Efficient Frontier Analysis Research Articles

Power generation mix in Colombia including wind power: Markowitz portfolio efficient frontier analysis with machine learning

The Colombian power market is hydro-dominated since 67 % of the power produced comes from hydro-power sources. In addition, it has thermal power from natural gas and coal, and in the last years, alternative energy sources such as wind and solar have been introduced, although so far their share is not significant. Due to this condition, the Colombian power market is very volatile and depends on weather conditions. Usually, in rainy seasons prices are low and power is available, while in dry seasons, prices are high and power can be scarce. One of the main advantages of the new energy sources is that they are complementary to hydro-power, in the case of wind regimes, they are higher during dry seasons and lower during rainy seasons. We propose a complementarity analysis in the energy mix using Markowitz Portfolio analysis to determine if the efficient frontier is improved by introducing wind power to the system and the traditional port-folio analysis is improved by introducing Machine Learning (ML) into calculations. Results show that wind power improves the return while minimizing risk. Therefore, wind power would significantly reduce prices in Colombia's power mix while reducing volatility. This work follows the Open Innovation (OI) paradigm, the intersection of Machine Learning, portfolio optimization, and renewable energy presents a promising landscape for research and practical applications. Continued interdisciplinary collaboration and innovation are essential for harnessing the full potential of these technologies for a sustainable energy future.

Portfolio Optimization Strategies for the Common Investor

Abstract: Financial Analytics is a key field to making investment decisions and has been developed only recently. It involves analytical thinking, computational knowledge and creative thinking about investment strategies. There are many ways to invest money. Some people invest them in Gold, some in real estate, some create a fixed deposit, some in the stock market. Some people diversify their money into different sectors of the market and invest to get an optimal profit by understanding the market. This kind of investment is called portfolio management. Unlike gambling, understanding of the portfolio and its management can actively minimize the risks associated with investment. In the proposed research we tried to study the different strategies of investing in the different sectors and building a portfolio, with the express aim of creating optimal diversified portfolios. Our methods include optimizing the weights of different investment instruments in different sectors, with implementations carried out in Python and using time-series Python libraries. We have focussed on three different investment strategies in particular: (1) Genetic algorithms help us to divide the portfolio (chromosome) into the genes (sectors) and understand it in a better way. Exploiting the existing algorithms for optimizing fitness functions in genetic algorithms, we have implemented one strategy for optimizing portfolios; (2) Efficient frontier analysis from Markowitz theory helps in investing and creating our own portfolio. We developed some of the strategies that help in displaying portfolio allocation and efficient frontier graphs; (3) We have also implemented a new criterion in vogue in the financial markets today, the “Kelly Criterion” preferred by many investors all over the world. We used real time financial stock data to validate and test our functions. All the strategies developed are modular and we also show a proof-of-concept web interface for one of the developed strategies. It is hoped that our work enables investors in making better decisions about where to park their money and converting their wealth into high-yield portfolios.

The Diversification Benefits of Foreign Real Estate: Evidence from 40 Years of Data

We investigate the potential of global real estate to improve the long-term performance of a US equity portfolio, utilizing a recent dataset of 40 years’ worth of US stocks, US real estate, 13 foreign stock markets, and 13 foreign real estate markets across diverse regions. Despite a modest performance in terms of risk and return, foreign real estate has consistently lower correlations with US stocks compared to foreign equities. Rolling correlation analysis indicates that foreign real estate markets remain relatively segmented compared to foreign equity, despite increasing financial market correlations over time. Efficient frontier analysis demonstrates that portfolios including foreign real estate consistently outperform those limited to US stocks and US real estate or those including foreign stocks, indicating the importance of foreign real estate in optimizing portfolio performance. Subperiod analysis reveals that foreign real estate retains its diversification benefits even in the latter, more integrated period. Our results are robust when using Conditional Value-at-Risk as a measure of risk. Overall, our findings highlight the persistent diversification benefits and superior risk-adjusted returns from incorporating foreign real estate into US equity portfolios.

