Small Illustrative Example Research Articles

A note on valid inequalities for minimizing the total tardiness in a two-machine flow shop

This note reconsiders the valid inequalities designed by Kharbeche and Haouari (2013) for mixed-integer programming formulations of minimizing the total tardiness in a two-machine flow shop scheduling problem. While the majority of their proposed valid inequalities are able to substantially improve the computational time to find an optimal solution, we show that one of them is incorrect, due to the misinterpretation of a dominance criterion proven in Pan and Fan (1997). As a consequence, in some instances, all optimal solutions are excluded from the solution space, resulting in suboptimal solutions. To resolve this issue, we first demonstrate the suboptimality of the proposed valid inequality with a small illustrative example. Second, we formulate a new valid inequality, which correctly captures the dominance criteria of Pan and Fan (1997). Finally, we show the effect of this correction on the solution quality in a numerical study with scheduling instances that have 10 to 20 jobs. Depending on the number of jobs, between 10% and 22% of the supposedly optimal solutions with the incorrect valid inequality are in fact suboptimal. In terms of the objective function value, the error results in a loss of up to 12%.

Fuel-optimal truck path and speed profile in dynamic conditions: An exact algorithm

We consider optimizing a truck's choice of path and speed profile to minimise fuel consumption, exploiting real-time predictive information on dynamically varying traffic conditions. Time-varying traffic conditions provide particular challenges, both from network-level interactions (e.g. slowing to consume more fuel locally may be beneficial to avoid congested periods downstream) and link-level phenomena (e.g. interaction between acceleration and gradient profiles). A multi-level, discrete-time decomposition of the problem is presented in which: (i) [sub-problems] speed profiles are optimized within each link, given boundary conditions of entry/exit times and speeds; (ii) [master problem] a space-time extended network representation is used to encode the dynamic interactions, within which the joint choice of path and speed profile is made. By instantiating the space-time network in (ii) with the optimal link profiles from (i), we are able to devise a tractable algorithm while optimizing speed profiles over a fine timescale. The solution approach is to pre-solve offline the computationally-intensive step (i), meaning that the representation in (ii) can be efficiently produced online in response to the real-time predictive information, whereby optimization of the path and speed profile is solved by a single shortest path search in the space-time network, for which many exact algorithms exist. The method is extended to additionally consider choice of discretionary stops and (pre-trip) departure time. Two representations are presented and investigated, depending on whether constraints are additionally imposed to ensure consistency of speed profiles across link boundaries. Numerical experiments are reported on a small illustrative example and a case-study network.

Market Equilibria With Energy Storage as Flexibility Resources

Uncertain and variable real-time availability of renewable generation can increase the need for supply-side flexibility in power systems. Energy storage is a potential source of such flexibility. This paper examines the participation of multiple competing strategic profit-maximizing energy storage in a spot electricity market and its impact on consumers, producers, and market equilibria. To this end, we develop a two-stage stochastic bi-level model that has each energy-storage firm determine its market offers at the upper level to maximize its expected profit. The lower level represents market clearing under scenarios with different flexibility needs. We recast the bi-level model as a single-level optimization. A small illustrative example and larger case study show that energy storage can increase market efficiency and reduce renewable-energy curtailment. We show that energy-storage firms neglecting uncertainty in optimizing their market offers can yield profit losses.

Toward a better integration of requirements and model‐based specifications

AbstractAs of today, most specifications of technical systems still rely on requirements written in natural language. However, this approach is known to be problem‐prone, due to the inherent ambiguity of natural languages. On the other hand, fully formal or model‐based approaches seem to be out of reach in many practical cases, especially in early design phases of systems. In this article, we study how to combine in a pragmatic way natural language requirements with models. We propose to keep both formats and to link pieces of text in requirements with elements of models. In other words, corpuses of requirements are managed as hypertexts with links to models. For this approach to be fully efficient, the text of requirements is not free, but relies on controlled natural language techniques leading to a partial structuring of the text. We show that this makes it possible to design (semi)automatic verifications on requirements and models, which would be impossible with unconstrained natural language. We illustrate here our approach on a small illustrative example and we report results obtained on a full size industrial application.

