Search

Regions with abundant wind resources usually have no ready access to the existing electric grid. However, building transmission lines that instantaneously deliver all geographically distributed wind energy can be costly. Energy storage (ES) systems can help reduce the cost of bridging wind farms and grids and mitigate the intermittency of wind outputs. In this paper, we propose models of transmission network planning with colocation of ES systems. Our models determine the sizes and sites of ES systems as well as the associated topology and capacity of the transmission network under the feed-in-tariff policy instrument. We first formulate a location model as a mixed-integer second-order-conic program to solve for the ES-transmission network design with uncapacitated storage. Then we propose a method to choose ES sizes by deriving a closed-form upper bound. The major insight is that, in most cases, using even small-sized ES systems can significantly reduce the total expected cost, but their marginal values diminish faster than those of the transmission lines as their capacities expand. Despite uncertainties in climate, technologies, and construction costs, the cost-efficient infrastructure layout is remarkably robust. We also identify the major bottleneck cost factors for different forms of ES technologies.

We study an inventory system wherein a customer may leave the seller's market after experiencing an inventory stockout. Traditionally, researchers and practitioners assume a single penalty cost to model this customer behavior of stockout aversion. Recently, a stream of researchers explicitly model this customer behavior and support the traditional penalty cost approach. We enrich this literature by studying the statistical learning of service-dependent demand. We build and solve four models: a baseline model, where the seller can observe the demand distribution; a second model, where the seller cannot observe the demand distribution but statistically learns the demand distribution; a third model, where the seller can learn or pay to obtain the exact information of the demand distribution; and a fourth model, where demand in excess of available inventory is lost and unobserved. Interestingly, we find that all four models support the traditional penalty cost approach. This result confirms the use of a state-independent stockout penalty cost in the presence of demand learning. More strikingly, the first three models imply the same stockout penalty cost, which is larger than the stockout penalty cost implied by the last model.

We consider an assortment optimization problem where a retailer chooses an assortment of products that maximizes the profit subject to a capacity constraint. The demand is represented by a multinomial logit choice model. We consider both the static and dynamic optimization problems. In the static problem, we assume that the parameters of the logit model are known in advance; we then develop a simple algorithm for computing a profit-maximizing assortment based on the geometry of lines in the plane and derive structural properties of the optimal assortment. For the dynamic problem, the parameters of the logit model are unknown and must be estimated from data. By exploiting the structural properties found for the static problem, we develop an adaptive policy that learns the unknown parameters from past data and at the same time optimizes the profit. Numerical experiments based on sales data from an online retailer indicate that our policy performs well.

Reliable facility location models consider unexpected failures with site-dependent probabilities, as well as possible customer reassignment. This paper proposes a compact mixed integer program (MIP) formulation and a continuum approximation (CA) model to study the reliable uncapacitated fixed charge location problem (RUFL), which seeks to minimize initial setup costs and expected transportation costs in normal and failure scenarios. The MIP determines the optimal facility locations as well as the optimal customer assignments and is solved using a custom-designed Lagrangian relaxation (LR) algorithm. The CA model predicts the total system cost without details about facility locations and customer assignments, and it provides a fast heuristic to find near-optimum solutions. Our computational results show that the LR algorithm is efficient for mid-sized RUFL problems and that the CA solutions are close to optimal in most of the test instances. For large-scale problems, the CA method is a good alternative to the LR algorithm that avoids prohibitively long running times.

We study a two-echelon supply chain with one warehouse and N (nonidentical) retailers facing stochastic demand. An easy-to-implement inventory policy, the so-called power-of-two (POT) policy, is proposed to manage inventory for the system. To maintain a certain service level, safety stocks are kept at the warehouse and each retailer outlet to buffer random demand. Our analysis highlights the important role of the warehouse safety stock level, which, in addition to the length of the warehouse order interval, significantly affects the lengths of the retailers' order intervals. By combining the length of the warehouse order interval with the warehouse safety stock level, we introduce a plane partition method and develop a polynomial time algorithm to find a POT policy for arbitrary target service levels. The long-run average cost of the proposed POT policy is guaranteed to be no more than 1.26 times the optimal POT policy cost. We also show that our proposed policy can be computed in O(N3).

Following the multistage design approach, we propose two asymptotically efficient truthful double auction mechanisms, the BC-LP mechanism and the MBC mechanism, for an exchange market with many buyers and sellers. In this market, each buyer wants to procure a bundle of commodities and each seller supplies one unit of a commodity. Furthermore, various transaction-related costs will be incurred when a buyer trades with a seller. We prove that under both mechanisms, truthful bidding is a dominant strategy for all buyers and sellers when the buyers' bundle information and the transaction cost information are common knowledge. The BC-LP mechanism can be implemented by just solving two linear programs, whereas the MBC mechanism has a higher complexity. The empirical study shows that the MBC mechanism achieves higher efficiency over the BC-LP mechanism and that both outperform the KSM-TR mechanism, the only known truthful mechanism for a more restrictive exchange market.

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.