Enhancing Portfolio Allocation by LSTM Model

Accurate forecasting of stock prices and the construction of optimized portfolios are essential for investors in the dynamic technology sector. This paper proposes a comprehensive approach that combines Long Short-Term Memory (LSTM) models with portfolio construction techniques specifically tailored to the stocks of Apple Inc. (AAPL), Meta Platforms Inc. (META), Amazon.com Inc. (AMZN), Microsoft Corporation (MSFT), and NVIDIA Corporation (NVDA) from January 1st ,2018 to May 31st, 2023. By leveraging the sequential nature of historical stock price data(80% of data), LSTM models capture complex patterns and dependencies, enabling more precise predictions of Adjusted Close (Adj Close) prices. Subsequently, the forecasted prices (20% of data)are utilized to construct optimized portfolios that maximize returns and minimize risks within the technology sector using Monte Carlo simulations, efficient frontier analysis, and key risk-return metrics. The overall result of the prediction data is similar to the actual data which implies that the integration of LSTM-based forecasting and portfolio construction provides a robust framework for informed investment decision-making and risk management. And the application of Monte Carlo simulations, efficient frontier analysis, and key risk-return metrics gave us two portfolio allocation options : Minimum Variance model (40% of AAPL,60% of MSFT) and Maximum Sharpe Ratio model ( 47% of META, 53% of NVDA). The evaluation of the two portfolios show that the strategy can significantly beat the SP500 index.

Selection of Appropriate Portfolio Optimization Strategy

Portfolio optimization is a critical task in financial management, aiming to maximize expected returns while minimizing risk. This study compares the performance of Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Dynamic Programming (DP), and Differential Evolutionary Algorithm (DEA) in optimizing portfolios in the NIFTY 50 market. Using daily stock data from March 2023 to May 2023, we evaluate the algorithms based on performance metrics including the Sharpe ratio, expected return, volatility and Sortino ratio. Then an integrated multi-criteria decision making (MCDM) framework of Logarithmic Percentage Change-driven Objective Weighting (LOPCOW) and Compromise Ranking of Alternatives from Distance to Ideal Solution (CRADIS) methods has been used to compare the evolutionary algorithms for portfolio optimization. The results show that PSO outperforms the other algorithms in terms of Sharpe Ratio and Expected Return, while DEA exhibits the lowest portfolio risk. Furthermore, the efficient frontier analysis confirms PSO's ability to generate portfolios with higher expected returns at the same risk level. This research highlights the effectiveness of optimization algorithms in portfolio management and provides valuable insights for investors and portfolio managers in maximizing returns and managing risks.

Investable Real Estate Allocations in a Mixed Asset Portfolio; Both Long Term and During Different Cycles

The NCREIF Property Index (NPI) data starts in 1978 and has been used as a benchmark index for over 45 years. In 2006 NCREIF created the NCREIF Open-End Diversified Core Equity Index (ODCE) and used historic fund level data to create performance data back to 1978. ODCE was the first “investable index ” in direct real estate for institutional investors, family offices, and high net worth investors who can meet these direct funds’ minimum investment levels (typically $5 million). Individual investors with less money can also access ODCE returns through Interval Funds or “Fund-of-Funds” that invest in and are designed to track or beat the ODCE Index. Since 2009 general partners of funds are required to update their net asset value (NAV) to “fair market value” on a quarterly basis as a result of Topic 820 of the Financial Accounting Standards Board. Both ODCE funds and interval funds have improved their liquidity with either monthly or quarterly redemption options, making them more competitive (from a liquidity aspect) with publicly traded securities. We analyze portfolio allocations over 45 years – the longest time frame ever studied and over 6 NEBR economic cycles and 4 ODCE real estate return cycles using Markowitz efficient frontier analysis. We inspect up-cycle and down-cycle periods separately and add to the literature by analyzing the ¼, ½, and ¾ points (low, medium, and high risk/return points) along the Markowitz efficient frontier. Our findings support many of the 45 studies published, but conflict with some depending upon their study methodology and time frame (9 to 25 years) studied. We conclude that real estate would have improved historic risk adjusted returns in many cycle periods.

