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This research aims to design a bi-level optimization model for a supply chain that integrates decentralized quantitative and qualitative decisions at strategic and tactical levels. The manufacturer, as upper-level decision-maker, offers quantity discounts to encourage customers to order more quantity. At the lower level, customers tend to obtain economies of scale by aggregating their orders through cooperative purchasing. This is one of the first studies that investigate the model of customer expectations with the optimization model of manufacturers at the same time with real data from the supply chain in order to find the optimal solutions to the problem of the medical equipment supply chain in Iran. In addition, there have been no studies to date that consider quantitative discount strategies for the seller and customer behavior in a bi-level planning model simultaneously. The results and analyses reveal that the designed bi-level model compared to the one-level model for the customer and the manufacturer is more suited to the real world and will lead to a long-term relationship between the parties through customer participation. Research suggestions and directions for future research are also provided.

Nowadays the efficiency-o7666riented performance evaluation of complex systems be-comes increasingly important for investment and management decisions. This paper proposes a new formulation approach based on dynamic network DEA (DN–DEA) models for multi-period and multi-division (MPMD) systems to measure and decompose the overall efficiency. Although conventional DEA models provide magnificant modeling idea of efficiency measures in the multi-input and -output contexts, they do not account for the multi-division transformation process of decision-making units (DMUs) and present “black-box” measures of their efficiency scores wich causes incorrect estimates of the efficiency points of the units by ignoring the information about the internal operations of the system. As an illustrative case study, the present research applies the proposed approach to evaluate the efficiencies of 13 universities of Iran over the three-year period and the rate of innovation has been measured according to each division, every period, as well as total innovation.

Designing the business portfolio is a key decision in corporate-level strategy and is bonded with strategic concepts such as vertical integration and diversification. Nevertheless, most of the previous researches have proposed general conceptual models, or investment portfolio optimization models based on financial approach. In this paper, a mathematical model is proposed, firstly to utilize quantitative methods in strategic decision makings and secondly, to considers non-financial, strategic variables in modeling process. To address this need, a mathematical framework for formulating synergies between businesses in a value chain is developed. Although the conceptual structure is applicable for different industries, the model is developed for a multi-business company in petroleum industry of Iran and is solved by genetic algorithm.

In the selection of a collection of investment assets, the expected utility of investor is determined via risk and return criteria. Regarding the uncertainty of the investor about the future, portfolio diversification is a common path towards risk reduction in investment problem. In this study, not only the Euclidean Distance Criterion (EDI) was introduced to be a measure of portfolio diversification, but also a multi-objective model was designed for portfolio selection. This model intended to maximize the return and diversification of portfolio, and also to minimize non-systematic risk of it. Since this is a non-linear model and in terms of complexity is among "NP-hard", regarding the computational efficiency of the Genetic Algorithms (GA) in optimization, it was used for solving the model. Results from the implementation of the dual-objective model (return and diversification) and triple-objective model (return, diversification, and non-systematic risk) with multiple-repetition showed that the average return of the portfolio selected by perposed model was higher than the favorable level. Investigation into portfolio performance indices indicates the efficiency of the dual-objective model (return and diversification).