Single‐commodity stochastic network design under demand and topological uncertainties with insufficient data

Stochastic network design is fundamental to transportation and logistic problems in practice, yet faces new modeling and computational challenges resulted from heterogeneous sources of uncertainties and their unknown distributions given limited data. In this article, we design arcs in a network to optimize the cost of single‐commodity flows under random demand and arc disruptions. We minimize the network design cost plus cost associated with network performance under uncertainty evaluated by two schemes. The first scheme restricts demand and arc capacities in budgeted uncertainty sets and minimizes the worst‐case cost of supply generation and network flows for any possible realizations. The second scheme generates a finite set of samples from statistical information (e.g., moments) of data and minimizes the expected cost of supplies and flows, for which we bound the worst‐case cost using budgeted uncertainty sets. We develop cutting‐plane algorithms for solving the mixed‐integer nonlinear programming reformulations of the problem under the two schemes. We compare the computational efficacy of different approaches and analyze the results by testing diverse instances of random and real‐world networks. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 154–173, 2017Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137236/1/nav21739_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137236/2/nav21739.pd

Integrated supply chain management via randomized rounding

We consider the supply chain problem of minimizing ordering, distribution and inventory holding costs of a supply chain formed by a set of warehouses and retailers over a finite time horizon, that we call Production and Distribution Problem (PDP). This is a common generalization of the classical Metric Facility Location Problem and Joint Replenishment Problem, that coordinates the network design and inventory management decisions in an integrated manner. This coordination can represent significant economy for many applications, where network design and operational costs are normally considered separately. This problem is considered when the instances satisfy assumptions such as metric space of warehouse and retailer locations, and monotonic increasing inventory holding costs. In this work, we give a 2.77-approximation based on the randomized rounding of the natural mixed integer programming relaxation. Also, we give a 5-approximation for the case that objective function includes retailer ordering costs