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This paper introduces the concept of entropic value-at-risk (EVaR), a new coherent risk measure that corresponds to the tightest possible upper bound obtained from the Chernoff inequality for the value-at-risk (VaR) as well as the conditional value-at-risk (CVaR). We show that a broad class of stochastic optimization problems that are computationally intractable with the CVaR is efficiently solvable when the EVaR is incorporated. We also prove that if two distributions have the same EVaR at all confidence levels, then they are identical at all points. The dual representation of the EVaR is closely related to the Kullback-Leibler divergence, also known as the relative entropy. Inspired by this dual representation, we define a large class of coherent risk measures, called g-entropic risk measures. The new class includes both the CVaR and the EVaR.

In this paper, we investigate the coordination of cooperative advertising decisions in a supply chain with one manufacturer and one retailer. The manufacturer and the retailer invest in national and local advertising, respectively. The manufacturer also agrees to share part of the total local-advertising costs with the retailer. The model is analyzed using game theory. We also compare the results of our analysis with similar results from the literature developed for cooperative advertising.

This paper deals with permutation flowshops with considering transportation times of carrying semi-finished jobs from a machine to another one. The transportation between machines can be done using two types of transportation systems: multi-transporter and single-transporter systems. We formulate the problem with both systems as six different mixed integer linear programs. We also provide solution methods including heuristics and metaheuristics in order to solve large-sized problems. The heuristics are the adaptations of well-known heuristics and the proposed metaheuristics are based on artificial immune systems incorporating an effective local search heuristic and simulated annealing. A comprehensive experiment is conducted to compare and evaluate the performance of the models as well as the algorithms. All the results show the effectiveness of the proposed models and algorithms.

This short addendum consists of two sections. The first provides proofs that were omitted in Ahmadi-Javid (J. Optim. Theory Appl., 2012 ) for the sake of brevity, and also demonstrates that the dual representation of the entropic value-at-risk, which is given in Ahmadi-Javid (J. Optim. Theory Appl., 2012 ) for the case of bounded random variables, holds for all random variables whose moment-generating functions exist everywhere. The second section provides a few corrections.

In this paper, we present a distribution network design problem in a supply chain system that minimises the total cost of location, inventory, and delivery delay. Customers' demands are random, and multiple capacity levels are available for the distribution centers. The problem is first formulated as a mixed integer convex programming model to optimally solve medium-sized instances, and then a heuristic is developed for solving large-sized instances. [PUBLICATION ABSTRACT]

This paper presents a model to study quality management in a supply chain system with one manufacturer and one retailer. The manufacturer invests in production quality, and the retailer compensates to improve service quality. The model is analysed using game theory. [PUBLICATION ABSTRACT]

This paper studies a new continuous single facility location problem. In this problem the locations of the customers (or the previously located facilities) vary, randomly, and the objective is to locate a new facility so as to maximise the mean service level considered to be the mean number of the customers whose distances from the new facility are smaller than a predefined desirable distance. The problem is formulated, and then an approximate solution method is presented to solve the problem. Also, we apply our results to locate the capital of Iran as a case study. [PUBLICATION ABSTRACT]

ENGLISH ABSTRACT: In this paper, we present a distribution network design problem in a supply chain system that minimises the total cost of location, inventory, and delivery delay. Customers’ demands are random, and multiple capacity levels are available for the distribution centers. The problem is first formulated as a mixed integer convex programming model to optimally solve medium-sized instances, and then a heuristic is developed for solving large-sized instances. AFRIKAANSE OPSOMMING: In hierdie artikel word ‘n distribusienetwerkprobleem in ‘n voorsieningsketting voorgehou waar die totale koste van die ligging, voorraad en afleweringsvertragings geminimiseer word. Die vraag is lukraak en verskeie kapasiteitsvlakke is beskikbaar in die verspreidingsentra. Die problem word eers geformuleer as ‘n gemengde-heeltal-konvekse model sodat mediumgrootte gevalle geoptimiseer kan word, waarna ‘n heuristieke benadering ontwikkel word vir die oplos van grootskaalse aktiwiteite.

ENGLISH ABSTRACT: This paper presents a model to study quality management in a supply chain system with one manufacturer and one retailer. The manufacturer invests in production quality, and the retailer compensates to improve service quality. The model is analysed using game theory. AFRIKAANSE OPSOMMING: ’n Toevoerketting waar gehaltebestuur aangewend word deur ’n enkele vervaardiger en ’n enkele verbruiker word gemodelleer via die spelteorie. Die vervaardiger en die verbruiker neem deel aan besluitneming oor optimum befondsing van die bestuursaksies.

Memory-type statistical control charts, such as exponentially weighted moving average (EWMA) and cumulative sum (CUSUM), are broadly-used statistical feedback policies for detecting small quality changes in univariate and multivariate processes. Many papers on economic-statistical design of these control charts used the general formula proposed by Lorenzen and Vance (Technometrics 28(1):3–10, 1986) as a semi-closed-form expression of the long-run average quality cost. Contrary to popular opinion, this paper argues that this old formula is not correct for memory-type control charts and shows how the formula can be corrected by using concepts such as conditional average run lengths (ARLs), mean of ARLs (MARL), and average number of false alarms (ANFA). The paper also proposes a simulation method as an alternative to directly estimate the cost function, which can be easily adapted for nonstandard assumptions. The results for the EWMA, multivariate EWMA, and CUSUM control charts indicate that the correct computation of the objective function results in significantly different optimal designs, which implies that the old formula is not an acceptable approximation for memory-type control charts. A numerical study is also conducted to compare the numerical efficiency and stability of the simulation method and the computational procedure based on the corrected formula. The required codes are provided.