Mathematics and Statistics

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A model for predicting food security status among households in developing countries
(International Journal of Development and Sustainability, 2013) Mbukwa, Justine N.
Food security prediction has been challenging aspects in developing countries particularly in African countries such as Tanzania. Consequently, government lack proper stimulated information that is necessary in making decision on efforts required for stabilizing food situation and status in their countries. Scientifically it has been observed in research and practical that this is caused by lack of proper mechanisms, tools and approach suitable for modeling and predicting food status among households. This paper proposes a logistic regression based model for analysis and prediction of food security status. The proposed model is empirically test using practical data collected from one district in Tanzania.
A new method for intuitionistic fuzzy multi-objective linear fractional optimization problem and its application in agricultural land allocation problem
(Elsevier, 2023) Moges, Demmelash Mollalign; Mushi, Allen R.; Wordofa, Berhanu Guta
This paper presents a new method for solving an intuitionistic fuzzy multi-objective linear fractional optimization (IFMOLFO) problem with crisp and intuitionistic fuzzy constraints. Here, all uncertain parameters are represented as triangular intuitionistic fuzzy numbers. We used an accuracy ranking function and variable transformation in the proposed method to convert an IFMOLFO problem into a crisp multi-objective linear optimization problem. Then, we formulated the first phase of the weighted intuitionistic fuzzy goal programming (WIFGP) model to obtain an intuitionistic fuzzy non-dominant (IFND) solution for the IFMOLFO problem. Several strategies for obtaining an IFND solution to the IFMOLFO problem have been proposed in the literature. However, in addition to constructing the phase-I WIFGP model, this study shows that the IFND solution may not be Pareto-optimal when some of the under-deviation variables are zero. As a result, the second phase of the WIFGP model is applied to address this issue. The benefits of both models are merged to provide a novel method, unlike any other method in the literature, for producing optimal solutions that satisfy both IFND and Pareto-optimal requirements. The suggested algorithm’s efficiency and reliability are demonstrated by addressing a real-life case study of an agricultural production planning problem and followed by solving a numerical example from literature.
Analysis of multi-SIM behaviour in Tanzania’s telecom market using binary logit model
(Tanzania Journal of Development Studies, 2022) Ilembo, Bahati ; Walwa, Jackson
This paper examines factors for multi SIMs usage in the mobile services, and its economic implications to mobile operators in Tanzania. A random sample of 288 mobile phones subscribers from six mobile operators were included in the study. The study used binary logit model to estimate drivers for multi-SIMs usage, with marginal effects calculated to indicate appropriately the probabilities of usage for individual parameters used in the model. The findings showed that differences in perceiving quality of services and product differentiation are the main drivers for multi-SIMs usage. The multi-SIMs users are satisfied with multiple operators as no one operator provides a combination of their communication needs successfully. Also, customer-care related reasons like inaccessibility of sim swap raises customer’s SIM multiplicity. The behaviour of customers to own multiple SIM cards increases the level of customer spending to multiple operators and reduces customer’s profitability. This demands that network managements improve network quality, promotional activity, and customer care to win customers’ share of usage.
Application of K-Means and Partitioning Around Mediods (PAM) clustering techniques on Maize and Beans yield in Tanzania
(KY Publications, 2016) Mbukwa, Justine Nkundwe; Anjaneyulu, G.V.S.R.
This paper contributes to the application of k-means and k-mediods multivariate statistical methods for the purpose of revealing optimal clusters and assessing the consistency of individual districts within the group. Data used were extracted from united republic of Tanzania (Ministry of Agriculture, Livestock and Fisheries(MALF) (2003/12) consisted a total of (n=36 districts) with both maize and beans yield. The R-statistical computing version (3.1.1) was used. The study findings revealed that 36 districts were grouped into six clusters using k-means algorithm. Using the k-mediods, it was revealed that only 11 districts were found to very well structured since their silhouette width (Si) is above 0.5. Nevertheless, the clusters validation was done in such a way that individual district whose silhouette width (Si) close to 1 was regarded as highly consistency clustered whereas districts with (Si) greater or equal to 0.25 were said to be somehow well clustered and otherwise. The paper concludes that few districts that are very consistent given the threshold margin should to be monitored and evaluated effectively to ascertain productivity. The study recommends that the government should pay attention on allocating the scarce resources to the consistency clusters along with policy review in favour of smallholder farmers through access and timely for all important farm inputs in future.
Aretrospective evaluation of the intellectual structure of private agricultural and food standards research in global trade
(International Trade, Politics and Development, 2023) Lwesya, Francis; Mbukwa, Justine N.
