Welfare maximization with production costs: A primal dual approach

Welfare Maximization with Production Costs: A Primal Dual Approach

We study online combinatorial auctions with production costs proposed by Blum et al. [4] using the online primal dual framework. In this model, buyers arrive online, and the seller can produce multiple copies of each item subject to a nondecreasing marginal cost per copy. The goal is to allocate items to maximize social welfare less total production cost. For arbitrary (strictly convex and diff...

Dual Competing Photovoltaic Supply Chains: A Social Welfare Maximization Perspective

In the past decades, the inappropriate subsidy policies in many nations have caused problems such as serious oversupply, fierce competition and subpar social welfare in the photovoltaic (PV) industry in many nations. There is a clear shortage in the PV industry literature regarding how dual supply chains compete and the key decision issues regarding the competition between dual PV supply chains...

3 The primal - dual approach

Approximating k-Forest with Resource Augmentation: A Primal-Dual Approach

In this paper, we study the k-forest problem in the model of resource augmentation. In the k-forest problem, given an edge-weighted graph G(V,E), a parameter k, and a set of m demand pairs ⊆ V × V , the objective is to construct a minimum-cost subgraph that connects at least k demands. The problem is hard to approximate—the best-known approximation ratio is O(min{√n, √ k}). Furthermore, k-fores...

Welfare Maximization with Multiple Goods

When multiple goods are being auctioned off, it is often the case that each bidder values different subsets of goods differently. In general, we cannot completely describe the preferences of each bidder with a single scalar value, and so we move to a multi-parameter setting, where multiple numbers must be used to completely describe the type of each bidder. Auctions where multiple goods are bei...