Applications – OR and Management Sciences

Sparse/Robust Estimation and Kalman Smoothing with Nonsmooth Log-Concave Densities: Modeling, Computation, and Theory

Categories Applications - OR and Management Sciences, Applications - Science and Engineering, Convex and Nonsmooth Optimization

Piecewise linear quadratic (PLQ) penalties play a crucial role in many applications, including machine learning, robust statistical inference, sparsity promotion, and inverse problems such as Kalman smoothing. Well known examples of PLQ penalties include the l2, Huber, l1 and Vapnik losses. This paper builds on a dual representation for PLQ penalties known from convex analysis. … Read more

Competitive location in networks with threshold-sensitive customer behaviour

Categories Applications - OR and Management Sciences Tags , , , , ,

We consider the (r|X_p)-medianoid problem in networks. Goods are assumed to be essential and the only decision criterion is the travel distance. The portion of demand captured by the competitors is modelled by a general capture function which includes the binary, partially binary and proportional customer choice rules as specific cases. We prove that, under … Read more

Asymptotic Analysis of Sample Average Approximation for Stochastic Optimization Problems with Joint Chance Constraints via CVaR/DC Approximations

Categories Applications - OR and Management Sciences, Stochastic Programming Tags , , , , ,

Conditional Value at Risk (CVaR) has been recently used to approximate a chance constraint. In this paper, we study the convergence of stationary points when sample average approximation (SAA) method is applied to a CVaR approximated joint chance constrained stochastic minimization problem. Specifically, we prove, under some moderate conditions, that optimal solutions and stationary points … Read more

Exact Penalization, Level Function Method and Modified Cutting-Plane Method for Stochastic Programs with Second Order Stochastic Dominance Constraints

Categories Finance and Economics, Stochastic Programming Tags , , ,

Level function methods and cutting plane methods have been recently proposed to solve stochastic programs with stochastic second order dominance (SSD) constraints. A level function method requires an exact penalization setup because it can only be applied to the objective function, not the constraints. Slater constraint qualification (SCQ) is often needed for deriving exact penalization. … Read more

Strongly Polynomial Primal-Dual Algorithms for Concave Cost Combinatorial Optimization Problems

Categories Combinatorial Optimization, Supply Chain Management

We introduce an algorithm design technique for a class of combinatorial optimization problems with concave costs. This technique yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists for the fixed-charge counterpart of the problem. For many practical concave cost problems, the fixed-charge counterpart is a well-studied combinatorial optimization … Read more

Improved Load Plan Design Through Integer Programming Based Local Search

Categories (Mixed) Integer Linear Programming, Transportation Tags , ,

We present integer programming models of the service network design problem faced by less-than-truckload (LTL) freight transportation carriers, and a solution approach for the large-scale instances that result in practical applications. To accurately represent freight consolidation opportunities, the models use a fine discretization of time. Furthermore, the models simultaneously route freight and empty trailers, and … Read more

A Constructive Proof of the Existence of a Utility in Revealed Preference Theory

Categories Approximation Algorithms, Finance and Economics, Generalized Convexity/Monoticity Tags , ,

Within the context of the standard model of rationality within economic modelling we show the existence of a utility function that rationalises a demand correspondence, hence completely characterizes the associated preference structure, by taking a dense demand sample. This resolves the problem of revealed preferences under some very mild assumptions on the demand correspondence which … Read more

Layered Formulation for the Robust Vehicle Routing Problem with Time Windows

Categories Integer Programming, Robust Optimization, Transportation Tags , , , ,

This paper studies the vehicle routing problem with time windows where travel times are uncertain and belong to a predetermined polytope. The objective of the problem is to find a set of routes that services all nodes of the graph and that are feasible for all values of the travel times in the uncertainty polytope. … Read more

Large Neighborhood Search for LNG Inventory Routing

Categories Transportation

Liquefied Natural Gas (LNG) is steadily becoming a common mode for commercializing natural gas. Due to the capital intensive nature of LNG projects, the optimal design of LNG supply chains is extremely important from a profitability perspective. Motivated by the need for a model that can assist in the design analysis of LNG supply chains, … Read more

Solving multi-stage stochastic mixed integer linear programs by the dual dynamic programming approach

Categories Applications - OR and Management Sciences, Cutting Plane Approaches, Stochastic Programming

We consider a model of medium-term commodity contracts management. Randomness takes place only in the prices on which the commodities are exchanged, whilst state variable is multi-dimensional, and decision variable is integer. In our previous article, we proposed an algorithm based on the quantization of random process and a dual dynamic programming type approach to … Read more