In this paper, we study a multisourcing supply network design problem, in which each retailer faces uncertain demand and can source products from more than one distribution center DC. The decisions to be simultaneously optimized include DC locations and inventory levels, which set of DCs serves each retailer, and the amount of shipments from DCs to retailers. We propose a nonlinear mixed integer programming model with a joint chance constraint describing a certain service level. Two approaches-set-wise approximation and linear decision rule-based approximation-are constructed to robustly approximate the service level chance constraint with incomplete demand information. Both approaches yield sparse multisourcing distribution networks that effectively match uncertain demand using on-hand inventory, and hence successfully reach a high service level. We show through extensive numerical experiments that our approaches outperform other commonly adopted approximations of the chance constraint.

Containers are widely used in the shipping industry mainly because of their capability to facilitate multimodal transportation. How to effectively reposition the nonrevenue empty containers is the key to reduce the cost and improve the service in the liner shipping industry. In this paper, we propose a two-stage robust optimization model that takes into account the laden containers routing as well as the empty container repositioning, and define the robustness for this model with uncertainties in the supply and demand of the empty containers. Based on this definition, we present the robust formulations for the uncertainty sets corresponding to the ℓp-norm, where p = 1, 2, and ∞, and analyze the computational complexities for all of these formulations. The only polynomial-time solvable case corresponds to the ℓ1-norm, which we use to conduct the numerical study. We compare our approach with both the deterministic model and the stochastic model for the same problem in the rolling horizon simulation environment. The computational results establish the potential practical usefulness of the proposed approach.

We develop practical operations research models to support decision making in the design and management of public bicycle-sharing systems. We develop a network flow model with proportionality constraints to estimate the flow of bicycles within the network and the number of trips supported, given an initial allocation of bicycles at each station. We also examine the effectiveness of periodic redistribution of bicycles in the network to support greater flow, and the impact on the number of docks needed. We conduct our numerical analysis using transit data from train operators in Singapore. Given that a substantial proportion of passengers in the train system commute a short distance—more than 16% of passengers alight within two stops from the origin—this forms a latent segment of demand for a bicycle-sharing program. We argue that for a bicycle-sharing system to be most effective for this customer segment, the system must deploy the right number of bicycles at the right places, because this affects the utilization rate of the bicycles and how bicycles circulate within the system. We also identify the appropriate operational environments in which periodic redistribution of bicycles will be most effective for improving system performance.

In this paper, we study approximation algorithms for two supply chain network design problems, namely, the warehouse-retailer network design problem (WRND) and the stochastic transportation-inventory network design problem (STIND). These two problems generalize the classical uncapacitated facility location problem by incorporating, respectively, the warehouse-retailer echelon inventory cost and the warehouse cycle inventory together with the safety stock costs. The WRND and the STIND were initially studied, respectively, by Teo and Shu (Teo CP, Shu J (2004) Warehouse-retailer network design problem. Oper. Res. 52(3):396–408) and Shu et al. (Shu J, Teo CP, Shen ZJM (2005) Stochastic transportation-inventory network design problem. Oper. Res. 53(1):48–60), where they are formulated as set-covering problems, and column-generation algorithms were used to solve their linear programming relaxations. Both problems can be regarded as special cases of the so-called facility location with submodular facility costs proposed by Svitkina and Tardos (Svitkina Z, Tardos É (2010) Facility location with hierarchical facility costs. ACM Trans. Algorithms 6(2), Article No. 37), for which only a logarithmic-factor approximation algorithm is known. Our main contribution is to obtain efficient constant-factor approximation algorithms for the WRND and the STIND, which are capable of solving large-scale instances of these problems efficiently.

We study the stochastic transportation-inventory network design problem involving one supplier and multiple retailers. Each retailer faces some uncertain demand, and safety stock must be maintained to achieve suitable service levels. However, risk-pooling benefits may be achieved by allowing some retailers to serve as distribution centers for other retailers. The problem is to determine which retailers should serve as distribution centers and how to allocate the other retailers to the distribution centers. Shen et al. (2003) formulated this problem as a set-covering integer-programming model. The pricing problem that arises from the column generation algorithm gives rise to a new class of the submodular function minimization problem. In this paper, we show that by exploiting certain special structures, we can solve the general pricing problem in Shen et al. efficiently. Our approach utilizes the fact that the set of all lines in a two-dimension plane has low VC-dimension. We present computational results on several instances of sizes ranging from 40 to 500 retailers. Our solution technique can be applied to a wide range of other concave cost-minimization problems.