An integer-valued data envelopment analysis model with bounded outputs

Integer-valued data envelopment analysis (DEA) with alternative returns to scale technology has been introduced and developed recently by Kuosmanen and Kazemi Matin. The proportionality assumption of their introduced "natural augmentability" axiom in constant and nondecreasing returns to scale technologies makes it possible to achieve feasible decision-making units (DMUs) of arbitrary large size. In many real world applications it is not possible to achieve such production plans since some of the input and output variables are bounded above. In this paper, we extend the axiomatic foundation of integer-valuedDEAmodels for including bounded output variables. Some model variants are achieved by introducing a new axiom of "boundedness" over the selected output variables. A mixed integer linear programming (MILP) formulation is also introduced for computing efficiency scores in the associated production set. © 2011 The Authors. International Transactions in Operational Research © 2011 International Federation of Operational Research Societies.

Zero weights and non-zero slacks:different solution to the same problem

This paper re-assesses three independently developed approaches that are aimed at solving the problem of zero-weights or non-zero slacks in Data Envelopment Analysis (DEA). The methods are weights restricted, non-radial and extended facet DEA models. Weights restricted DEA models are dual to envelopment DEA models with restrictions on the dual variables (DEA weights) aimed at avoiding zero values for those weights; non-radial DEA models are envelopment models which avoid non-zero slacks in the input-output constraints. Finally, extended facet DEA models recognize that only projections on facets of full dimension correspond to well defined rates of substitution/transformation between all inputs/outputs which in turn correspond to non-zero weights in the multiplier version of the DEA model. We demonstrate how these methods are equivalent, not only in their aim but also in the solutions they yield. In addition, we show that the aforementioned methods modify the production frontier by extending existing facets or creating unobserved facets. Further we propose a new approach that uses weight restrictions to extend existing facets. This approach has some advantages in computational terms, because extended facet models normally make use of mixed integer programming models, which are computationally demanding.

A spatiotemporal Data Envelopment Analysis (S-T DEA) approach:the need to assess evolving units

One of the major challenges in measuring efficiency in terms of resources and outcomes is the assessment of the evolution of units over time. Although Data Envelopment Analysis (DEA) has been applied for time series datasets, DEA models, by construction, form the reference set for inefficient units (lambda values) based on their distance from the efficient frontier, that is, in a spatial manner. However, when dealing with temporal datasets, the proximity in time between units should also be taken into account, since it reflects the structural resemblance among time periods of a unit that evolves. In this paper, we propose a two-stage spatiotemporal DEA approach, which captures both the spatial and temporal dimension through a multi-objective programming model. In the first stage, DEA is solved iteratively extracting for each unit only previous DMUs as peers in its reference set. In the second stage, the lambda values derived from the first stage are fed to a Multiobjective Mixed Integer Linear Programming model, which filters peers in the reference set based on weights assigned to the spatial and temporal dimension. The approach is demonstrated on a real-world example drawn from software development.

Non-stationary stochastic inventory lot-sizing with emission and service level constraints in a carbon cap-and-trade system

Firms worldwide are taking major initiatives to reduce the carbon footprint of their supply chains in response to the growing governmental and consumer pressures. In real life, these supply chains face stochastic and non-stationary demand but most of the studies on inventory lot-sizing problem with emission concerns consider deterministic demand. In this paper, we study the inventory lot-sizing problem under non-stationary stochastic demand condition with emission and cycle service level constraints considering carbon cap-and-trade regulatory mechanism. Using a mixed integer linear programming model, this paper aims to investigate the effects of emission parameters, product- and system-related features on the supply chain performance through extensive computational experiments to cover general type business settings and not a specific scenario. Results show that cycle service level and demand coefficient of variation have significant impacts on total cost and emission irrespective of level of demand variability while the impact of product's demand pattern is significant only at lower level of demand variability. Finally, results also show that increasing value of carbon price reduces total cost, total emission and total inventory and the scope of emission reduction by increasing carbon price is greater at higher levels of cycle service level and demand coefficient of variation. The analysis of results helps supply chain managers to take right decision in different demand and service level situations.

Network lifetime maximization with cross-layer design in wireless sensor networks

This paper investigates a cross-layer design approach for minimizing energy consumption and maximizing network lifetime (NL) of a multiple-source and single-sink (MSSS) WSN with energy constraints. The optimization problem for MSSS WSN can be formulated as a mixed integer convex optimization problem with the adoption of time division multiple access (TDMA) in medium access control (MAC) layer, and it becomes a convex problem by relaxing the integer constraint on time slots. Impacts of data rate, link access and routing are jointly taken into account in the optimization problem formulation. Both linear and planar network topologies are considered for NL maximization (NLM). With linear MSSS and planar single-source and single-sink (SSSS) topologies, we successfully use Karush-Kuhn-Tucker (KKT) optimality conditions to derive analytical expressions of the optimal NL when all nodes are exhausted simultaneously. The problem for planar MSSS topology is more complicated, and a decomposition and combination (D&C) approach is proposed to compute suboptimal solutions. An analytical expression of the suboptimal NL is derived for a small scale planar network. To deal with larger scale planar network, an iterative algorithm is proposed for the D&C approach. Numerical results show that the upper-bounds of the network lifetime obtained by our proposed optimization models are tight. Important insights into the NL and benefits of cross-layer design for WSN NLM are obtained.

