PROGRAM FOR FRIDAY, APRIL 11TH

Stochastic integer programs of industrial size are almost always unsolvable to optimality. One possible path to better understand and solve such models is to investigate how uncertainty affects optimal solutions to such programs; What characterizes optimal solutions – are there structures that emerge? This can be done by studying small scale problems that are solvable by off-the-shelf software. Inevitably we are led into the area of options theory to understand what is happening. This talk will report on such structural analyses for several classes of network design problems, and also show how the structures can be used to develop good (constructive) heuristics.

The log-optimal portfolio is known to outperform any other portfolio in the long run if stock returns are i.i.d. and follow a known distribution. In this talk, we establish similar guarantees for finite investment horizons where the distribution of stock returns is ambiguous. By focusing on fixed-mix portfolios, we exploit temporal symmetries to formulate the emerging distributionally robust optimization problems as tractable conic programs whose sizes are independent of the investment horizon.

We consider a class of mathematical programs with robust equilibrium constraints represented by a system of semi-infinite complementarity constraints (SICC). We propose a numerical scheme for tackling SICC. Specifically, by relaxing the complementarity constraints and then randomizing the index set of SICC, we employ the well-known entropic risk measure to approximate the semi-infinite constraints with a finite number of stochastic inequality constraints. Under some moderate conditions, we quantify the approximation in terms of the feasible set and the optimal value. The approximation scheme is then applied to a class of two stage stochastic mathematical programs with complementarity constraints in combination with the polynomial decision rules. Finally, we extend the discussion to a mathematical program with distributionally robust equilibrium constraints which is essentially a one stage stochastic program with semi-infinite stochastic constraints indexed by some probability measures from an ambiguity set defined through the KL-divergence.

Over the last two decades, robust optimization has emerged as a computationally viable approach to formulate and solve single-stage decision problems affected by uncertainty. More recently, robust optimization has been successfully applied to multi-stage problems with continuous recourse. This research takes a step towards extending the robust optimization methodology to problems with integer recourse, which have largely resisted solution so far. To this end, we approximate two-stage robust integer programs by their corresponding K-adaptibility problems, in which the decision maker pre-commits to K second-stage policies here-and-now and implements the best policy once the uncertain parameters are observed. We study the approximation quality and the computational complexity of the K-adapatibility problem, and we propose two mixed-integer linear programming reformulations that can be solved with off-the-shelf software. We demonstrate the effectiveness of our reformulations in numerical experiments.

The optimality of Cover’s universal portfolio (UP) is one of the main reasons behind the popularity of this algorithm in the on-line portfolio selection literature [Cov91]. The ability of successfully utilizing a portfolio selection algorithm in practice requires the possibility to include risk management. This has been neglected in previous theoretical works, ignoring the necessity of risk-adjustment in real applications. In [DMS14] a risk-adjusted online portfolio selection algorithm (RAPS) is derived, that performs provably as well as UP in the worst-case. Contrary to UP, RAPS takes into account the trading risk by the maximum possible return fluctuation of the constant-rebalanced portfolio. Based on the growth rate of the assets within the portfolio UP reallocates the capital invested, while RAPS reallocates based on the assets’ volatility. We give an experimental investigation of RAPS and UP assuming a finite investment horizon. A stochastic market model with two assets is applied, and results are compared to the theoretical analysis of [DMS14] and [Cov91]. By means of a Monte-Carlo simulation we investigate the impact of an assets’ (i) growth rate, (ii) volatility, and (iii) correlation on the performance of UP and RAPS. Not surprisingly, besides (iii), the main success drivers of UP and RAPS are (i) and (ii), respectively. The higher the volatility the higher is the probability to beat the best asset in the market. In general, RAPS outperforms UP if we aim to the best stock [BYG04].

[BYG04] Borodin, A.; El-Yaniv, R., and Gogan, V.: Can we Learn to Beat the Best Stock. Journal of Artificial Intelligence Research (21) (2004) 579-594 [Cov91] Cover, T.: Universal portfolios. Mathematical Finance 1(1) (1991) 1–29 [DMS14] Dochow, R., Mohr, E., and Schmidt, G.: Risk-adjusted On-line Portfolio Selection. Selected Papers of the Annual International Conference of the German and the Dutch Operations Research Society, University of Rotterdam, September 3-6 (2013), in press.

In this paper, a model for the accumulated reserve and the pricing process of a portfolio of different Non-Life insurance products is considered. The decision for today’s reserve depends on the level of reserve for the last t periods, and the price of the premium is the control parameter of the model. We show how in general we can setup the problem in a finite dimensional space and then we find a necessary and sufficient condition for the existence of a viable reserve control path by using Fenchel-duality.