Identifying and Characterizing Non-Convexities in Feasible Spaces of Optimal Power Flow Problems

Optimal power flow (OPF) is an important problem in the operation of electric power systems. The solution to an OPF problem provides a minimum cost operating point that satisfies constraints imposed by both the non-linear power flow equations and engineering limits. These constraints can yield non-convex feasible spaces that result in significant computational challenges. This brief proposes an algorithm that identifies and characterizes non-convexities in OPF feasible spaces. This algorithm searches for a pair of feasible points whose connecting line segment contains an infeasible point. Such points certify the existence of a non-convexity in the OPF feasible space. Moreover, the constraint violations at the infeasible point along the connecting line segment physically characterize a cause of the non-convexity. Numerical demonstrations include a small illustrative example as well as applications to various test cases.

Application of formal verification and falsification to large-scale chemical plant automation systems

In this paper, we apply formal verification and falsification of temporal logic specifications to analyze chemical plant automation systems. We present new results, obtained by applying a recently-developed approach to handle combined invariance and reachability requirements. In addition, we develop a set of tests that can be generated automatically for a given control system, some of which have the same form as those in the existing literature, and some of which combine invariance and reachability, to which we apply the new approach mentioned previously. In both cases, we work with abstractions of the automation systems in order to apply symbolic model checking to industrial-scale problems. We demonstrate the results using a series of small illustrative examples, and also report results from an industrial case study. The methods that we apply are implemented in a pair of open-source software tools, which we describe briefly.

Renewable generation expansion under different support schemes: A stochastic equilibrium approach

Following the deregulation of electricity markets, a current challenge of policy makers is to facilitate the transition to a sustainable power system at the highest welfare for society. In this paper we investigate the efficiency of different support schemes, such as a feed-in tariff, a feed-in premium and tradable green certificates, with respect to incentivizing the required investments in renewable generation. We consider a number of generation expansion problems, and formulate stochastic equilibrium models that account for uncertainty in demand and renewable supply, the risk-aversion of investors and the competitiveness of the market. The problem of the policy maker is formulated as a mathematical program with equilibrium constraints (MPEC) and as a non-linear complementarity problem (NCP) for the feed-in schemes and the certificate market, respectively. Our models are solved for a small illustrative example and a larger case study based on the Danish power system. The results confirm that the main driver for the optimal choice of renewable support scheme is the aversion of power producers towards price and volume risk, while the competitiveness of the market rarely affects such choice.

Joint optimisation of capacity and safety stock allocation

We study the joint optimisation of capacity and safety stock allocation in assembly systems. Particularly, we consider capacitated systems with base-stock policies and periodic review. Capacity allocation is restricted by budget constraints, which can connect multiple systems. Our objective is to minimise overall inventory holding costs while satisfying service level as well as budget constraints. We propose an algorithm to jointly approximate optimal capacity allocation and base-stock levels. To this end, we introduce a set of convex approximations for this non-convex optimisation problem. In order to solve the resulting convex programmes, we analytically compute sample path derivatives via infinitesimal perturbation analysis. By iteratively adapting the approximations, we achieve good capacity allocations and base-stock levels for the original problem. Furthermore, we introduce a heuristic to allocate capacity, which originates from link capacity allocation in communication networks and use it as a benchmark. The algorithm is applied to small illustrative examples as well as cases motivated by the semiconductor manufacturing process at IBM Systems. It turns out that particularly for high utilisation levels, our algorithm can achieve significant improvements compared to the capacity allocation heuristic.

Combining different models

Portfolio selection is one of the most important areas of modern finance, both theoretically and practically. Reliance on a single model is fraught with difficulties, so attempting to combine the strengths of different models is attractive; see, for example, Geweke and Amisano (J Econom 164(1):130–141, 2011) and the many references therein. This paper contributes to the model combination literature, but with a difference: the models we consider here are making statements about different sets of assets. There appear to be no studies making this structural assumption, which completely changes the nature of the problem. This paper offers suggestions for principles of model combination in this situation, characterizes the solution in the case of multivariate Gaussian distributions, and provides a small illustrative example.