Decision Support Model for Allocating Maintenance Budgets for Bridges

This paper introduces a newly developed decision support model for allocating a budget for bridge maintenance. The model is built based on capturing the experts’ knowledge for the prioritization of criteria for selecting a bridge maintenance plan. A literature review and interviews with a group of nine local experts were carried out to identify the criteria for bridge prioritization for maintenance. A questionnaire survey was then designed and administered, utilizing multi-criteria decision-making techniques through face-to-face meetings with local bridge maintenance managers to determine the weights of the identified criteria and develop the utility curves for each criterion. The developed model consists of four major modules: (1) bridge ranking module; (2) prioritization module of bridge structural elements; (3) optimization-based simulation module; and (4) the outputs module. The model was validated in a hypothetical network of four bridges. The validation reveals that the model can assist bridge maintenance managers in setting a bridge maintenance plan, with a high level of confidence using efficient frontier analysis technique. Utilizing frontier analysis enables comparisons of mean costs of different bridge maintenance plans against different levels of risk to enable decision-makers to make informed decisions. The result of this study indicated that bridge structural condition was the most important criterion amongst all the criteria influencing the decision of bridge prioritization for maintenance, followed by traffic and bridge location. Moreover, bridge deck and parapet, followed by bearing pads, were found to be the most important of the bridge’s structural elements.

An integrated decision support framework for selecting envelope and AC systems in hot-humid climate

This paper aims to introduce a framework that applies life cycle cost (LCC)-based optimization, life cycle assessment (LCA) and multi-criteria decision-making (MCDM) methods for the selection of optimum envelope materials and AC systems for housing projects. A total of 37 selection criteria and 28 material alternatives were first identified through a comprehensive literature review and interviews with local experts. “DesignBuilder”, a computer simulation software, was used to conduct the LCC-based optimization and LCA for the identified alternatives. Furthermore, uncertainties and risk associated with the selected alternatives were computed using Monte Carlo simulation via the Crystal Ball software and Efficient Frontier analysis via the Excel Spreadsheets. The identified selection criteria were then prioritized and assigned with utility scores based on the analytical hierarchy process (AHP) and multi-attribute utility theory (MAUT) methods. Seven scenarios with different objectives were set for an existing case study. The implementation of the framework showed that when taken into account the application of multi-criteria methods, the highest saving combination of materials is selected by the framework. The validation process was carried out through conducting interviews with local experts based on the results obtained from real case project. The experts agreed that the proposed framework can be beneficial to the industry as it takes into consideration not only quantitative criteria, but also qualitative criteria that are important to owners and designers.

Planning Efficiency Assessments of Street Houses considering the Tradeoffs of Multi-Objective Optimization Problems and Architect’s Planning Preferences

一般而言，建築師於規劃設計建築物時，經常將建築物之機能、安全、經濟及美觀列為四項重要規劃目標。但這些目標彼此之間常產生衝突，造成建築師規劃設計建築物時的無所適從，如何權衡這些衝突目標即為多目標最佳化問題。此外，目前的建築物規劃效率評估方法，大部份僅客觀地評估建築物單一目標的效率，較少考量建築師的主觀規劃偏好，無法反應建築物規劃設計具有主客觀因素的本質，如何發展兼顧主客觀因素的規劃效率評估方法，乃成為一個值得研究的課題。據營建署2015年住宅調查資料統計，街屋約占住宅類型中49.20%之比例，本論文即以此重要的建築型態為研究對象，探討建築師於規劃設計階段時，如何有效解決多目標最佳化問題。所採用的研究方法包含:模糊理論、無異曲線、效率前緣以及資料包絡分析法。模糊理論可發展建築師的偏好函數;無異曲線可定義建築師的規劃偏好及權重;效率前緣理論則可以從街屋案例中，以資料包絡分析法求出較有效率的一群案例，此群案例可建構出街屋之效率前緣曲線，做為建築師評估街屋規劃效率的依據。本論文即以上述理論，發展新的規劃效率評估方法。並以台灣地區的街屋為實證案例，以詮釋所發展的方法論。從研究結果中可得知，本論文所發展的方法論，可適切解決建築物多目標最佳化及建築師規劃偏好之問題。研究成果可提供建築師使用，所發展的研究方法亦可供學術界後續研究的參考。Generally speaking, architects often regard the function, safety, economy and aesthetics of the buildings as four important targets. However, these planning targets usually conflict with each other, which often confuses architects when planning buildings. How to trade off these conflicting targets is a multi-objective optimization problem (MOOP). Besides, most of the current building efficiency assessment methods only objectively evaluate the single target of building efficiency, but seldom consider the subjective planning factors of architects. How to develop a planning efficiency evaluation method that integrates subjective and objective factors has become a topic worthy of exploration. According to the statistics of the 2015 housing survey of Construction and Planning Agency, street houses occupied 49.20% of the housing types. This paper takes this important building type as the research object to study how architects can effectively solve the MOOP during the planning and design stage. The research methods include: fuzzy theory, indifference curve, efficient frontier and data envelopment analysis. Through the principles of fuzzy theory, the architect’s preference function can be developed. With the help of indifference curve, the planning preferences and weights of architects can be defined. The efficient frontier theory is used to find the optimal efficient cases from the street houses via data envelopment analysis. The efficient frontier curve of street houses can be constructed by this group of cases, and can be used as a basis for architects when evaluating the planning efficiencies of the street houses. This paper developed a new planning efficiency assessment method based on the above theories, taking the street houses in Taiwan as empirical cases to interpret the developed methodologies. The research results show that the methodologies developed in this paper can properly solve the buildings’multi-objective optimization problems and the architects' planning preferences. These results can be used by architects, and the developed methodologies can also be utilized as a reference for academia.