Purpose The aim of this article was to present a retrospective assessment of the intellectual structure of private agricultural and food standards research in global trade. This study was motivated by the increasing role of standards and certifications in governing global agricultural and food trade. Design/methodology/approach The current investigation was carried out with bibliometric methods using VOSviewer software. Techniques such as citation, co-citation, keyword co-occurrence, keyword evolution and co-authorship analyses were performed to tackle the research questions. Articles were extracted from Scopus database for the period 1998–2022 (30th August 2022) with selected keywords (“Private food standard*” OR “food standard*” OR “agri-food standard*” AND “agri*” OR “agro*” OR “farm*” OR “food*” AND “international trade” OR “global trade” OR “international business”) along certain filters (subject – Economics and Business management: language – English: Document – article and review articles and source – journals). Findings The results show that the intellectual structure of private agricultural and food standards research in global trade has evolved around five clusters, namely: (1) the political economy of food standards, (2) food standards and their challenges in global trade, (3) food standards and integration into value chains, (4) food standards and market access and (5) food standards and exports from developing countries. However, the authors found the research gaps in each of the thematic clusters. Research limitations/implications The main limitation of this study is that the authors focused their attention on certain aspects of bibliometric review, such as the intellectual structure of the field, the citation analysis and the collaboration network. Future research could attempt to explore new field development through bibliographic coupling and deepening of conceptual structure using content analysis by incorporating the research methods used in the respective studies. Practical implications The emerging research areas in private agricultural and food standards in global trade are related to topics on food quality, sustainable development, genetically modified organisms, World Trade Organization, tariff structure, trade agreements, food industry and European Union. However, there is less research and little collaboration between Africa and developed countries. For example, Africa's total publications were (15), while the US had (46), China (15), Belgium (23), Germany (27), Italy (32) and the UK (24). Originality/value There are limited studies that have conducted a retrospective evaluation of the intellectual structure of private agricultural and food standards research in the global trade using bibliometric analysis. The present investigation is novel in identifying the thematic research clusters, emerging issues and future research directions. This is more important to developing countries as their agricultural produce face challenges to access markets of the developed world.
Asset liability management for Tanzania: Pension funds by stochastic programming
(Afrika Statistika, 2018) John, Andongwisye; Larsson, Torbjörn; Singull, Martin; Mushi, Allen R.
We present a long-termmodel of asset liability management for Tanzania pension funds. The pension system is pay-as-you-go where contributions are used to pay current benefits. The pension plan is a final salary defined benefit. Two kinds of pension benefits, a commuted (at retirement) and a monthly (old age) pension are considered. A decisive factor for a long-term asset liability management is that, Tanzania pension funds face an increase of their members’ life expectancy, which will cause the retirees to contributors dependence ratio to increase. We present a stochastic programming approach which allocates assets with the best return to raise the asset value closer to the level of liabilities. The model is based on work by Kouwenberg in 2001, with features from Tanzania pension system. In contrast to most asset liability management models for pension funds by stochastic programming, liabilities are modeled by using number of years of life expectancy for monthly benefit. Scenario trees are generated by using Monte Carlo simulation. Numerical results suggest that, in order to improve the long-term sustainability of the Tanzania pension fund system, it is necessary to make reforms concerning the contribution rate, investment guidelines and formulate target funding ratios to characterize the pension funds’ solvency situation.
Bayesian multilevel modelling of the association between socio-economic status and stunting among under-five-year children in Tanzania
(Journal of Health, Population and Nutrition, 2023) Musheiguza, Edwin; Mbegalo, Tukae; Mbukwa, Justine N.
Background: Stunting is associated with socioeconomic status (SES) which is multidimensional. This study aimed to compare different SES indices in predicting stunting. Methods: This was the secondary data analysis using Tanzania Demographics and Health Surveys (TDHS). The study used 7492, 6668, and 8790 under-five-year children from TDHS 2004/5, 2010, and 2015/16, respectively. The Household Wealth Index (HWI); Water and Sanitation, Assets, Maternal education and Income (WAMI); Wealth Assets, Education, and Occupation (WEO); and the Multidimensional Poverty Index (MPI) indices were compared. The summated scores, principal component analysis (PCA), and random forest (RF) approaches were used to construct indices. The Bayesian and maximum likelihood multilevel generalized linear mixed models (MGLMM) were constructed to determine the association between each SES index and stunting. Results: The study revealed that 42.3%, 38.4%, and 32.4% of the studied under-five-year children were stunted in 2004/5, 2010, and 2015/16, respectively. Compared to other indicators of SES, the MPI had a better prediction of stunting for the TDHS 2004/5 and 2015/16, while the WAMI had a better prediction in 2010. For each score increase in WAMI, the odds of stunting were 64% [BPOR = 0.36; 95% CCI 0.3, 0.4] lower in 2010, while for each score increase in MPI there was 1 [BPOR = 1.1; 95% CCI 1.1, 1.2] times higher odds of stunting in 2015/16. Conclusion: The MPI and WAMI under PCA were the best measures of SES that predict stunting. Because MPI was the best predictor of stunting for two surveys (TDHS 2004/5 and 2015/16), studies dealing with stunting should use MPI as a proxy measure of SES. Use of BE-MGLMM in modelling stunting is encouraged. Strengthened availability of items forming MPI is inevitable for child growth potentials. Further studies should investigate the determinants of stunting using Bayesian spatial models to take into account spatial heterogeneity.