Bad Data Detection in the Context of Leverage Point Attacks in Modern Power Networks

This paper demonstrates a concept to detect bad data in state estimation when the leverage measurements are tampered with gross error. The concept is based on separating leverage measurements from non-leverage measurements by a technique called diagnostic robust generalized potential, which also takes care of the masking or swamping effect, if any. The methodology then detects the erroneous measurements from the generalized studentized residuals. The effectiveness of the method is validated with a small illustrative example, standard IEEE 14-bus and 123-bus unbalanced network models and compared with the existing methods. The method is demonstrated to be potentially very useful to detect attacks in smart power grid targeting leverage points in the system.

In the quantitative automata zoo

Quantitative model checking and performance evaluation deal with the analysis of complex systems that must not only satisfy correctness requirements, but also meet performance and reliability goals. Models of such systems therefore need to represent the necessary quantitative information about probabilistic decisions, real-time phenomena, or continuous dynamics. At the same time, nondeterminism needs to be properly captured as in classical verification, so as to enable abstraction and compositional modelling. These aspects span a large spectrum of automata-based quantitative models which have been studied in the verification and performance evaluation literature. In this paper, we embark on a guided tour through this zoo of quantitative models. Starting from the basic formalisms of labelled transition systems and also Markov chains, we look at how timed and hybrid automata add real-time aspects as well as continuous dynamics, and we study extensions that provide for behaviour governed by discrete and continuous probability distributions. For each of the automata models, we outline its definition, provide a small illustrative example, summarise its expressive power, and survey available formal analysis techniques as well as selected practical applications.

Ambulance location under stochastic demand: A sampling approach

In this paper, we investigate the problem of choosing the location and number of ambulances and their bases in a certain region. The goal is to minimize the total cost for installing (and maintaining) these facilities but assuring a minimum coverage level. Demand is assumed to be stochastic. A scenario-indexed formulation is considered for the problem. By using a small illustrative example we show that even when demand can be captured by a finite number of scenarios, rapidly the number of scenarios becomes too large, thus preventing the effective use of the model. We also show that the possibility of considering just one sample of scenarios can lead to a totally misleading solution. These insights motivate the development of a sampling approach in which we draw several samples of scenarios and solve the restricted model associated with each of them. The sample of optimal values obtained by this procedure can be combined in order to estimate the optimal value of the original problem. The same happens with the sample of optimal solutions obtained, which can be combined heuristically to produce a feasible solution to the whole problem. We test the new approach using a set of random instances.

Discrete Pump Scheduling and Leakage Control Using Linear Programming for Optimal Operation of Water Distribution Systems

AbstractPump station scheduling is a major issue in optimal water system operation. Pump operation may be of an on/off form or of a fluctuating form using a variable-frequency drive (VFD). This research proposes an iterative linear discrete pump-scheduling algorithm using linear programming (LP). The examined problem includes nonlinear convex headloss, leakage, and varying total-head pump energy consumption constraints. A discrete pump operation index is proposed to select time steps on which to enforce a discrete pump operation constraint. After each iteration step, the index is recalculated based on the previous iteration steps’ results and the discrete operation constraint is added or removed from the time steps accordingly. The iterative process stops when all time steps have been discretely evaluated. The algorithm is first demonstrated on a small illustrative example application and compared to the global minimal results found by enumeration. Next, the algorithm is demonstrated on two complex exampl...

Poverty, Vulnerability, and Reference‐Dependent Utility

The numerous proposed measures of multi‐period poverty and vulnerability have until now not taken into account the insights from behavioral economics. In this paper we argue that recent evidence on individuals' decision making is of high relevance for the measurement of poverty when switching from a static and certain to a dynamic and uncertain framework. Building on reference‐dependent utility we propose new measures of both (perceived) multi‐period poverty and vulnerability, where the poverty status of an individual is a function not only of (expected) consumption levels but also of (expected) losses and gains in consumption. We demonstrate the implications of the proposed measures with a small illustrative example.

