In this paper we present a method of pricing catastrophe bonds (cat bonds) using stochastic programming. Stochastic programming is a method ubiquitous in operations research when decision problems involve uncertainty. We demonstrate the method for pricing cat bonds which bypasses the need to define the equivalent martingale measure or estimate the market price of risk. The price of the cat bond is simply the coupon that needs to be paid that attains a specified return on investment given a set of constraints that define the payoffs.

In this paper we apply robust optimization techniques to the shift generation problem in workforce planning. At the time that the shifts are generated, there is often much uncertainty in the workload predictions. We propose a model to generate shifts that are robust against this uncertainty. An adversarial approach is used to solve the resulting robust optimization model. In each iteration an integer nonlinear knapsack problem is solved to calculate the worst case workload scenario. We apply the approach to generate shifts in a real-life Air Traffic Controller workforce planning problem. The numerical results show the value of our approach.

The customer lifetime value (CLV) is an important concept increasingly considered in the field of general marketing and in the management of firms, of organizations to increase the captured profitability. It represents the total value that a customer produces during his or her lifetime, or better represents the measure of the potential profit generating by a customer. The companies use the customer lifetime value to segment customers, analyze probability of churn, allocate resources or formulate strategies and, therefore, they increasingly derive revenue from the creation and from sustenance of long-term relationships with their customers. For this reason, the customer lifetime value is increasingly considered a touchstone for the management of customer relationships. In this article, the authors deepen the concept and use of customer lifetime value and present some mathematical models for its determination. There is many models for this purpose but most of them are theoretic, complex and not applicable. Though not exhaustive, the major contribution of this paper is that it provides a general mathematical formulation to estimate the CLV and that it has a context less specific compared to papers, present in literature, on the customer lifetime.

In this paper, we develop a stochastic programming model for economic dispatch of a power system with operational reliability and risk control constraints. By defining a severity-index function, we propose to use conditional value-at-risk (CVaR) for measuring the reliability and risk control of the system. The economic dispatch is subsequently formulated as a stochastic program with CVaR constraint. To solve the stochastic optimization model, we propose a penalized sample average approximation (SAA) scheme which incorporates specific features of smoothing technique and level function method. Under some moderate conditions, we demonstrate that with probability approaching to 1 at an exponential rate with the increase of sample size, the optimal solution of the smoothing SAA problem converges to its true counterpart. Numerical tests have been carried out for a standard IEEE-30 DC power system.

We consider optimal decision-making problems in an uncertain environment. In particular, we consider the case in which the distribution of the input is unknown, yet there is abundant historical data drawn from the distribution. In this paper, we propose a new type of distributionally robust optimization model called the likelihood robust optimization (LRO) model for this class of problems. In contrast to previous work on distributionally robust optimization that focuses on certain parameters (e.g., mean, variance, etc.) of the input distribution, we exploit the historical data and define the accessible distribution set to contain only those distributions that make the observed data achieve a certain level of likelihood. Then we formulate the targeting problem as one of optimizing the expected value of the objective function under the worst-case distribution in that set. Our model avoids the over-conservativeness of some prior robust approaches by ruling out unrealistic distributions while maintaining robustness of the solution for any statistically likely outcomes. We present statistical analyses of our model using Bayesian statistics and empirical likelihood theory. Specifically, we prove the asymptotic behavior of our distribution set and establish the relationship between our model and other distributionally robust models. To test the performance of our model, we apply it to the newsvendor problem and the portfolio selection problem. The test results show that the solutions of our model indeed have desirable performance.

In this paper, we introduce a class of (weak) composite vector variational-like inequality problems and establish its relationship with composite vector optimization problem. We also prove the relation of a vector critical point in composite vector optimization problem with its weak efficient point, under the assumption of composite pseudo invexity. Using KKM Lemma, we derive result for existence of solutions of composite vector variational-like inequality problem. Furthermore, we define a gap function for the composite vector variational-like inequality problem and finally, as an application, we study a system of composite vector optimization problems and system of vector variational-like inequality problems, whose solutions imply the solution of Nash equilibrium problem. Examples are provided to illustrate the derived results.

This paper considers model uncertainty for multistage stochastic programs. The data and information structure of the baseline model is a tree, on which the decision problem is defined. We consider “ambiguity neighborhoods” around this tree as alternative models which are close to the baseline model. Closeness is defined in terms of a distance for probability trees, called the nested distance. This distance is appropriate for scenario models of multistage stochastic optimization problems as was demonstrated in Pflug and Pichler (SIAM J Optim 22:1–23, 2012). The ambiguity model is formulated as a minimax problem, where the the optimal decision is to be found, which minimizes the maximal objective function within the ambiguity set. We give a setup for studying saddle point properties of the minimax problem. Moreover, we present solution algorithms for finding the minimax decisions at least asymptotically. As an example, we consider a multiperiod stochastic production/inventory control problem with weekly ordering. The stochastic scenario process is given by the random demands for two products. We determine the minimax solution and identify the worst trees within the ambiguity set. It turns out that the probability weights of the worst case trees are concentrated on few very bad scenarios.

Wright’s learning curve (WLC) assumes every unit of production has an acceptable level of quality, which is not the case in many production environments. Many studies reported that a production process may go out-of-control therefore generating defective items requiring rework. Jaber and Guiffrida (Int J Prod Econ 127(1):27–38, 2004) have modified the WLC by accounting for rework time. In a later study, Jaber and Guiffrida (Eur J Oper Res 189(1):93–104, 2008) allowed for production interruption to restore the quality of the production process to reduce the number of defective items per lot. Although these works were the first analytical models that linked learning to quality, their results cannot be generalized as they considered a single (first) production cycle. This assumption ignores the transfer of learning that occurs between cycles in intermittent production environments. This paper addresses this limitation and considers the knowledge transferred to deteriorate because of forgetting. The results indicate that the performance function of the process has a convex form under certain conditions. The performance of the system improves with faster learning in production and rework, frequent process restorations, and transfer of learning between cycles.