Implied volatility is a key value in financial mathematics. We demonstrate the shortcomings of the standard ways to compute this quantity, i.e. numerical inversion of the well-known Black-Scholes formula or asymptotic expansion approximations, and propose a new way to directly calculate the implied variance in a local volatility framework as the solution of a quasilinear degenerate parabolic partial differential equation. Since the numerical solution of this equation may result in large nonlinear systems and thus high computation times compared to the classical approaches, we apply model reduction techniques to achieve computational efficiency. A popular method for the derivation of reduced-order models is Proper Orthogonal Decomposition (POD). This strategy is additionally combined with the Discrete Empirical Interpolation Method (DEIM) to deal with the nonlinear terms. Numerical results prove the quality of our approach compared to other methods.

The aircraft conflict detection and resolution problem takes an important role within the air traffic management. Given a set of aircraft configuration, the aim of the problem is to provide a new configuration in such a way that every conflict situation is detected as well as solved. A conflict situation is such an event in which two or more aircraft violate the safety distances that the must keep during their flights. In order to deal with this problem, a mixed integer nonconvex nonlinear optimization model is presented where velocity, heading angle and altitude changes are allowed to be performed by each aircraft. Three different multi-objective criteria are also studied: lexicographical, compromise and a mixture of two phases in which firstly the maximum deviation from the initial configuration is minimized and secondly the compromise criterion is used. The lexicographical criterion takes into account the comfort of the passengers, compared with the other two criteria based on economic costs. Comfort and economic costs are facing each other since in terms of comfort, the preferences on the maneuvers are: velocity, heading angle and altitude, whereas in terms of economy, the preferences are: altitude, heading angle and velocity. Due to the difficulty of the model solving, a metaheuristic approach based on sequentially solving a set of mixed integer linear optimization models is presented. The angle range is discretized and the nonlinear constraints of the model are linearized by using a set of binary variables. The total computing time for solving the set of linear models is smaller than the time required for solving the nonlinear one for large scale problems, where Cplex (been iteratively used) and Minotaur are the estate-of-the-art solvers of choice, respectively. A broad computational experience is presented.

A metaheuristic, so named Fix-and-Relax Coordination algorithm (FRCA), is presented for solving large-scale multiperiod stochastic mixed 0-1 optimization problems. The large-scale character can be motivated by the intrinsic dimensions of the problem as well as due to the large number of additional 0-1 and continuous variables and constraints required by the risk averse strategy to use, in our case the time consistent stochastic dominance constraints based recourse-integer (T- SDC) strategy. The inexact approach that is proposed in this work handles the uncertainty of the parameters by a set of scenarios structured in a tree. One of its main characteristics consists of considering macro-periods along the time horizon dynamically included by sets of consecutive periods. For each scenario group that belongs to the first period of any macro-period a mixture of multistage and two-stage stochastic mixed 0-1 subproblems is solved, by relaxing the integrality and non-anticipativity constraints in successor groups of the scenario groups that belong to the last period in the macro-period. A backward procedure is introduced such that the macro-periods are dynamically adjusted. The T-SDC strategy considers a set of profiles at each selected time period. Each profile is included by a threshold to satisfy, its failure probability and expected shortfall bounds as soft constraints, and a maximum shortfall allowed as a hard constraint.

In this communication we propose a new exact method to solve

Multiple Objective Integer Stochastic Linear Programming problem. Once the

problem is converted into a deterministic one by adapting the 2-levels recourse

approach, an aggregation of the expected objective functions is optimized on

the admissible region taking into account an additional penalty cost due to

violation of some stochastic constraints.

A list of all non dominated solutions is formed progressively and the domain is being reduced until it becomes empty. A detailed didactic example is given to illustrate different steps of our developed algorithm.

The Supplier Selection Problem consists of the definition of models and methods to analyze and measure the performance of a set of suppliers in order to improve customer competitiveness. It is an intrinsically multi-attribute problem, since many qualitative and quantitative factors, very often conflicting with each other, should be taken into account. This decision is considered more complex because the diversity of quantitative and qualitative criteria considered in the decision-making process. In this research, we propose a new methodology for supplier selection based on meaningful suitability indices. This index is computed for ranking and selecting the right suppliers for all cardinal and ordinal criteria. Moreover, this index is meaningful whatever the representation of the measurement scale considering the point of view of decision-maker to other. Also, we based on the measurement theory and the multi-criteria decision analysis to determine the meaningful suitability indices. In other hand, on the basis of the meaningful suitability indices, the buyer can determined the order lot-sizing and distributed proportionally the total demand among suppliers.

