Proactive Scheduling under Uncertainty:  A Parametric Optimization Approach

Abstract

This paper presents a novel methodology using parametric programming techniques to solve scheduling problems under uncertainty. The uncertainty present in processing times and equipment availabilities is incorporated into scheduling models, which are then transformed to multiparametric mixed-integer linear programming (mp-MILP) problems. A solution procedure that is based on recently proposed state-of-the-art mp-MILP algorithms is then discussed. A key advantage of the proposed methodology is that the complete map of optimal schedules can be obtained as a function of various parameters; rescheduling can thus be performed via simple function evaluations without any further optimization. Therefore, the proposed methodology contributes to the construction of a proactive scheduling system. Numerical examples are presented to illustrate the potential of the proposed methodology.

Model-based multi-parametric programming strategies towards the integration of design, control and operational optimization

“…Integration of scheduling and control: Similarly to MPC, multi-parametric programming approaches for scheduling have been presented in the past [202,203,299,300]. However, the recently developed representation of scheduling problems in a state-space model [335] has allowed for the applicability of the concepts of mp-MPC in scheduling [183].…”

Scheduling With Uncertainty

“…El algoritmo consta de dos partes: (a) un algoritmo de programación lineal paramétrica, basada en el algoritmo branch and bound, para solucionar el problema de Job-shop con tiempo de finalización fija y (b) un algoritmo de expansión del problema para encontrar el momentoóptimo de finalización. En [29], se abordó el problema en dos niveles de la toma de decisiones en condiciones de incertidumbre, en el contexto optimizar optimización la cadena de suministro en toda la empresa. El primer nivel corresponde a un problema de planificación de planta, mientras que el otro a un problema de la red de distribución.…”

Theoretical and computational comparison of continuous‐time process scheduling models for adjustable robust optimization

“…The second category relies upon a proactive scheme, where uncertainty is anticipated and accounted for in the optimization stage. One of the representatives of this category is parametric programing, where the parameter space is mapped in order to specify the optimal deterministic solution given any specific realization of uncertainty. Using this approach, one may identify a solution that exhibits satisfactory performance across a sufficiently wide range of parameter realizations.…”