Midterm Supply Chain Planning under Uncertainty: A Multiobjective Chance Constrained Programming Framework

Abstract

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.

Optimal supply chain design and operations under multi‐scale uncertainties: Nested stochastic robust optimization modeling framework and solution algorithm

“…The chanceconstrained approach has been used to handle the trade-off between customer demand satisfaction and production cost 25,26 and uncertainties in damage model parameters for sustainability analysis. 27 In cases that the decision maker values feasibility higher than optimality, adaptive robust optimization can be used to hedge against the worst case of uncertainty realization.…”

Synthesis and optimisation of biomass-based tri-generation systems with reliability aspects

“…This method is useful to deal with inequality constraints of which satisfaction is highly desirable, but not absolutely essential or possible [21e23]. CCP has been applied in various areas such as waste management [24], and chemical batch industries [25] and supply chain planning [26]. Finally, a multi-period approach is used to reflect multiple supply and demand scenarios.…”

An uncertainty based formal approach towards parametric sensitivity: A case study on epoxy polymerization

“…In case of CCP, the problem size of the deterministic equivalent problem does not grow exponentially as it is mentioned in case of TSSP even if the number of uncertain parameters is large which is a big advantage of CCP over TSSP. Applications of CCP in process system engineering literature are relatively less [28–32].…”