A nonlinear state marginal price vector model for the task of business valuation. A case study: The dimensioning of IT-service companies under nonlinear synergy effects Abstract In the present contribution we present a nonlinear extension of the innovative linear investment-oriented company valuation method and so-called state marginal price vector model of Toll which represents a two-step procedure separated into a base and a valuation approach. As novel aspect we address nonlinear synergy effects in M&A’s. For this purpose we introduce a nonlinear framework within a semi-discrete convex optimization approach. As capital market assumption we simulate an imperfect market. To demonstrate the usefulness of the method, we address a case study of a merger of two IT-service companies. The related valuation and dimensioning of capacities is done by solving a multi-period newsvendor model under stochastic demand. The demonstrated nonlinear framework is shown to be suitable for a wide range of business valuation tasks.

Interval-valued n-person cooperative games with satisfactory degree constraints Abstract The aim of this study is to develop several nonlinear programming models for interval-valued cooperative games in which taking into account the decision makers’ risk attitudes. First, we investigate several existing used satisfactory degree comparison methods for ranking interval-valued fuzzy numbers, and point out by an example that the method proposed by Liu et al. (Soft Comput 22:2557–2565, 2018) is more efficient than the method proposed by Hong and Li (Oper Res 17:1–19, 2016). Second, by taking into account decision makers’ risk attitudes, several corresponding nonlinear programming models are constructed based on satisfactory degree formulas that were proposed by Liu et al. (2018). Third, an illustrative example in conjunction with comparative analyses are employed to demonstrate the validity and applicability of the proposed models. Finally, to further highlight the validity of the proposed method, we discuss the relationship of the satisfactory degree formulas between Hong and Li (2016)’s method and Xu and Da (J Syst Eng 18:67–70, 2003)’s method.

On the efficiency of local electricity markets under decentralized and centralized designs: a multi-leader Stackelberg game analysis Abstract In this paper, we analytically compare centralized and decentralized market designs involving a national and local market operators, strategic generators having market power and bidding sequentially in local markets, to determine which design is more efficient for the procurement of energy. In the centralized design, used as benchmark, the national market operator optimizes the exchanges between local markets and the generators’ block bids. In the decentralized design, generators act as Stackelberg leaders, anticipating the local market prices and the flows on the transmission lines. Clearing of the local markets can be either simultaneous or sequential. The resulting two-stage game with competitive leaders that are not price takers is formulated as a bilevel mathematical programming problem which is reformulated as a Nash–Cournot game, and conditions for existence and uniqueness of market equilibrium are studied. Imperfect information is also considered, resulting from the lack of incentives from the generators to share their RES-based generations. Through a case study, we determine that the decentralized design is as efficient as the centralized one with high share of renewables, using as performance measure the price of anarchy, and that imperfect information has a limited impact on the efficiency of the decentralized market design. Furthermore, we check numerically that there exists an upper-limit on the block bid length maximizing the social welfare under both centralized and decentralized designs.

An integrated data envelopment analysis and mixed integer non-linear programming model for linearizing the common set of weights Abstract The problem of ranking efficient decision making units (DMUs) is of interest from both theoretical and practical points of view. In this paper, we propose an integrated data envelopment analysis and mixed integer non-linear programming (MINLP) model to find the most efficient DMU using a common set of weights. We linearize the MINLP model to an equivalent mixed integer linear programming (MILP) model by eliminating the non-linear constraints in which the products of variables are incorporated. The formulated MILP model is simpler and computationally more efficient. In addition, we introduce a model for finding the value of epsilon, since the improper choice of the non-Archimedean epsilon may result in infeasible conditions. We use a real-life facility layout problem to demonstrate the applicability and exhibit the efficacy of the proposed model.

