Midterm supply chain planning under uncertainty: A multiobjective chance constrained programming framework

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 e-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 CCP-based 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, 269 1] and discuss various aspects of uncertainty in the context of this problem.