Developing a decision framework for the strategic sourcing of biomass

The deployment of bioenergy technologies is a key part of UK and European renewable energy policy. A key barrier to the deployment of bioenergy technologies is the management of biomass supply chains including the evaluation of suppliers and the contracting of biomass. In the undeveloped biomass for energy market buyers of biomass are faced with three major challenges during the development of new bioenergy projects. What characteristics will a certain supply of biomass have, how to evaluate biomass suppliers and which suppliers to contract with in order to provide a portfolio of suppliers that best satisfies the needs of the project and its stakeholder group whilst also satisfying crisp and non-crisp technological constraints. The problem description is taken from the situation faced by the industrial partner in this research, Express Energy Ltd. This research tackles these three areas separately then combines them to form a decision framework to assist biomass buyers with the strategic sourcing of biomass. The BioSS framework. The BioSS framework consists of three modes which mirror the development stages of bioenergy projects. BioSS.2 mode for early stage development, BioSS.3 mode for financial close stage and BioSS.Op for the operational phase of the project. BioSS is formed of a fuels library, a supplier evaluation module and an order allocation module, a Monte-Carlo analysis module is also included to evaluate the accuracy of the recommended portfolios. In each mode BioSS can recommend which suppliers should be contracted with and how much material should be purchased from each. The recommended blend should have chemical characteristics within the technological constraints of the conversion technology and also best satisfy the stakeholder group. The fuels library is made up from a wide variety of sources and contains around 100 unique descriptions of potential biomass sources that a developer may encounter. The library takes a wide data collection approach and has the aim of allowing for estimates to be made of biomass characteristics without expensive and time consuming testing. The supplier evaluation part of BioSS uses a QFD-AHP method to give importance weightings to 27 different evaluating criteria. The evaluating criteria have been compiled from interviews with stakeholders and policy and position documents and the weightings have been assigned using a mixture of workshops and expert interview. The weighted importance scores allow potential suppliers to better tailor their business offering and provides a robust framework for decision makers to better understand the requirements of the bioenergy project stakeholder groups. The order allocation part of BioSS uses a chance-constrained programming approach to assign orders of material between potential suppliers based on the chemical characteristics of those suppliers and the preference score of those suppliers. The optimisation program finds the portfolio of orders to allocate to suppliers to give the highest performance portfolio in the eyes of the stakeholder group whilst also complying with technological constraints. The technological constraints can be breached if the decision maker requires by setting the constraint as a chance-constraint. This allows a wider range of biomass sources to be procured and allows a greater overall performance to be realised than considering crisp constraints or using deterministic programming approaches. BioSS is demonstrated against two scenarios faced by UK bioenergy developers. The first is a large scale combustion power project, the second a small scale gasification project. The Bioss is applied in each mode for both scenarios and is shown to adapt the solution to the stakeholder group importance and the different constraints of the different conversion technologies whilst finding a globally optimal portfolio for stakeholder satisfaction.

Online trendy topics detection in microblogs with selective user monitoring under cost constraints

As microblog services such as Twitter become a fast and convenient communication approach, identification of trendy topics in microblog services has great academic and business value. However detecting trendy topics is very challenging due to huge number of users and short-text posts in microblog diffusion networks. In this paper we introduce a trendy topics detection system under computation and communication resource constraints. In stark contrast to retrieving and processing the whole microblog contents, we develop an idea of selecting a small set of microblog users and processing their posts to achieve an overall acceptable trendy topic coverage, without exceeding resource budget for detection. We formulate the selection operation of these subset users as mixed-integer optimization problems, and develop heuristic algorithms to compute their approximate solutions. The proposed system is evaluated with real-time test data retrieved from Sina Weibo, the dominant microblog service provider in China. It's shown that by monitoring 500 out of 1.6 million microblog users and tracking their microposts (about 15,000 daily) with our system, nearly 65% trendy topics can be detected, while on average 5 hours earlier before they appear in Sina Weibo official trends.

Cost-effective node monitoring for online hot event detection in sina weibo microblogging

We propose a cost-effective hot event detection system over Sina Weibo platform, currently the dominant microblogging service provider in China. The problem of finding a proper subset of microbloggers under resource constraints is formulated as a mixed-integer problem for which heuristic algorithms are developed to compute approximate solution. Preliminary results show that by tracking about 500 out of 1.6 million candidate microbloggers and processing 15,000 microposts daily, 62% of the hot events can be detected five hours on average earlier than they are published by Weibo.

A fuzzy AHP based integer linear programming model for the multi-criteria transshipment problem

Purpose – The purpose of this research is to develop a holistic approach to maximize the customer service level while minimizing the logistics cost by using an integrated multiple criteria decision making (MCDM) method for the contemporary transshipment problem. Unlike the prevalent optimization techniques, this paper proposes an integrated approach which considers both quantitative and qualitative factors in order to maximize the benefits of service deliverers and customers under uncertain environments. Design/methodology/approach – This paper proposes a fuzzy-based integer linear programming model, based on the existing literature and validated with an example case. The model integrates the developed fuzzy modification of the analytic hierarchy process (FAHP), and solves the multi-criteria transshipment problem. Findings – This paper provides several novel insights about how to transform a company from a cost-based model to a service-dominated model by using an integrated MCDM method. It suggests that the contemporary customer-driven supply chain remains and increases its competitiveness from two aspects: optimizing the cost and providing the best service simultaneously. Research limitations/implications – This research used one illustrative industry case to exemplify the developed method. Considering the generalization of the research findings and the complexity of the transshipment service network, more cases across multiple industries are necessary to further enhance the validity of the research output. Practical implications – The paper includes implications for the evaluation and selection of transshipment service suppliers, the construction of optimal transshipment network as well as managing the network. Originality/value – The major advantages of this generic approach are that both quantitative and qualitative factors under fuzzy environment are considered simultaneously and also the viewpoints of service deliverers and customers are focused. Therefore, it is believed that it is useful and applicable for the transshipment service network design.