain: A review. European Journal of Operational Research 196(1), 1–20 (2009)
Averbakh, I.: Computing and minimizing the relative regret in combinatorial optimization with interval data. Discrete Optimization 2(4), 273–287 (2005)
Bertsimas, D., Sim, M.: The price of robustness. Operations Research 52(1), 35–53 (2004)
Borodin, V., Bourtembourg, J., Hnaien, F., Labadie, N.: A discrete event simulation model for harvest operations under stochastic conditions. In: ICNSC 2013, pp. 708–713 (2013)
Cao, M., Huang, G., He, L.: An approach to interval programming problems with left-hand-side stochastic coefficients: An application to environmental decisions analysis. Expert Systems with Applications 38(9), 11538–11546 (2011)
Dai, C., Li, Y., Huang, G.: An interval-parameter chance-constrained dynamic programming approach for capacity planning under uncertainty. Resources, Conservation and Recycling 62, 37–50 (2012)
Dentcheva, D., Prékopa, A., Ruszczyński, A.: Bounds for probabilistic integer programming problems. Discrete Applied Mathematics, 55–65 (October 2002)
Gabrel, V., Murat, C., Remli, N.: Linear programming with interval right hand sides. International Transactions in Operational Research 17(3), 397–408 (2010)
Inuiguchi, M., Sakawa, M.: Minimax regret solution to linear programming problems with an interval objective function. European Journal of Operational Research 86(3), 526–536 (1995)
Kacprzyk, J., Esogbue, A.: Fuzzy dynamic programming: Main developments and applications. Fuzzy Sets and Systems 81(1), 31–45 (1996)
Kall, P., Wallace, S.N.: Stochastic Programming. John Wiley and Sons (1994)
Kasperski, A., Zielińki, P.: Minmax regret approach and optimality evaluation in combinatorial optimization problems with interval and fuzzy weights. European Journal of Operational Research 200(3), 680–687 (2010)
List, G., Wood, B., Nozick, L., Turnquist, M., Jones, D., Kjeldgaard, E., Lawton, C.: Robust optimization for fleet planning under uncertainty. Transportation Research Part E: Logistics and Transportation Review 39(3), 209–227 (2003)
Liu, B.: Dependent-chance programming: A class of stochastic optimization. Computers & Mathematics with Applications 34(12), 89–104 (1997)
Liu, B., Iwamura, K.: Modelling stochastic decision systems using dependent-chance programming. European Journal of Operational Research 101(1), 193–203 (1997)
Luo, J., Li, W.: Strong optimal solutions of interval linear programming. Linear Algebra and its Applications 439(8), 2479–2493 (2013)
Miller, L., Wagner, H.: Chance-constrained programming with joint constraints. Operational Research, 930–945 (1965)
Chinneck, J.W., Ramadan, K.: Linear programming with interval coefficients. The Journal of the Operational Research, 209–220 (2000)
Ruszczyński, A., Shapiro, A.: Stochastic programming models. Handbooks in Operations Research and Management Science, pp. 1–64. Elsevier (2003)
Sengupta, A., Pal, T., Chakraborty, D.: Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming. Fuzzy Sets and Systems 119(1), 129–138 (2001)
Shapiro, A., Dentcheva, D.: Lectures on stochastic programming: Modelling and Theory. Society for Industrial and Applied Mathematics, Philadelphia (2009)
Sheu, J.-B.: A novel dynamic resource allocation model for demand-responsive city logistics distribution operations. Transportation Research Part E: Logistics and Transportation Review 42(6), 445–472 (2006)
Moore, R.E.: Automatic Error Analysis in Digital Computation. Sunnyvale, Calif. (1959)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Borodin, V., Bourtembourg, J., Hnaien, F., Labadie, N. (2014). An Interval Programming Approach for an Operational Transportation Planning Problem. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2014. Communications in Computer and Information Science, vol 442. Springer, Cham. https://doi.org/10.1007/978-3-319-08795-5_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-08795-5_13
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08794-8
Online ISBN: 978-3-319-08795-5
eBook Packages: Computer ScienceComputer Science (R0)