In this study we are interested in measuring job satisfaction by developing a Decision Support System (DSS) based on the Multi-criteria Satisfaction Analysis (MUSA) method and the genetic algorithm. The objective is to help the organization evaluate and measure the employees’ satisfaction. Our study is decomposed on two parts. Firstly, we propose a genetic algorithm to solve the MUSA method in order to obtain a robust solution of good performance. The aim of the development of this algorithm is to verify its efficiency regarding the algorithm proposed by Grigoroudis and Siskos in 2002. In the second part we present our Decision Support Systems called “GMUSA System”. Our approach was applied at Sfax University to measure teachers’ job satisfaction.

Two measures of power excel to evaluate the importance of individual decision-making in a democratic institution under uncertainty. These measures are known as success and decisiveness and are widely applied in management.

It is known that if the probability of voting yes is equal to the probability of voting no for all players, the notions of success and decisiveness are related in an affine relationship and therefore there are no essential differences between them.

In this work we consider any arbitrary probability distribution for players and establish conditions under which these two notions are ordinally equivalent. The main result obtained, by means of optimization, helps to clarify the similarities and distinctions between the two concepts. The binary approach is then extended to situations with multiple alternatives for input and output highlighting similarities and differences with the binary model.

In a stochastic interdiction game a proliferator aims to minimize the expected duration of a nuclear weapons development project, while an interdictor endeavors to maximize the project duration by delaying some of the project tasks. We formulate static and dynamic versions of the interdictor's decision problem where the interdiction plan is either pre-committed or adapts to new information revealed over time, respectively. The static model gives rise to a stochastic program, while the dynamic model is formalized as a multiple optimal stopping problem in continuous time and with decision-dependent information. Under a memoryless probabilistic model for the task durations, we prove that the static model reduces to a mixed-integer linear program, while the dynamic model reduces to a finite Markov decision process in discrete time that can be solved via efficient value iteration. We then generalize the dynamic model to account for uncertainty in the outcomes of the interdiction actions. We also discuss a crashing game where the proliferator can use limited resources to expedite tasks so as to counterbalance the interdictor's efforts. The resulting problem can be formulated as a robust Markov decision process.

Cooperative games with transferable utilities belong to a branch of game theory where groups of players can form coalitions in order to jointly achieve the groups’ objectives. Under a cooperative setting, having a payoff distribution among the players in such a way that ensures the stability of the game becomes one of the most important questions to be answered. Classical solutions concepts such as the core and the least core are defined only in games with deterministic characteristic functions. However, the payoff function might be stochastic, e.g. through estimation or approximation of the reality, and classical solutions concepts are no longer applicable. We redefine the concept of stability in a stochastic setting and introduce new concepts for robust payoff distribution. We demonstrate these to a number of games including the stochastic newsvendor games. Properties and numerical schemes for finding the robust solutions are presented.

We study the robust capacitated vehicle routing problem (robust CVRP), which asks for the minimum cost delivery of a product to geographically dispersed customers using capacity-constrained vehicles. Contrary to the deterministic CVRP, which postulates that the customer demands for the product are deterministic and known, the robust CVRP models the customer demands as random variables, and it determines a minimum cost delivery plan that is feasible for all anticipated demand realizations. We show that the robust CVRP can be modelled as a two-stage robust optimization problem that has an equivalent reformulation as a mixed-integer linear program (MILP). We generalize the classical rounded capacity inequalities to the robust setting and illustrate how they expedite the solution of the MILP in a branch-and-cut framework. We also discuss how the robust CVRP relates to the chance-constrained CVRP, which allows a controlled degree of supply shortfall to decrease delivery costs.

In this work we consider the problem of constructing a market neutral portfolio. This is a portfolio of financial assets that (ideally) exhibits performance independent from that of an underlying market as represented by a benchmark index. We formulate this problem as a mixed-integer nonlinear program, minimising the absolute value of the correlation between portfolio return and index return. Our model is a flexible one that incorporates decisions as to both long and short positions in assets. Computational results, obtained using the software package Minotaur, are given for constructing market neutral portfolios for eleven different problem instances derived from universes defined by S\&P international equity indices. We also compare our approach against an alternative approach based on minimising the absolute value of  regression slope (the zero-beta approach).

