zbMATH — the first resource for mathematics

Two alternative models for farm management: Discrete versus continuous time horizon. (English) Zbl 1012.90014
Summary: Crop production entails many decision making processes aimed at improving productivity and achieving the best yield from scarce resources. Assuming that there is a set of tasks to be carried out within a given time horizon, and each task can be performed in different ways, the problem consists of determining how and when to carry out each task, in such a way that the tasks are scheduled in sequence at the minimum cost, taking into account any precedence relationships among them, the time window constraints for performing the tasks and the resources availability. This paper presents two alternative mathematical models to attain the proposed objective. The first model splits the time into discrete units spread throughout the planning horizon; it is presented in connection with flexible manufacturing. The second model keeps a continuous time horizon; a scheduling model is used for which a family of incompatibility conditions is introduced to avoid a certain type of simultaneous usage of resources. This type of conditions require to introduce a new structure so-called conditional disjunction. Computational experience is reported for real-life problems.

90B50 Management decision making, including multiple objectives
90B35 Deterministic scheduling theory in operations research
Full Text: DOI
[1] van den Akker, M.; Hurkens, C.A.J.; Savelsbergh, M.W.P., Time-indexed formulations for machine scheduling problems: column generation, INFORMS journal on computing, 12, 111-124, (2000) · Zbl 1034.90004
[2] Balas, E., Machine sequencing via disjunctive graphs: an implicit enumeration algorithm, Operations research, 17, 941-957, (1969) · Zbl 0183.49404
[3] Beale, E.M.L.; Tomlin, J.A., Special facilities in a general mathematical programming system for nonconvex problems using ordered sets of variables, (), 447-454
[4] Birge, J.R.; Louveaux, F., Introduction to stochastic programming, (1997), Springer-Verlag Berlin · Zbl 0892.90142
[5] Darby-Dowman, K.; Barker, S.; Audsley, E.; Parsons, D., A two-stage stochastic programming with recourse model for determining robust planting plans in horticulture, Journal of the operational research society, 51, 83-89, (2000) · Zbl 1107.90423
[6] J. van Elderen, Heuristic strategy for scheduling farm operations, Centre for Agricultural Publishing and Documentation, PUDOC Wageningen, 1977
[7] van Elderen, J., Scheduling of field operations, (1981), Bayer. Landwirtsch
[8] Escudero, L.F., S3 sets. an extension of the beale – tomlin special ordered sets, Mathematical programming, 42, 113-123, (1988) · Zbl 0644.90049
[9] Fokkens, G.; Puylaert, R.J., A linear programming model for daily harvesting operations at the large-scale grain farm of the ijsselmeerpolders development authority, Journal of the operational research society, 32, 535-547, (1981)
[10] Z. Gu, G.L. Nemhauser, M.W.P. Savelsberg, Lifted cover inequalities for 0-1 integer programs, In: Computation, COG 94-09, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, USA, 1994
[11] Lee, Y.; Sherali, H.F., Unrelated machine scheduling with time-window and machine-downtime constraints: an application to a naval battle group problem, Annals of operations research, 50, 339-365, (1994) · Zbl 0812.90067
[12] Nemhauser, G.L.; Wolsey, L.A., Integer and combinatorial optimization, (1988), Wiley New York · Zbl 0469.90052
[13] Ortuño, M.T.; Recio, B.; Vitoriano, B., Modelización del problema de planificación y asignación de recursos para una explotación agraria, Investigación operacional, 19, 116-127, (1998)
[14] B. Recio, Sistema de Soporte a la Decisión para la Planificación de Operaciones de Cultivo, Aplicación al Cultivo de Cereal en Navarra, PhD Thesis, Universidad Politécnica de Madrid, 1992
[15] Sousa, J.; Wolsey, L.A., Time-indexed formulations of non-preemptive single machine scheduling problems, Mathematical programming, 54, 353-367, (1992) · Zbl 0768.90041
[16] Wolsey, L.A., Valid inequalities for mixed integer programs with generalised and variable upper bound constraints, Discrete applied mathematics, 25, 251-261, (1990) · Zbl 0718.90067
[17] Wolsey, L.A., MIP modelling of changeouvers in production planning and scheduling problems, European journal of operational research, 99, 154-165, (1997) · Zbl 0923.90088
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.