Using Linear Programming in a Business-to-Business Auction Mechanism

Business to business interactions are largely centered around contracts for procurement or for distribution. Negotiations and sealed bid tendering are the most common techniques used for price discovery and generating the terms and conditions for contracts. Sealed bid tenders collect bids (that is private information between the two companies) and then pick a winning bid/s from among the submitted bids. The outcome of such interactions can be analyzed based on the theory of sealed bid auctions and have been studied extensively [7]. In contrast, negotiations tend to be more dynamic where a buyer (supplier) might be interacting with several suppliers (buyers) simultaneously and the contractual terms being negotiated with one supplier might directly impact the negotiations with another.An approach that is often used for this setting is to design an interactive mechanism where based on a "market signal" such as price for each item, the agents can propose bids based on a decentralized private cost model. A general setting for decentralized allocation is one where there are multiple agents with a utility function for the different resources and the allocation problem is to distribute the resources in an optimal way. A key difference from classical optimization is that the utility functions of the agents are private information and are not explicitly known to the decision maker. The key requirements for such a design to be practical are: (i) convergence to an "equilibrium solution" in a finite number of steps, and (ii) the "equilibrium solution" is optimal for each of the agents, given the market signal. One approach for implementing such mechanisms is the use of primal-dual approaches where the resource allocation problem is formulated as a linear program and the dual prices are used as market signals |2, 3, 8, 1, 4, 6|. Each agent can then use the dual price vector to propose a profit maximizing bid, for the next round, based on her private cost model. Here, the assumption is that the agents attempt to maximize their profits in each round. This assumption is referred to as the myopic best response |5|. In a procurement setting with a single buyer and multiple suppliers, the buyer uses a linear program to allocate her demand by choosing a set of cost minimizing bids and then use the dual price variables to signal the suppliers. In order to guarantee convergence a large enough price decrement is used on all non-zero dual prices in each iteration.In this paper we explore an alternate design where, the market signal provided to each supplier is based on the current cost of procurement for the buyer. Each supplier is then required to submit new bid proposals that reduce the procurement cost (assuming other suppliers keep their bids unchanged) by some large enough decrement d > a. We show that, for each supplier, generating a profit maximizing bid that decreases the procurement cost for the buyer by at least d can be done in polynomial time. This implies that in designs where the bids are not common knowledge, each supplier and the buyer can engage in an "algorithmic conversation" to identify such proposals in a polynomial number of steps. In addition, we show that such a mechanism converges to an "equilibrium solution" where all the suppliers are at their profit maximizing solution given the cost and the required decrement d. At the heart of this design lies a fundamental sensitivity analysis problem of linear programming - given a linear program and its optimal solution, identify the set of new columns such that any one of these columns when introduced in the linear program reduces the optimum solution by at least d.

A Framework for Supporting Intelligent Fault and Performance Management for Communication Networks

In this paper, we present a framework for supporting intelligent fault and performance management for communication networks. Belief networks are taken as the basis for knowledge representation and inference under evidence. When using belief networks for diagnosis, we identify two questions: When can I say that I get the right diagnosis and stop? If right diagnosis has not been obtained yet, which test should I choose next? For the first question, we define the notion of right diagnosis via the introduction of intervention networks. For the second question, we formulate the decision making procedure using the framework of partially observable Markov decision processes. A heuristic dynamic strategy is proposed to solve this problem and the effectiveness is shown via simulation

Finite-Sum Smooth Optimization with SARAH

The total complexity (measured as the total number of gradient computations) of a stochastic first-order optimization algorithm that finds a first-order stationary point of a finite-sum smooth nonconvex objective function F(w)=1n∑ni=1fi(w) has been proven to be at least Ω(n−−√/ϵ) for n≤O(ϵ−2) where ϵ denotes the attained accuracy E[∥∇F(w~)∥2]≤ϵ for the outputted approximation w~ (Fang et al., 2018). In this paper, we provide a convergence analysis for a slightly modified version of the SARAH algorithm (Nguyen et al., 2017a;b) and achieve total complexity that matches the lower-bound worst case complexity in (Fang et al., 2018) up to a constant factor when n≤O(ϵ−2) for nonconvex problems. For convex optimization, we propose SARAH++ with sublinear convergence for general convex and linear convergence for strongly convex problems; and we provide a practical version for which numerical experiments on various datasets show an improved performance

Development of the Integrated Environmental Control Model. Quarterly Progress Report, [July--September 1993]

The purpose of this contract is to develop and refine the Integrated Environmental Control Model (IECM) created and enhanced by Carnegie Mellon University (CMU) for the US Department of Energy`s Pittsburgh Energy Technology Center (DOE/PETC) under contract Numbers FG22-83PC60271 and AC22-87PC79864. In its current configuration, the IECM provides a capability to model various conventional and advanced processes for controlling air pollutant emissions from coal-fired power plants before, during, or after combustion. The principal purpose of the model is to calculate the performance, emissions, and cost of power plant configurations employing alternative environmental control methods. The model consists of various control technology modules, which may be integrated into a complete utility plant in any desired combination. In contrast to conventional deterministic models, the IECM offers the unique capability to assign probabilistic values to all model input parameters, and to obtain probabilistic outputs in the form of cumulative distribution functions indicating the likelihood of different costs and performance results. The most recent version of the IECM, implemented on a Macintosh II computer, was delivered to DOE/PETC at the end of the last contract in May 1991. The current contract will continue the model development effort to provide DOE/PETC with improved model capabilities, including new software developments to facilitate model use and new technical capabilities for analysis of environmental control technologies. Integrated environmental control systems involving pre-combustion, combustion, and post-combustion control methods will be considered

