Electricity market near-equilibrium under locational marginal pricing and minimum profit conditions

This paper provides a tool to determine the near-equilibrium of an electric energy market. This market works under locational marginal pricing, i.e., generating units and demand loads are paid and pay, respectively, the locational marginal prices corresponding to the nodes they are connected to. The near-equilibrium is defined as the energy transaction levels for which generating companies maximize their respective profits and consumption companies maximize their respective utilities. An independent system operator clears the market maximizing the social welfare. Conditions that ensure minimum profit for generating units can be included. However, these conditions may render a generating unit uncompetitive and expel it from the market. Demands are taken to be non-constant and values are determined as part of the solution. The near-equilibrium is obtained through the solution of a mixed-integer quadratic problem equivalent to a mixed linear complementarity problem that includes the minimum profit conditions. It is important to note that the near-equilibrium concept presented in this paper does not solve a market equilibrium when indivisibilities such as start up costs or the like are present. Lastly, we validate the proposed model on a case study using data from the IEEE Reliability Test System.     

Unobservable or omitted production variables in data envelopment analysis through unit-specific production trade-offs

The paper focuses upon situations in which decision-making units carry out their production activities with some inputs or outputs unobservable (or possibly omitted), and when there are a priori known constraints on the relative significance of otherwise observable (or explicitly considered) inputs and outputs. For such settings, the paper proposes a modification that alters traditional construction of the production possibility set and isolates the role of the unobservable (or omitted) variables in production by means of restrictions on virtual inputs and outputs being converted into production trade-offs. In effect, the proposed procedure induces unit-specific production possibility sets that derive from production trade-offs framed for units assessed separately to reflect their specific observed production conditions. The modification is implemented within a weighted slacks-based measure with restricted direction of slacks in order to make technical efficiency measurement more informative and consistent with the operating conditions under which production activities are accomplished. These ideas are illustrated and models implemented in a case study of bank branch performance measurement.     

DEA-based production planning considering influencing factors

When planning production in a centralized decision-making environment using data envelopment analysis (DEA), previous researches usually plan for units by selecting best-practice points within the entire production possibility set or adhering to their original abilities so that potentials may not be fully explored. In practice, there often exist factors that influence units’ production abilities. Difficulties may occur when improving inefficient units’ performances or they can only be improved in a limited room. This paper takes these influencing factors into account to avoid new plans beyond units’ abilities or not fully exploring their potentials. Depending on performance variability, two DEA-based production planning approaches are proposed to optimize the total resource utilization assuming demand changes in the next production season can be forecasted. When performances are improvable, units are grouped according to the influencing factors they face. Simple numerical examples and a real world data set are used to illustrate the proposed approaches.     

Efficiency measurement for parallel production systems

In the real world there are systems which are composed of independent production units. The conventional data envelopment analysis (DEA) model uses the sum of the respective inputs and outputs of all component units of a system to calculate its efficiency. This paper develops a parallel DEA model which takes the operation of individual components into account in calculating the efficiency of the system. A property owned by this parallel model is that the inefficiency slack of the system can be decomposed into the inefficiency slacks of its component units. This helps the decision maker identify inefficient components and make subsequent improvements. Another property is that the efficiency calculated from this model is smaller than that calculated from the conventional DEA model. Few systems will have perfect efficiency score; consequently, a stronger discrimination power is gained. In addition to theoretical derivations, a case of the national forests of Taiwan is used as an example to illustrate the whole idea.     

The Effect of Area Measurement Tools on Student Strategies: The Role of a Computer Microworld

