Allocating revenues in a Smart TV ecosystem (2019). International Transactions Inoperational Research, 1-22.

Francisco López Navarrete (Miguel Hernández University of Elche), Joaquín Sánchez Soriano (Miguel Hernández University), and Óscar Martínez Bonastre (Miguel Hernández University of Elche).

Abstract. This paper deals with the problem of allocating the revenues generated by subscription fees, advertising, and pay-per-view in a Smart TV (STV) ecosystem between the provider of the Internet TV service and the content producers. The goal is to obtain a suitable mechanism for the allocation of the revenues such that all stakeholders agree with it. For this purpose, we define cooperative STV games that reflect the revenue generated by the STV system. We characterize the core of these games and obtain simple formulas for their Shapley and Tijs values, which we prove belonging to the core.

Keywords. revenue allocation; Smart TV; game theory; Shapley value

An approach to calmness of linear inequality systems from Farkas lemma (2019). Optimization Letters (Springer), 13, 295-307.

María Josefa Cánovas (Miguel Hernández University of Elche), N. Dinh (International University of Vietnam), D. H. Long (Tien Giang University) and Juan Parra (Miguel Hernández University of Elche).

Abstract. We deal with the feasible set mapping of linear inequality systems under right-hand side perturbations. From a version of Farkas lemma for difference of convex functions, we derive an operative relationship between calmness constants for this mapping at a nominal solution and associated neighborhoods where such constants work. We also provide illustrative examples where this approach allows us to compute the sharp Hoffman constant at the nominal system.

Keywords. Calmness; Hoffman constants; Local error bounds; Global error bounds; Feasible set mapping; Linear programming; Variational analysis

The measurement of revenue inefficiency over time: An additive perspective (2019). Omega, 83, 167-180.

Samah Jradi (Kedge Business School), Tatiana Bouzdine Chameeva (Kedge Business School) and Juan Aparicio (Miguel Hernández University of Elche).

Abstract. In this paper, we measure and decompose revenue inefficiency over time while accounting for all sources of technical inefficiencies. Our proposed decomposition exploits the dual relationship between the weighted additive distance function and revenue inefficiency in Aparicio et al. With the aid of the Luenberger indicator, we decompose this indicator into productivity change, and overall allocative change components. The importance of such decomposition is that it provides a complete picture of the sources of productivity change, thus obtaining a slack free allocative component. Finally, the model is ap- plied to the French wine sector to illustrate its practicality: we track how revenue inefficiency evolves in French wine regions over the 2004–2013 period, before and after the implementation of Common Market Organization policies in Europe in 2008.

Keywords. Data envelopment analysis; Revenue Luenberger-type indicator; Weighted additive distance function; French wine regions; Common market organization

DEA-based benchmarking for performance evaluation in pay-for-performance incentive plans (2018). Omega, 84, 45-54.

Wade D. Cook (York University of Toronto), Nuria Ramón (Miguel Hernández University of Elche), José Luis Ruiz (Miguel Hernández University of Elche), Inmaculada Sirvent (Miguel Hernández University of Elche) and Joe Zhu (Worcester Polytechnic Institute).

Abstract. Incentive plans involve payments for performance relative to some set of goals. In this paper, we extend Data Envelopment Analysis (DEA) to the evaluation of performance in the specific context of pay-for-performance incentive plans. The approach proposed ensures that the evaluation of performance of decision making units (DMUs) that follow the implementation of incentive plans, is made in terms of targets that are attainable, as well as representing best practices. A model is developed that adjusts the benchmarking to the goals through the corresponding payment of incentives, thus DEA targets are established taking into consideration the improvement strategies that were set out in the incentive plans. To illustrate, we examine an application concerned with the financing of public Spanish universities.

Keywords. Benchmarking; Target setting; Incentive plans; Goals; Data envelopment analysis

The probabilistic pickup-and-delivery travelling salesman problem (2019). Expert Systems with Applications, 121, 313-323.

Enrique Benavent (University of Valencia), Mercedes Landete (Miguel Hernández University of Elche), Juan José Salazar González (University of La Laguna) and Gregorio Tirado (Complutense University of Madrid).

Abstract. Transportation problems are essential in commercial logistics and have been widely studied in the litera- ture during the last decades. Many of them consist in designing routes for vehicles to move commodities between locations. This article approaches a pickup-and-delivery single-vehicle routing problem where there is susceptibility to uncertainty in customer requests. The probability distributions of the requests are assumed to be known, and the objective is to design an a priori route with minimum expected length. The problem has already been approached in the literature, but through a heuristic method. This article proposes the first exact approach to the problem. Two mathematical formulations are proposed: one is a compact model (i.e. defined by a polynomial number of variables and constraints); the other one contains an exponential number of inequalities and is solved within a branch-and-cut framework. Computational results show the upsides as well as the breakdowns of both formulations.

Keywords. Travelling Saleman; Pickup-and-delivery; Probabilistic TSP

A Parallel Application of Matheuristics in Data Envelopment Analysis (2019). Springer International Publishing AG, part of Springer Nature, 172–179.

Martín González (Miguel Hernández University of Elche), José Juan López Espín (Miguel Hernández University of Elche), Juan Aparicio (Miguel Hernández University of Elcheand Domingo Giménez (University of Murcia).

Abstract. Data Envelopment Analysis (DEA) is a non-parametric methodology for estimating technical efficiency and benchmarking. In general, it is desirable that DEA generates the efficient closest targets as benchmarks for each assessed unit. This may be achieved through the application of the Principle of Least Action. However, the mathematical models associated with this principle are based fundamentally on combinatorial NP-hard problems, difficult to be solved. For this reason, this paper uses a parallel matheuristic algorithm, where metaheuristics and exact methods work together to find optimal solutions. Several parallel schemes are used in the algorithm, being possible for them to be configured at different stages of the algorithm. The main intention is to divide the number of problems to be evaluated in equal groups, so that they are resolved in different threads. The DEA problems to be evaluated in this paper are independent of each other, an indispensable requirement for this algorithm. In addition, taking into account that the main algorithm uses exact methods to solve the mathematical problems, different optimization software has been evaluated to compare their performance when executed in parallel. The method is competitive with exact methods, obtaining fitness close to the optimum with low computational time.