We discuss a risk measure recently advocated in the academic literature, E-VaR, which hinges on the statistical concept of expectile. The paper derives an asset allocation procedure that minimises E-VaR by using piecewise linear programming. Moreover, we show that a straightforward generalization of our framework can be used to incorporate a dynamic model of E-VaR. As a result, the information available from time series of asset returns is used to learn about the evolution of downside risk at portfolio level. Risk is then minimised by targeting the predicted E-VaR. The numerical efficiency and stability of our approach are illustrated through a number of asset allocation examples.

Second order Stochastic Dominance (SSD) has a well recognised importance in portfolio selection, since it provides a natural interpretation of the theory of risk-averse investor behaviour. Recently, SSD-based models of portfolio choice have been proposed; these assume that a reference distribution is available and a portfolio is constructed, whose return distribution dominates the reference distribution with respect to SSD. We present an empirical study which analyses the effectiveness of such strategies in the context of enhanced indexation. Several datasets, drawn from FTSE 100, SP 500 and Nikkei 225 are investigated through portfolio rebalancing and back-testing. Three main conclusions are drawn. First, the portfolios chosen by the SSD based models consistently outperformed the indices and the traditional index trackers. Secondly, the SSD based models do not require imposition of cardinality constraints since naturally a small number of stocks are selected. Thus, they do not present the computational difficulty normally associated with index tracking models. In this paper we present a unified framework which incorporates (a) SSD, (b) downside risk (Conditional Value-at-Risk) minimisation and (c) enhanced indexation.

A significantly condensed modeling approach to planning and scheduling optimization is to pose the problem as differential and algebraic equations (DAEs) with either continuous or discrete variables. The APMonitor modeling language solves large-scale and complex systems of DAEs not only for dynamic optimization but also for model reconciliation to data. Some of the recent applications in APMonitor include computational biology, unmanned aerial systems, chemical process control, solid oxide fuel cells, grid-scale energy storage, and oil & gas upstream systems. Highlighted in this presentation is a capacity expansion of a district heating network. This study evaluates the investment decision timing and type of capacity expansion. An optimal investment schedule is determined over a 30 year horizon with stochastic inputs (e.g. fuel prices, carbon tax costs, electricity prices) as well as daily dynamics across seasonal variations. This is formulated as a dynamic optimization problem in which an initial system configuration is modified by decisions to drive from an initial state to an optimal state. In this case, the underlying DAE model is discretized into an equivalent set of nonlinear equations with mixed-integer variables. The APMonitor Optimization Suite facilitates this transformation so that problems can be solved with capable mixed-integer (MINLP) solvers. In addition to forward predictions, there is also value in "looking backward" in time to align these same models to available measurements through state and parameter estimation. Once the system is aligned with dynamic data, the model with updated parameters is projected forward in time and solved as an MINLP problem to solve capacity planning scenarios. The solution of this MINLP problem drives the system along a desired trajectory or best meets multiple objectives. Recent progress with parallelization, web services architecture, and remaining challenges with large-scale and complex dynamic systems are reviewed.

We present JuMP, an open-source algebraic modeling language embedded in Julia, a new high-level language for scientific computing. JuMP uses Julia's modern language features such as just-in-time compilation and metaprogramming to achieve performance competitive with hand-written matrix generators while providing a familiar algebraic syntax. Benchmarks with state-of-the-art modeling packages such as AMPL and Pyomo are provided. We discuss our most recent feature, a solver-independent interface for MIP callbacks supporting lazy constraints and user cuts, compatible with Gurobi, CPLEX, and GLPK.

Modeling languages for formulating and analyzing optimization problems are essentially declarative, in that they are founded on a symbolic description of a model’s objective function and constraints rather than a procedural specification of how a problem instance is to be generated and solved. Yet successful optimization modeling languages have come to offer many of the same facilities as procedural, high-level programming languages, in two ways: by extension of their syntax to interpreted scripting languages, and by exposure of their functions through application programming interfaces (APIs). How can scripting and APIs benefit the user of a declarative language, and what do they offer in comparison to modeling exclusively in a general-purpose language? This presentation suggests a variety of answers, through examples in which the AMPL modeling language is applied to parametric analysis, solution generation (via cuts and via solver options), heuristic optimization, pattern generation, and decomposition. Concluding comments discuss the design of new AMPL scripting features and the new AMPL API for Java, MATLAB, and other platforms.

I first consider the What , Why and How of (business) analytics and its close coupling with information systems in general and data in particular. OR analysts and Management Science specialists have made huge contributions over the period of last fifty years; the modelling methodologies and  software technologies have evolved. New research results have been adopted to address old business problems better as well as new problems which did not exist fifty years ago. In this closing session I will present my observations of Where we are heading with analytics.