Modelling Operations Dynamics, Planning and Scheduling

Abstract

The greatest challenge to any thinker is stating the problem in a way that will allow a solution. Bertrand Russell 12.1 Research Approach The proposed approach is based on fundamental scientific results of the modern optimal control theory (Okhtilev et al. 2006, Sethi and Thompson 2006) in combination with the optimization methods of OR. This mathematical model is the extended application to the SCM domain of the scheduling model for complex technical systems (Kalinin and Sokolov 1985, 1987, 1996, Sokolov and Yusupov 2004, Okhtilev et al. 2006) and reflects the conceptual cybernetic framework of SC planning and execution presented for different SCM domains in Ivanov et al. The proposed approach has the following particular features. First, we consider planning and scheduling as an integrated function within an adaptive framework. Recent studies (Moon et al. 2008, Shao et al. 2009) have provided evidence that the performance of SCs can be improved greatly if planning and scheduling are not performed in a sequential way but are integrated and considered simultaneously. Second, we formulate the planning and scheduling models as optimal control problems, taking into account the discreteness of decision making and the continuity of flows. By special techniques for process dynamics models and constraint formulation, we will show how to transform the non-linear operations dynamics model into a linear one. In doing so, the dimensionality of problems can be reduced and discrete optimization methods of linear programming can be applied for solution within the general dynamic non-linear model. In the model, a multi-step procedure for solving a multiple objective task of adaptive planning and scheduling is implemented. In doing so, at each instant of time while calculating solutions in the dynamic model with the help of the maximum principle, the linear programming problems to allocate jobs to resources and integer programming problems for (re)distributing material and time resources solved. The process control model will be presented as a dynamic linear system while the non-linearity and non-stationarity will be transferred to the model constraints. This allows us to ensure convexity and to use the interval constraints. As such, the constructive possibility of discrete problem solving in a continuous manner occurs.