This study focuses on the role of tools, provided by a computer microworld (C.AR.ME), on the strategies developed by 14-year-old students for the area measurement of a non-convex polygon. Students' strategies on a transformation and a comparison task were interpreted and classified into categories in terms of the tools used for their development. The analysis of the data shows that an environment providing the students with the opportunity to select various tools and asking them to produce solutions `in any possible way' can stimulate them to construct a plurality of solution strategies. The students selected tools appropriate for their cognitive development and expressed their own individual approaches regarding the concept of area measurement. The nature of tools used affected the nature of solution strategies that the students constructed. Moreover, all students were involved in the tasks and succeeded in completing them with more than one correct solution strategy thereby developing a broader view of the concept, although not all of them realized the same strategies. Three different approaches to area measurement emerged from the strategies which were constructed by the students in this microworld: automatic area measurement, provided by the environment, the operation of area measurement using spatial units and the use of area formulae. Almost all the students experienced qualitative aspects of area measurement through being involved in the process of covering areas using spatial units. Students also managed to use the area formulae meaningfully by studying it in relation to automatic area measurement and to area measurement using spatial units. Through these strategies, the concepts of conservation of area and its measurement as well as area formulae were viewed by the students as interrelated. Finally, some basic difficulties regarding area measurement were overcome in this computer environment.This revised version was published online in September 2005 with corrections to the Cover Date.     

Characteristics of Second Graders' Mathematical Writing

This study compared the characteristics of second graders' mathematical writing between an intervention and comparison group. Two six‐week Project M2 units were implemented with students in the intervention group. The units position students to communicate in ways similar to mathematicians, including engaging in verbal discourse where they themselves make sense of the mathematics through discussion and debate, writing about their reasoning on an ongoing basis, and utilizing mathematical vocabulary while communicating in any medium. Students in the comparison group learned from the regular school curriculum. Students in both the intervention and comparison groups conveyed high and low levels of content knowledge as indicated in archived data from an open‐response end‐of‐the‐year assessment. A multivariate analysis of variance indicated several differences favoring the intervention group. Both the high‐ and low‐level intervention subgroups outperformed the comparison group in their ability to (a) provide reasoning, (b) attempt to use formal mathematical vocabulary, and (c) correctly use formal mathematical vocabulary in their writing. The low‐level intervention subgroup also outperformed the respective comparison subgroup in their use of (a) complete sentences and (b) linking words. There were no differences between groups in their attempt at writing and attempts at and usage of informal mathematical vocabulary.     

The trim-loss and assortment problems: A survey

A wide variety of materials are manufactured in bulk by processes in which the dimensions of the units of production are constrained by the nature of the machinery being used. The assortment problem is that of deciding, given the constraints, what the dimensions of the production units should be. The trim-loss problem is that of formulating a scheme for the cutting of the production units into pieces of the sizes ordered by customers.A variety of methods, both exact and heuristic, have been applied to these problems. This paper presents a taxonomy of the problems and reviews the techniques which have been proposed for their solution.     

A taxonomy of flexible flow line scheduling procedures

We present a taxonomy for flexible flow line scheduling procedures. Flexible flow lines are flow lines with parallel machines on some or all production stages. The taxonomy groups procedures according to their general solution approach. It distinguishes optimal and heuristic procedures. Heuristic procedures are split into holistic and decomposition approaches. While holistic approaches consider the complete scheduling problem in an integrated way, decomposition approaches divide the problem with respect to the production stages, the individual jobs, or the sub-problems to be solved (batching, loading, and sequencing). We explicitly mention the inclusion of setups in a study and list the respective objective criteria.     

Spatial classification

The aim of a spatial classification is to position the units on a spatial network and to give simultaneously a set of structured classes of these units “compatible” with the network. We introduce the basic needed definitions: compatibility between a classification structure and a tessellation, (m,k)-networks as a case of tessellation, convex, maximal and connected subsets in such networks, spatial pyramids and spatial hierarchies. As like Robinsonian dissimilarities induced by indexed pyramids generalize ultrametrics induced by indexed hierarchies we show that a new kind of dissimilarity called “Yadidean” induced by spatial pyramids generalize Robinsonian dissimilarities. We focus on spatial pyramids where each class is a convex for a grid, and we show that there are several one-to-one correspondences with different kinds of Yadidean dissimilarities. These new results produce also, as a special case, several one-to-one correspondences between spatial hierarchies (resp. standard indexed pyramids) and Yadidean ultrametrics (resp. Robinsonian) dissimilarities. Qualities of spatial pyramids and their supremum under a given dissimilarity are considered. We give a constructive algorithm for convex spatial pyramids illustrated by an example. We show finally by a simple example that spatial pyramids on symbolic data can produce a geometrical representation of conceptual lattices of “symbolic objects”.     