Portfolio Shading up - A Portfolio composed by NVDA, NVO, KO AND C Using Efficient Frontier and Mean Variance Analysis

This article illustrates that since last century investment becomes more and more popular as a way for people to save or spend money, but during the recovery of the pandemic, how we could make a suitable investment. This article, it demonstrates how to make an optimal portfolio with high return and low risk, with the introduction of the Variance and Mean model and efficient frontier, accompanied with the aid of Excel functions, and let it helps to get the solution best fitted in our expectations. The companies we chose for this portfolio are NVDA, KO, C and NVO, which are outstanding firms from four different industries. And another method of shading up the portfolio is also mentioned in this article, Potter's five force analysis and ESG analysis and rating scale, in a way that could increase the practical usefulness and validity in the reality of our portfolio. And these measures are also expected to be used in the future portfolio shading up.

The effects of ethnic diversity and friendship ties on managers' emotional exhaustion: a network-based case study of Caribbean information technology firms

PurposeThe purpose of this article is to empirically examine the relationship between managers' emotional exhaustion and the ethnic diversity, workload requirements, and friendship ties within their work-groups.Design/methodology/approachThe research employs a full-network sample of all managers from an indigenously owned ethnically diverse IT firm located in the Caribbean island nation of Trinidad and Tobago. Using a social network design within a regression model, the relationship between managerial power and operational workload and the burnout dimension of emotional exhaustion is initially examined as a baseline model. Work-group ethnicity and friendship ties are then examined as moderators to this relationship. The authors then examine the role of work-group ethnicity and friendship ties as a buffer mechanism using an efficient frontier analysis where managers act as decision-making units.FindingsThe study indicates that ethnic diversity acts more as a “negative moderator” to emotional exhaustion, while friendship ties act as both a “positive moderator” and “buffer” to work-related emotional exhaustion.Originality/valueThis is one of the few empirical studies that has examined the issues of ethnic diversity and burnout using social network and efficient frontier methodologies. This is also one of the first empirical studies to investigate these issues using an in-depth, full-sample case study of actual, real-work network relationships.

Macroprudential policy and house prices in an estimated Dynamic Stochastic General Equilibrium model for South Africa

AbstractThis article examines the interaction of housing‐related macroprudential policies and monetary policy. The study uses housing cycles in a Dynamic Stochastic General Equilibrium (DSGE) model with a small open‐economy framework. We estimate the model with Bayesian techniques using South African data covering the period from 2000Q1 to 2018Q4. The results indicate that monetary policy has small effects on house prices. We consider a loan‐to‐value (LTV) tool for macroprudential policy. The results show that a 1% rise in the LTV ratio, a tight macroprudential policy, leads to increasing house prices, with significant effects on Consumer Price Index (CPI) inflation. The effects on CPI inflation suggest that monetary policy is not very effective. Efficient policy frontier analysis indicates that the introduction of macroprudential policy yields an improved effective outcome that lowers output and inflation volatility. The findings suggest monetary policy and macroprudential policy require coordination.

