Queuing approach and optimal inventory decisions in a stochastic supply ‎chain network design

This paper addresses an integrated multi-echelon location-allocation-inventory problem in a ‎stochastic supply chain. In a bid to be more realistic, the demand and lead time are considered ‎to be hemmed in by uncertainty. To tackle the proposed supply chain network design problem, ‎a two-phase approach based on queuing and optimization models is devised. The queuing ‎approach is first deployed, which is able to cope with inherent uncertainty of parameters. ‎Afterwards, the proposed supply chain network design problem is formulated using a mixed‏-‏integer nonlinear model. Likewise, the convexity of the model is proved and the optimal ‎inventory policy as closed-form is acquired. Inasmuch as the concerned problem belongs to ‎NP-hard problems, two meta-heuristic algorithms are employed, which are capable of ‎circumventing the complexity burden of the model. The numerical examples evince the efficient ‎and effective performance of the solving algorithms. Lastly, sensitivity analyses are conducted ‎through which interesting insights are gained.