Integration of scheduling and control in process manufacturing systems has traditionally resulted in greater coordination between the different layers of hierarchy in optimization and control. However, the effectiveness of this coordination as well as the overall responsiveness of the manufacturing system could be greatly improved if such integration explicitly accounts for parametric variations at each of the layers. This paper proposes an approach to the problem of robust integration of the scheduling and control layers in an uncertainty analysis framework so as to yield robust manufacturing systems that can perform well in the presence of the parametric variations. The uncertainty analysis is performed here using different uncertainty approaches such as the chance constrained programming, fuzzy mathematical programming, and robust optimization. In this paper, we propose to analyze the impact of the uncertainty on the different manufacturing objectives in a multiobjective Pareto sense. The deterministic integrated scheduling and control model taken from published work Grossmann, I. E. Ind. Eng. Chem. Res. 2006, 45, 6698] forms the basis of our work toward addressing the uncertainty issues. We demonstrate the development of improved and robust integration of the scheduling and control tasks using the proposed frameworks.

Uncertainty issues associated with a multisite, multiproduct supply chain planning problem has been analyzed in this paper, using the chance constrained programming (CCP) approach. In the literature, such problems have been addressed using the scenario-based two-stage stochastic programming approach. Although this approach has merits, in terms of decomposition, the computational complexity, even for small-size planning problems, is generally quite large, leading to either huge time consumption in solving the problem or an inability to solve big instances of problems under a standard solver environment. To make the aforementioned lacunea of two-stage stochastic programming more tractable, the problems under uncertainty have been recast in this paper in a CCP framework that uses a more suitable representation of uncertainty. Addressing uncertainty issues in product demands and machine uptime, using the CCP approach, leads to the evaluation of multiobjective tradeoffs that are analyzed here in the Pareto sense, and the ε-constraint approach is used to generate those Pareto optimal (PO) points. Different aspects of uncertainty issues are analyzed in detail by taking a few PO points among the total set of PO solutions found for this problem. It is seen that this CCPbased approach is quite generic, relatively simple to use and can be adapted for bigger size planning problems, as the equivalent deterministic problem does not blow up in size with the CCP approach. We demonstrate the analysis on a relatively moderate size midterm planning problem taken from published work [McDonald, C. M.; Karimi, I. A. Ind. Eng. Chem. Res. 1997, 36, 2691 and discuss various aspects of uncertainty in the context of this problem.

a b s t r a c tFormulation of a multi-site, multi-product, multi-period supply chain planning problem under uncertainty has been presented and analyzed in this paper using the fuzzy mathematical programming approach. Such problems have been popularly addressed in literature using the two-stage stochastic programming approach that has primarily following two demerits: (i) the size of the planning problem exponentially increases with the increase in number of uncertain parameters thus leading to either huge time consumption or inability to solve big instances of problems, and (ii) probability distribution for uncertain parameters should be known. To circumvent the above-mentioned demerits of two-stage scenario-based stochastic programming and make the analysis more tractable, the uncertainty problem have been recast in this paper in a fuzzy framework that uses a more suitable representation of uncertainty.Addressing uncertainty issues in product demands, machine uptime and various cost components using the fuzzy Eng Chem Res, 36: 2691-2700] and discuss various aspects of uncertainty in context of this problem. It is seen that this fuzzy approach is quite generic, relatively simple to use and can be adapted for bigger size planning problems, as the equivalent deterministic problem does not blow up in size with increase in number of uncertain parameters while using fuzzy approach.