Steady-state skill levels of workers in learning and forgetting environments: A dynamical system analysis

This article presents a study on the long-term (i.e., steady-state, convergence) characteristics of workers’ skill levels under learning and forgetting in processing units in a manufacturing environment, in which products are produced in batches. Assuming that all workers already have the basic knowledge to execute the jobs, workers learn (accumulate their skill) while producing units within a batch, forget during interruptions in production, and relearn when production resumes. The convergence properties in the paper are examined under assumptions of an infinite time horizon, a constant demand rate, and a fixed lot size. Our work extends the steady-state results of Teyarachakul, Chand, and Ward (2008) to the learning and forgetting functions that belong to a large class of functions possessing some differentiability conditions. We also discuss circumstances of manufacturing environments where our results would provide useful managerial information and other potential applications.     

Costly information acquisition under horizontal competition

We analyze endogenous acquisition of costly information for two firms that sell homogeneous products. Prior to determining its production quantity, either firm has an opportunity to acquire a costly forecast. There exists a correlation between errors in the acquired forecasts. We model the problem as a two-stage game in which the firms first decide whether to acquire their respective forecasts and then decide their production quantities. We derive the equilibrium outcome on information acquisition and production quantity.     

Joint Economic Ordering Policies of Multiple Wholesalers and a Single Manufacturer with Price-dependent Demand Functions

The economic ordering policies for multiple regional wholesalers and the production lot-sizing policy for a single manufacturer have been studied in a joint analysis under the assumption that the yearly demands of each region are functions of their respective retail proces. We obtained optimum EOQs for both linear and constant price elasticity demand functions. Although normally the wholesalers would order in quantities equal to their EOQs, they are encouraged to purchase in different quantities by the producer providing compensation to offset the wholesalers' increased costs. The production lot-size is determined to minimize the overall production cost.     

Ordered spatial sampling by means of the traveling salesman problem

In recent years, spatial sampling has been the subject of a flourishing literature. Its use had become widespread due to the availability of topographical information about statistical units, especially in the environmental context. New algorithms enable us to take advantage of spatial locations directly. In this paper, we present a new way of using spatial information by using traditional sampling techniques as systematic sampling. By means of a famous optimization method, the traveling salesman problem, it is possible to order the statistical units in a way that preserves the spatial correlation. Next ordered sampling methods are applied on the statistical units. Therefore we can render spatial some non-spatial methods. An economic application on real data is presented and different spatial and non-spatial methods are tested. Results are compared in terms of variance estimation and spatial balance, in order to establish the possibility of spatializing traditional sampling methods and of implementing them on data of different nature, among which economic ones.     

Efficiency analysis in multi-period systems: an application to performance evaluation in Czech higher education

Data envelopment analysis (DEA) is a non-parametric method for efficiency and performance analysis of decision making units. The paper deals with production systems where decision making units are described by their inputs and outputs in several consecutive periods. The paper presents (Park and Park in Eur J Oper Res 193(2):567–580, 2009) multi-period DEA model that is oriented on the “best” period of the unit under evaluation only. This aim of this paper is to overcome the disadvantage of this model and formulate new models of this class that allow evaluation the efficiency of decision making units within the whole production chain. The presented efficiency and super-efficiency multi-period DEA models are illustrated on a case study. The study consists in analysis of research and teaching performance of 19 Czech economic faculties in four years period from 2009 until 2012. The model considers two inputs (number of academic employees and labour costs) and two outputs for teaching efficiency (number of students and number of graduated). Research efficiency is expressed using the number of publications in various important categories and the number of so called RIV points that describe the quality of publications.     

The capacitated distribution and waste disposal problem

We study the problem of the simultaneous design of a distribution network with plants and waste disposal units, and the coordination of product flows and waste flows within this network. The objective is to minimize the sum of fixed costs for opening plants and waste disposal units, and variable costs related to product and waste flows. The problem is complicated by (i) capacity constraints on plants and waste disposal units, (ii) service requirements (i.e. production must cover total demand) and (iii) waste, arising from production, to be disposed of at waste disposal units. We discuss alternative mathematical model formulations for the two-level distribution and waste disposal problem with capacity constraints. Lower bounding and upper bounding procedures are analyzed. The bounds are shown to be quite effective when embedded in a standard branch and bound algorithm. Finally, the results of a computational study are reported.     