The Optimal Monetary and Macroprudential Policies for the South African Economy

AbstractWe investigate the optimal design and effectiveness of monetary and macroprudential policies in promoting macroeconomic (price) and financial stability for the South African economy. We develop a New Keynesian dynamic stochastic general equilibrium model featuring a housing market, a banking sector and the role of macroprudential and monetary policies. Based on the parameter estimates from the estimation, we conduct an optimal rule analysis and an efficient policy frontier analysis, and compare the dynamics of the model under different policy regimes. We find that a policy regime that combines a standard monetary policy rule and a macroprudential policy rule delivers a more stable economic system with price and financial stability. A policy regime that combines an augmented monetary policy (policy rate reacts to financial conditions) with macroprudential policy is better at attenuating the effects of financial shocks, but at a much higher cost of price instability. Our findings suggest that monetary policy should focus solely on its primary objective of price stability and let macroprudential policy facilitate financial stability on its own.

The impact of listing on banks’ performance: case study from Saudi Arabia

Using quarterly data from 2010 to 2019, this paper investigates the impact of listing status on the performance of the National Commercial Bank (NCB), the largest commercial bank in Saudi Arabia, by applying a combination of financial ratios analysis and efficient frontier analysis with a mix of parametric and non-parametric tests. The overall results show that although the NCB performance is superior compared to their counterparts, this superiority has deteriorated after the bank was listed in 2014. This result was captured by the deterioration in the efficiency measures of NCB, indicating the significance of using the efficient frontier analysis as an additional monitoring tool by the Saudi regulators. The financial ratios analysis also shows that even though the NCB profitability has increased, there is an increase in the bank’s overall risk after being listed. Therefore, Saudi regulators should closely monitor their listed banks as these banks are directed toward high-risk assets.

Multi-parameter Portfolio Selection Model with Some Novel Score-Deviation Under Dual Hesitant Fuzzy Environment

In risk investment, investors have to rely on uncertain information when it is difficult to obtain enough precise data. Dual hesitant fuzzy set (DHFS) is more applicable to deal with uncertain information because it involves membership degrees and non-membership degrees, which can validly describe positive and negative information, respectively. Although there has been research on decision-making based on the DHFS, the focus still remains on ranking the alternatives and choosing the best one, which cannot help investors to find the optimal portfolios. Therefore, to solve this problem, we mainly propose two novel portfolio selection models based on the DHFS in this paper. Firstly, we propose a Max-score dual hesitant fuzzy portfolio selection model with information preference (Model 3) for investors focusing on returns regardless of risks. Secondly, to consider the risks of portfolios, we improve Model 3 and develop a score-deviation dual hesitant fuzzy portfolio selection model with information preference and risk appetite (Model 5). Finally, a case study is conducted to highlight the effectiveness of the proposed models. A detailed sensitivity analysis and an efficient frontier analysis show that Model 5 can validly capture investors’ information preferences and risk appetites. Furthermore, compared with the hesitant fuzzy portfolio model, Model 5 can offer more options to the investors with different information preferences.

Chinese shadow banking, financial regulation and effectiveness of monetary policy

This paper studies the implications of the presence of shadow banking for economic activity and the effectiveness of monetary policy in China. To explore this topic, we develop a model of the Chinese economy using a DSGE framework that accommodates interacting traditional and shadow banks. China's two specific banking regulations, in the form of loan-to-deposit ratio (LDR) and loan quota, only applies to the traditional banks. Our estimates show that regulation shocks have been the major driver of China's rising shadow banking during 2009–2016. Shadow banking leads to a higher amount of credit in the economy by helping escape constraints from traditional intermediaries, however financial frictions in the shadow banking sector create a “dual financial acceleration” mechanism. We show how the presence of shadow banking negatively affects the transmission of monetary policy and the effectiveness of macroprudential policy. We also demonstrate that deleveraging policy, that has been implemented in China tightening shadow banking in the spirit of the “look-through”, may have a contractionary impact on the economy. Efficient policy frontier analysis suggests that coordinating monetary policy and leverage ratio regulation would have helped stabilize the economy while reduce the share of shadow banking.

House prices and macroprudential policy in an estimated DSGE model of New Zealand

We analyse macroprudential and monetary policies and their interactions using an estimated dynamic stochastic general equilibrium (DSGE) model tailored to New Zealand. Our estimates show that monetary policy has large spillover effects on house prices, however it has not been a major driver of house prices in New Zealand which have instead been driven by sector-specific shocks. We consider macroprudential policies, including the loan-to-value restrictions that have been implemented in New Zealand. We find that loan-to-value restrictions reduce house prices with negligible effects on consumer prices, suggesting they can be used without derailing monetary policy. Efficient policy frontier analysis suggests macroprudential policy is a useful addition to monetary policy, and the two do not need to be coordinated. We estimate that the loan-to-value restrictions imposed in New Zealand in 2013 reduced house prices by 3.8% and that greater forward guidance on their duration would have made them more effective.

