1,306 research outputs found
Solving Lotsizing Problems on Parallel Identical Machines Using Symmetry Breaking Constraints
Production planning on multiple parallel machines is an interesting problem, both from a theoretical and practical point of view. The parallel machine lotsizing problem consists of finding the optimal timing and level of production and the best allocation of products to machines. In this paper we look at how to incorporate parallel machines in a Mixed Integer Programming model when using commercial optimization software. More specifically, we look at the issue of symmetry. When multiple identical machines are available, many alternative optimal solutions can be created by renumbering the machines. These alternative solutions lead to difficulties in the branch-and-bound algorithm. We propose new constraints to break this symmetry. We tested our approach on the parallel machine lotsizing problem with setup costs and times, using a network reformulation for this problem. Computational tests indicate that several of the proposed symmetry breaking constraints substantially improve the solution time, except when used for solving the very easy problems. The results highlight the importance of creative modeling in solving Mixed Integer Programming problems.Mixed Integer Programming;Formulations;Symmetry;Lotsizing
Decentralized Supply Chain Formation: A Market Protocol and Competitive Equilibrium Analysis
Supply chain formation is the process of determining the structure and terms
of exchange relationships to enable a multilevel, multiagent production
activity. We present a simple model of supply chains, highlighting two
characteristic features: hierarchical subtask decomposition, and resource
contention. To decentralize the formation process, we introduce a market price
system over the resources produced along the chain. In a competitive
equilibrium for this system, agents choose locally optimal allocations with
respect to prices, and outcomes are optimal overall. To determine prices, we
define a market protocol based on distributed, progressive auctions, and
myopic, non-strategic agent bidding policies. In the presence of resource
contention, this protocol produces better solutions than the greedy protocols
common in the artificial intelligence and multiagent systems literature. The
protocol often converges to high-value supply chains, and when competitive
equilibria exist, typically to approximate competitive equilibria. However,
complementarities in agent production technologies can cause the protocol to
wastefully allocate inputs to agents that do not produce their outputs. A
subsequent decommitment phase recovers a significant fraction of the lost
surplus
Market Design for Dynamic Pricing and Pooling in Capacitated Networks
We study a market mechanism that sets edge prices to incentivize strategic
agents to organize trips that efficiently share limited network capacity. This
market allows agents to form groups to share trips, make decisions on departure
times and route choices, and make payments to cover edge prices and other
costs. We develop a new approach to analyze the existence and computation of
market equilibrium, building on theories of combinatorial auctions and dynamic
network flows. Our approach tackles the challenges in market equilibrium
characterization arising from: (a) integer and network constraints on the
dynamic flow of trips in sharing limited edge capacity; (b) heterogeneous and
private preferences of strategic agents. We provide sufficient conditions on
the network topology and agents' preferences that ensure the existence and
polynomial-time computation of market equilibrium. We identify a particular
market equilibrium that achieves maximum utilities for all agents, and is
equivalent to the outcome of the classical Vickery Clark Grove mechanism.
Finally, we extend our results to general networks with multiple populations
and apply them to compute dynamic tolls for efficient carpooling in San
Francisco Bay Area
Integration of Blockchain and Auction Models: A Survey, Some Applications, and Challenges
In recent years, blockchain has gained widespread attention as an emerging
technology for decentralization, transparency, and immutability in advancing
online activities over public networks. As an essential market process,
auctions have been well studied and applied in many business fields due to
their efficiency and contributions to fair trade. Complementary features
between blockchain and auction models trigger a great potential for research
and innovation. On the one hand, the decentralized nature of blockchain can
provide a trustworthy, secure, and cost-effective mechanism to manage the
auction process; on the other hand, auction models can be utilized to design
incentive and consensus protocols in blockchain architectures. These
opportunities have attracted enormous research and innovation activities in
both academia and industry; however, there is a lack of an in-depth review of
existing solutions and achievements. In this paper, we conduct a comprehensive
state-of-the-art survey of these two research topics. We review the existing
solutions for integrating blockchain and auction models, with some
application-oriented taxonomies generated. Additionally, we highlight some open
research challenges and future directions towards integrated blockchain-auction
models
- ā¦