DEA production games

In this paper, linear production games are extended so that instead of assuming a linear production technology with fixed technological coefficients, the more general, non-parametric, DEA production technology is considered. Different organizations are assumed to possess their own technology and the cooperative game arises from the possibility of pooling their available inputs, collectively processing them and sharing the revenues. Two possibilities are considered: using a joint production technology that results from merging their respective technologies or each cooperating organization keeping its own technology. This gives rise to two different DEA production games, both of which are totally balanced and have a non-empty core. A simple way of computing a stable solution, using the optimal dual solution for the grand coalition, is presented. The full cooperation scenario clearly produces more benefits for the organizations involved although the implied technology sharing is not always possible. Examples of applications of the proposed approach are given.     

Resource allocation and target setting for parallel production system based on DEA

The paper proposes methodology for resource allocation and target setting based on DEA (data envelopment analysis). It deals with organization can be modeled as consisting of several production units, each of which has parallel production lines. The previous studies in the DEA literature only deal with reallocating/allocating organizational resources to production units and set targets for them. In their researches, the production unit is treated as a black box. In such circumstances, how to arrange the production at production unit level is not clear. This paper serves to generate resource allocation and target setting plan for each production unit by opening the black box. The proposed model exploits production information of production lines in generating production plans. The resulting plan has following characteristics: (1) the performance of each production lines are evaluated under common weights; (2) the weights chose for evaluation keep the efficiency of the entire unit not worse off; (3) the worst behaved production line in the production unit under evaluation are improved as much as possible. Finally, the real data of a production system extracted from extant literature are used to demonstrate the proposed method.     

On a dual hybrid queueing system

This article deals with a hybrid system, in which a single server processes two different queues of units, one called primary and the other one — secondary. The queueing process in the primary system is formed by a Poisson flow of groups of units, while the secondary system is closed. The server’s primary appointment (in hybrid mode I) is to process units in batches until the buffer content drops significantly. In this case, the server takes over a queue in the secondary system (activating hybrid mode II), and he is to complete some minimum amount of jobs (rendered in groups of random sizes during random times). When he is done with this work, he returns to the primary system. If the queue there is not long enough, he waits, thereby activating hybrid mode III. The authors first apply and embellish some techniques from fluctuation theory to find the exit times from respective hybrid modes and queue levels in both systems in terms of their joint functionals. The results are then utilized for the subsequent (semi-regenerative) analysis of the evolution of queueing processes. The authors obtain explicit formulas for the limiting distribution of the queueing process and the mean number of units processed in the secondary system.     

Optimal scheduling of batch industrial facilities

An increasing interest in batch processing has been evident in recent years. This renewed interest is explained by the inherent flexibility of such plants that permits a high level of response to uncertain market conditions and requirements. This level of response does require the use of efficient tools to help the decision-making process at the design and operational level. This paper presents a Mixed Integer Linear Program (MILP) model to optimise the scheduling of batch facilities subject to changeovers and distribution constraints so as to guarantee a pre-defined objective. Such an objective can be defined as the minimum orders' total lateness or the maximum distribution units loading capacity, among others. A continuous-time representation is used as well as the concept of job predecessor and successor to effectively handle changeovers. Facilities having non-identical parallel units/lines, sequence-dependent orders, finite release times for units and orders, restrictions on the suitability of jobs to lines/units and different possible destinations to available distribution units are also considered. Based on these characteristics the proposed model is able to determine the optimal allocation of jobs to production lines/units, the sequence of jobs on every line/unit and the starting and completion production times of each order. Also, the usage and allocation of the distribution resources (eg trucks) to orders and destinations are obtained based on their availability and suitability to the orders. The model led to the development of a prototype information system that can be used as a tool to help the decision-making process at the operational plant level.Finally, the applicability of the proposed system/formulation is shown through the resolution of an industrial real case where the production of polymers is performed.