Climate change, food security, and diarrhoea prevalence nexus in Tanzania
(humanities and social sciences communications, 2024) Kitole, Felician A.; Mbukwa, Justine N.; Tibamanya, Felister Y.; Sesabo, Jennifer K.
The impact of climate change on food security and public health has hindered poverty reduction efforts in developing nations, including Tanzania, resulting in the impoverishment of millions and compromising both health and food production. To unravel these complex interactions, rigorous scientific research is indispensable. Leveraging three waves of the Agriculture Sample Census (2002/03, 2007/08, 2019/20), this study meticulously examines the interplay between climate change, food security, and diarrhoea prevalence in Tanzania. Employing Instrumental Variable Probit and Control Function Approach models to address endogeneity and heterogeneity, temperature anomalies serve as instrumental variables. The findings reveal a substantial impact of climate change on both food security (−0.331142, p < 0.01) and diarrhoea incidence (0.214602, p < 0.01). These results signify that climate change places significant stress on food security, rendering households more susceptible to insecurities, and heightens health concerns through increased diarrhoea prevalence. This underscores the urgency of prioritizing public health and well-being through an agricultural lens in climate change mitigation. A comprehensive strategy is imperative, entailing a synergy of sustainable agricultural practices, robust public health interventions, and targeted policies to fortify the adaptive capacity of communities. Special emphasis should be placed on cultivating climate-resilient agricultural systems, ensuring food security, and implementing health programs tailored to address the unique challenges posed by climate-induced factors. Moreover, community engagement and awareness initiatives play a pivotal role in fostering a collective understanding and commitment to sustainable practices, contributing to the overall resilience of societies amidst the challenges of climate change.
Effect of Statistics on Collaboration for Enhancing Institutional Sustainability: A Case of Mzumbe University-Tanzania
(Springer Nature Switzerland, 2024) Mbukwa, Justine N.; Mbegalo, Tukae; Lwaho, Joseph
The article discusses the effects of statistics on collaboration and its potential in spearheading sustainable industrial development. In this regard, three days’ workshop were conducted by Mzumbe University Laboratory for Interdisciplinary Analysis (MULISA) in collaboration with the Ifakara health institute. These activities are statistical literacy, scientific writing and winning the research grants. The objective was to create a smooth environment for the sustainability of the statistical laboratory through knowledge. The participants in the workshop were students and lecturers at Mzumbe University, and researchers and interns from Ifakara Research Institute (IHI). The majority of the participants in all three days of workshop were males. The results revealed that the workshop has increased the research and publication activities among MULISA collaborators after the workshop compared to before the workshop. This noted benefit derived from the sharing the skills and collaboration during the workshop. Therefore, the collaborative workshops and training are the engineering tool for sustainability because it allows sharing of new knowledge. The collaboration in writing enhances thoughts, ideas, and knowledge transferability to the next generation.
Implementation of a goal programming model for solid waste management: A case study of Dar es Salaam – Tanzania
(EDP Sciences, 2017) Lyeme, Halidi Ally; Mushi, Allen R.; Nkansah-Gyekye, Yaw
In this research article, the multi-objective optimization model for solid waste management problem is solved by the goal programming method. The model has three objectives: total cost minimization, minimization of f inal waste disposal to the landfill, and environmental impact minimization. First, the model is solved for the higher priority goal, and then its value is never allowed to deteriorate. The model is solved for the next priority goal and so on until the problem is solved. The model was tested with real data for solid waste management system from Dar es Salaam city. The results determine the best locations for recycling plants, separating plants, composting plants, incinerating plants, landfill and waste flow allocation between them. Furthermore, the solution shows a high reduction of the amount of waste to the landfill and greenhouse gas emissions by 78% and 57.5% respectively if fully implemented compared to the current system.
