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.