Towards resilient supply chains: uncertainty analysis using fuzzy mathematical programming

Formulation 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 approach leads to evaluation of multi-objective Pareto trade-offs among the total cost of the planning model, margin provided in the constraint violation and the extent of demand satisfaction. We demonstrate the analysis on a relatively moderate size mid-term planning problem taken from the work of McDonald and Karimi [McDonald, C.M. and Karimi, I.A., 1997, Planning and Scheduling of parallel semicontinuous processes. 1. Production planning, Ind 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.© Elsevie