Volatility and Correlations for Stock Markets in the Emerging Economies of Central and Eastern Europe: Implications for European Investors

This paper examines the implications for European investors of the recent EU expansion to encompass former Eastern block economies. What were the risk and return characteristics of these markets pre- and post-EU? What are the implications for investors within the Euro zone? Should investors diversify outside the CEE? The former Eastern block economies constitute emerging markets which typically offer attractive risk adjusted returns for international investors. In this paper, we explore a number of aspects of this important issue and their implications for CEE based investors culminating in a Markowitz efficient frontier analysis of these markets pre- and post-EU expansion. The results suggest the ‘advanced emerging’ markets of Poland, Hungary, and Czech Republic are less attractive post-EU to a portfolio based investor seeking diversification benefits than the ‘other emerging markets.’

The role of gold bullion in South African balanced portfolios

The objective of this paper is to establish the structural features that gold bullion brings to South African global–balanced portfolios and to establish a strategic weight for this potential asset. We consider two methodological approaches based on a 40-year history to establish a strategic allocation weight for gold bullion. Our first approach considers the strategic role of gold bullion in South African global–balanced portfolios by using a mean-variance efficient frontier framework. We also implement a second assessment methodology that utilises a non-parametric optimisation procedure. We find from our efficient frontier analysis that the primary strategic role of gold bullion in a South African multi-asset portfolio is to add diversification and reduce portfolio risk (rather than enhance return). Whilst our mean-variance results differ slightly from our non-parametric results we ultimately find evidence in support of an allocation of 4% to gold bullion for South African balanced portfolios. This finding is consistent with findings in the international literature.

An integrated shipment planning and storage capacity decision under uncertainty

Purpose – In transportation and distribution systems, the shipment decisions, fleet capacity, and storage capacity are interrelated in a complex way, especially when the authors take into account uncertainty of the demand rate and shipment lead time. While shipment planning is tactical or operational in nature, increasing storage capacity often requires top management’s authority. The purpose of this paper is to present a new method to integrate both operational and strategic decision parameters, namely shipment planning and storage capacity decision under uncertainty. The ultimate goal is to provide a near optimal solution that leads to a striking balance between the total logistics costs and product availability, critical in maritime logistics of bulk shipment of commodity items. Design/methodology/approach – The authors use simulation as research method. The authors develop a simulation model to investigate the effects of various factors on costs and service levels of a distribution system. The model mimics the transportation and distribution problems of bulk cement in a major cement company in Indonesia consisting of a silo at the port of origin, two silos at two ports of destination, and a number of ships that transport the bulk cement. The authors develop a number of “what-if” scenarios by varying the storage capacity at the port of origin as well as at the ports of destinations, number of ships operated, operating hours of ports, and dispatching rules for the ships. Each scenario is evaluated in terms of costs and service level. A full factorial experiment has been conducted and analysis of variance has been used to analyze the results. Findings – The results suggest that the number of ships deployed, silo capacity, working hours of ports, and the dispatching rules of ships significantly affect both total costs and service level. Interestingly, operating fewer ships enables the company to achieve almost the same service level and gaining substantial cost savings if constraints in other part of the system are alleviated, i.e., storage capacities and working hours of ports are extended. Practical implications – Cost is a competitive factor for bulk items like cement, and thus the proposed scenarios could be implemented by the company to substantially reduce the transportation and distribution costs. Alleviating storage capacity constraint is obviously an idea that needs to be considered when optimizing shipment planning alone could not give significant improvements. Originality/value – Existing research has so far focussed on the optimization of shipment planning/scheduling, and considers shipment planning/scheduling as the objective function while treating the storage capacity as constraints. The simulation model enables “what-if” analyses to be performed and has overcome the difficulties and impracticalities of analytical methods especially when the system incorporates stochastic variables exhibited in the case example. The use of efficient frontier analysis for analyzing the simulation results is a novel idea which has been proven to be effective in screening non-dominated solutions. This has provided the authors with near optimal solutions to trade-off logistics costs and service levels (availability), with minimal experimentation times.