Seasonal multi-year optimal management of quantities and salinities in regional water supply systems

A seasonal multi-year model for management of water quantities and salinities in regional water supply systems (WSS) was developed and implemented. Water is taken from sources which include aquifers, reservoirs, and desalination plants, and conveyed through a distribution system to consumers who require quantities of water under salinity constraints. The year is partitioned into seasons, and the operation is subject to technological, administrative, and environmental constraints such as water levels and salinities in the aquifers, capacities of the pumping, distribution system, and the desalination plants, and the desalination plants maximum removal ratios. The objective is to operate the system at minimum total cost. The objective function and some of the constraints are nonlinear, leading to a nonlinear optimization problem. The nonlinear optimization problem is solved efficiently by adapting (1) a set of manipulations that reduce the problem size and (2) a novel finite difference scheme for calculating the derivatives required by the optimization solver, entitled the Time-Chained-Method (TCM). The model is demonstrated on a small illustrative example and on a real sized regional water supply system in Israel.

Formally based tool support for model checking Erlang applications

Model checking as a verification technique has proved effective at the system design and hardware level, and is now beginning to be applied to program code. In this paper, we study the application of model checking techniques in the development of Erlang systems. Erlang is a concurrent functional language with specific support for the development of distributed, fault-tolerant systems with soft real-time requirements. It was designed from the start to support a concurrency-oriented programming paradigm and large distributed implementations that this supports. The methodology we describe in this paper consists of abstracting the behaviour of Erlang and OTP components into a process algebraic specification, specifically an mCRL2 specification, upon which the standard model checker CADP can be used to verify the system’s properties. In addition to rules that model the Erlang syntax, a translation mechanism for the OTP modules gen_server, supervisor and gen_fsm, and the timeout event are defined. A tool-set etomcrl2 has been developed to automate the process of translation. A small illustrative example is used to evaluate the effectiveness of the proposed techniques, and its results show that the proposed techniques are effective in both verifying properties as well as distinguishing between correct and faulty implementations of the design.

One class of separable optimization problems: solution method, application

A solution method for solving optimization problems with a max-separable objective function and min-separable inequality constraints is suggested. The method is based on the results of 5, 6. Application in some location problems and small illustrative numerical examples are presented.

Agent strands in the action language [formula omitted

The action language C + of Giunchiglia, Lee, Lifschitz, McCain and Turner is a formalism for specifying and reasoning about the effects of actions and the persistence (‘inertia’) of facts over time. An ‘action description’ in C + defines a labelled transition system of a certain kind. n C + is an extended form of C + designed for representing normative and institutional aspects of (human or computer) societies. The deontic component of n C + provides a means of specifying the permitted (acceptable, legal) states of a transition system and its permitted (acceptable, legal) transitions. We present this component of n C + , motivating its details with reference to some small illustrative examples, and elaborate the formalism by allowing scope for norms governing individual agents. We describe the various kinds of investigation possible on the semantic structures which n C + defines.

ERP investment analysis using the strategic alignment model

PurposeTo develop a model to assist in the analysis of enterprise resource planning (ERP) systems based upon a validated approach to aligning information systems with enterprise strategies.Design/methodology/approachThis paper presents a proposed analytic network process (ANP) model built on the strategic alignment model (SAM) to support the alignment of ERP investment decisions to strategies. The model developed is generic enough to be applied to a wide range of enterprises and applications while being based on the well‐documented SAM. A small illustrative example is provided to show the use and applicability of the model.FindingsThe SAM is found to provide a useful framework for investment analysis. ANP provides a conceptually easy to use but decisionally robust model which can be used to operationalize the SAM for investment analysis.Practical implicationsThe model provides practitioners a flexible tool for making investment decisions not only for ERP systems but also for other IS investments. The paper provides academics and researchers with a methodology for the important area of IS alignment.Originality/valueThe paper represents a novel use of the multi‐attribute decision‐making method of ANP. It is also a new applied tool within the area of strategic IS evaluation.

Multivariate calibration: What is in chemometrics for the analytical chemist?

Chemometrics has been used for some 30 years but there is still need for disseminating the potential benefits to a wider audience. In this paper, we claim that proper analytical chemistry (1) must in fact incorporate a chemometric approach and (2) that there are several significant advantages of doing so. In order to explain this, an indirect route will be taken, where the most important benefits of chemometric methods are discussed using small illustrative examples. Emphasis will be on multivariate data analysis (for example calibration), whereas other parts of chemometrics such as experimental design will not be treated here. Four distinct aspects are treated in detail: noise reduction; handling of interferents; the exploratory aspect and the possible outlier control. Additionally, some new developments in chemometrics are described.