The network data envelopment analysis models for non-homogenous decision making units based on the sun network structure Abstract This paper seeks to propose a network data envelopment analysis (DEA) framework for analysis of heterogeneous systems. The paper introduces the dummy connector so that every network structure can be transformed into the sun network structure. In his case, the dummy connector allows for heterogeneity of the decision making units (DMUs) in terms of their inner structure. Based on the sun network structure, the static and dynamic network DEA models are established. Thus, DMUs with different structures can be evaluated according to the static and dynamic network DEA models. The efficiency of each sub-unit, each period and each sub-unit in each period can also be obtained. Two simulated examples are presented using the static and dynamic DEA models.

Long-term load forecasting: models based on MARS, ANN and LR methods Abstract Electric energy plays an irreplaceable role in nearly every person’s life on earth; it has become an important subject in operational research. Day by day, electrical load demand grows rapidly with increasing population and developing technology such as smart grids, electric cars, and renewable energy production. Governments in deregulated economies make investments and operating plans of electric utilities according to mid- and long-term load forecasting results. For governments, load forecasting is a vitally important process including sales, marketing, planning, and manufacturing divisions of every industry. In this paper, we suggest three models based on multivariate adaptive regression splines (MARS), artificial neural network (ANN) and linear regression (LR) methods to model electrical load overall in the Turkish electricity distribution network, and this not only by long-term but also mid- and short-term load forecasting. These models predict the relationship between load demand and several environmental variables: wind, humidity, load-of-day type of the year (holiday, summer, week day, etc.) and temperature data. By comparison of these models, we show that MARS model gives more accurate and stable results than ANN and LR models.

Regional patterns in technological progress of Poland: the role of EU structural funds Abstract To the best of our knowledge, this paper is one of the first studies to analyze the evolution and determinants of regional patterns in the technological progress of one of the new EU members in transition—Poland. The results of the first part of the study prove that, after EU accession, the central region was the only part of Poland that not only reported a rapid rise in labor productivity but also managed to constantly increase its capital productivity. In the second part of the empirical analysis, we conduct a formal econometric analysis aimed at testing whether these differences in regional patterns in the technological progress of Poland could be caused by the inflow of EU structural funds.

Hurwicz’s criterion and the equilibria of duopoly models Abstract In this paper we investigate a model of duopolistic competition in an uncertain environment where the attitudes of the firms towards uncertainty are incorporated. In particular, we analyze an extension of a Cournot duopoly in which the firms face a different market demand in each of two scenarios, and make their output decisions before uncertainty is resolved. The way in which firms value the possible outcomes is critical when deciding their strategies. In real-life situations the attitudes that agents exhibit can vary from extreme pessimism to extreme optimism, and it is possible to characterize their behavior according to their degrees of optimism. In this context, we identify the sets of equilibria for the full range of degrees of optimism, and illustrate the results with the analysis of some cases in which the demand functions are linear.

Sensitivity in DEA: an algorithmic approach Abstract This paper considers an algorithmic approach to sensitivity in Data Envelopment Analysis for the CCR and Additive models. Specifically, it gives sufficient conditions that preserve the efficiency of a decision-making unit (DMU) under arbitrary perturbations of the inputs and/or outputs of the DMUs. The paper illustrates the results for the Additive model.

Robust optimization for the vehicle routing problem with multiple deliverymen Abstract This paper addresses the vehicle routing problem with time windows and multiple deliverymen in which the customer demands are uncertain and belong to a predetermined polytope. In addition to the routing decisions, this problem attempts to define the number of deliverymen used to service to the customers on each route. A new mathematical formulation is presented for the deterministic counterpart based on auxiliary variables that define the assignment of customers to routes. Building on this formulation, we apply a static robust optimization approach to obtain a robust counterpart formulation that captures the random nature of customer demand. Due to the difficulty in solving this formulation, we propose a constructive heuristic to generate a robust solution, which is used as a starting point for solving the robust counterpart formulation. The heuristic is an extension of Solomon’s heuristic I1. Computational results using problem instances from the literature and risk analysis via Monte-Carlo simulation indicate the potential of static robust optimization to address the trade-off between cost and risk. The results also reveal that the proposed approach provides good results even without exact knowledge of some probabilistic measure of the customer demand.