Development of the Integrated Environmental Control Model. Quarterly Progress Report, April 1995--June 1995

The purpose of this contract is to develop and refine the Integrated Environmental Control Model (IECM). In its current configuration, the IECM provides a capability to model various conventional and advanced processes for controlling air pollutant emissions from coal-fired power plants before, during, or after combustion. The principal purpose of the model is to calculate the performance, emissions, and cost of power plant configurations employing alternative environmental control methods. The model consists of various control technology modules, which may be integrated into a complete utility plant in any desired combination. In contrast to conventional deterministic models, the IECM offers the unique capability to assign probabilistic values to all model input parameters, and to obtain probabilistic outputs in the form of cumulative distribution functions indicating the likelihood of different costs and performance results. The work in this contract is divided into two phases. Phase I deals with further developing the existing version of the IECM and training PETC personnel on the effective use of the model. Phase H deals with creating new technology modules, linking the IECM with PETC databases, and training PETC personnel on the effective use of the updated model. The present report summarizes recent progress on the Phase I effort during the period April 1, 1995 through June 30, 1995. This report presents additional revisions to the new cost models of flue gas desulfurization (FGD) technology initially reported in our fourth quarterly report. For convenience, the complete description of the revised FGD models are presented here

Development of the Integrated Environmental Control Model: Performance and Cost Models for the NOXSO Process. Quarterly Progress Report

This Quarterly Report documents research efforts carried out under Contract No. DE-AC22-92PC91346 from the US Department of Energy. lie purpose of this contract is to develop and refine the Integrated Environmental Control Model (IECM) created and enhanced by Carnegie Mellon University (CMU) for the US Department of Energy`s Pittsburgh Energy Technology Center (DOE/PETC) under contract Numbers DE-FG2283PC60271 and DE-AC22-87PC79864. The work in this contract is divided into two phases. Phase I deals with further developing the existing version of the IECM and training PETC personnel on the effective use of the model. Phase II deals with creating new technology modules, linking the IECM with PETC databases, and training PETC personnel on the effective use of the updated model. The present report summarizes recent progress on the Phase I effort during the period July 1, 1995 through September 30, 1995. This report presents additional details on the new performance models of the NOXSO process. For convenience, the complete description of the NOXSO performance model is presented here, including information previously presented in the Quarterly Report submitted in April 1995. Also included in this report is a newly developed cost model for the NOXSO process. Illustrative results are presented using the new performance and cost models as implemented in the IECM

Development of the Integrated Environmental Control Model: Performance Model for the NOXSO Process. Quarterly Progress Report

In its current configuration, the IECM provides a capability to model various conventional and advanced processes for controlling air pollutant emissions from coal-fired power plants before, during, or after combustion. The principal purpose of the model is to calculate the performance, emissions, and cost of power plant configurations employing alternative environmental control methods. The model consists of various control technology modules, which may be integrated into a complete utility plant in any desired combination. In contrast to conventional deterministic models, the IECM offers the unique capability to assign probabilistic values to all model input parameters, and to obtain probabilistic outputs in the form of cumulative distribution functions indicating the likelihood of different costs and performance results. The most recent version of the IECM, implemented on a MacIntosh II computer, was delivered to DOE/PETC at the end of the last contract in May 1991. The current contract will continue the model development effort to provide DOE/PETC with improved model capabilities, including new software developments to facilitate model use and new technical capabilities for analysis of environmental control technologies. Integrated environmental control systems involving pre-combustion, combustion, and post-combustion control methods will be considered. Phase I involves developing the existing modules of the IECM. Phase II deals with creating new technology modules, linking the IECM with PETC databases, and training PETC personnel on the use of the updated models. The present report summarizes recent progress on the Phase I effort during the period January 1 - March 31, 1995. A preliminary summary is given of the new performance model developed for the NOXSO process. The performance model is developed from first principles and parametrized based on experimental data from pilot plants

Evaluation of WRF model seasonal forecasts for tropical region of Singapore

The Weather and Research Forecast (WRF) model is evaluated for the monsoon and inter-monsoon seasons over the tropical region of Singapore. The model configuration, physical parameterizations and performance results are described in this paper. In addition to the ready-to-use data available with the WRF model, the model configuration includes high resolution MODIS land use (500 m horizontal resolution) and JPL-NASA sea surface temperature (1 km horizontal resolution) data. The model evaluation is performed against near surface observations for temperature, relative humidity, wind speed and direction, available from a dense network of weather monitoring stations across Singapore. It is found that the high resolution data sets bring significant improvement in the model forecasts. The results also indicate that the model forecasts are more accurate in the monsoon seasons compared to the inter-monsoon seasons