Irrigation water allocation optimization using Multi-Objective Evolutionary Algorithm (MOEA): A review
(EDP Sciences, 2018) Fanuel, Ibrahim Mwita; Mushi, Allen R.; Kajunguri, Damian
This paper analyzes more than 40 papers with a restricted area of application of Multi-Objective Genetic Algorithm, Non-Dominated Sorting Genetic Algorithm-II and Multi-Objective Differential Evolution (MODE) to solve the multi-objective problem in agricultural water management. The paper focused on different application aspects which include water allocation, irrigation planning, crop pattern and allocation of available land. The performance and results of these techniques are discussed. The review finds that there is a potential to use MODE to analyzed the multi-objective problem, the application is more significance due to its advantage of being simple and powerful technique than any Evolutionary Algorithm. The paper concludes with the hopeful new trend of research that demand effective use of MODE; inclusion of benefits derived from farm byproducts and production costs into the model.
Mathematical model for Tanzania population growth
(Tanzania Journal of Science, 2019) Mwakisisile, Andongwisye; Mushi, Allen R.
In this paper, a mathematical model for Tanzania population growth is presented. The model is developed by using exponential and logistic population growth models. Real data from censuses conducted by Tanzania National Bureau of Statistics (NBS) are used. The Tanzania growth rate is obtained by using data of 1967 and 2012 censuses. The prediction of population for the period of 2013 to 2035 is done. Numerical results show that the population grows at the rate of 2.88%. In 2035 the population is expected to be 87,538,767 by exponential model and 85,102,504 by logistic model. The carrying capacity is 2,976,857,550, which implies that the population will still grow faster since it is far from its limiting value. Comparisons of the models with real data from the five censuses are done. Also NBS projections are compared with populations predicted by the two models. Both comparisons show that the exponential model is performing better than logistic model. Also, the projection up to 2050 gives the population of 135,244,161 by exponential model and 131,261,794 by logistic model.
Mathematical programming formulations for the examinations timetable problem: The case of the University of Dar es Salaam
(African Journal of Science and Technology, 2004) Mushi, Allen R.
Examinations Timetabling Problem (ETP) is the problem of assigning courses to be examined and candidates to time periods and examination rooms while satisfying a set of constraints. Every University has a different set of constraints and structure of examinations. Thus there is no general ETP model for all Universities around the world [1]. ETP is NP-Hard [2] and therefore no optimal algorithm is known for this problem which can solve a general problem within reasonable time. However, exact methods can be used to provide a benchmark for the heuristic methods. There is no general model for University Timetabling Problems because the problem feature differs from one University to another. In this paper we focus in the formulation of the ETP for the University of Dar as salaam. We formulate, test and compare three Integer Programming models. It is concluded that, although exact methods cannot give a solution to a real-size problem, these models give a good benchmark for testing the performance of other approaches. This paper also gives a direction for better exact models for the University of Dar es salaam’s ETP.
Multi-objective optimization model formulation for solid waste management in Dar es Salaam, Tanzania
(Asian Journal of Mathematics and Applications, 2017) Lyeme, Halidi Ally; Mushi, Allen R.; Nkansah-Gyekye, Yaw
Solid waste management is a challenging problem in developing nations. The health and environmental negative implications associated with solid waste management are very serious particularly in the developing nations where a large percent of waste is dumped into open areas. These implications are essentially on climate change and global warming due to environmental problems. In this paper, a multiobjective optimization model is developed to address the conflicting objectives of cost minimization, minimization of final waste disposal to the landfill, and environmental impact minimization. The model follows a mixed-integer programming formulation and tested by data from selected wards in Dar es Salaam city. The output is the best location of recycling plants, separating plants, composting plants, incinerating plants, landfill and waste flow allocation between them. The solution shows a high reduction of the amount of waste to the landfill and greenhouse gas emissions by 76% and 55.2% respectively compared to the current system.
On the use of Sparse Principal Component Analysis and Robust: Selection Features of Maize Yield in Rural Tanzania
(MANECH Pblications, 2017) Mbukwa, Justine N.; Anjaneyulu, GVSR
This paper has been motivated as a result of an existence of high dimensionality problem in maize yield. This means that an application of the Sparse Principal Component Analysis (SPCA) pattern recognition technique is unknown in selecting few consistent features and easier interpretation as opposed to classical PCA. This paper fulfills the existing knowledge gap in the context of Tanzania. A structure questionnaire was used to collect primary data from Mbozi and Mvomero Districts among small farming household in rural areas. The study was designed on the basis of hierarchical random sampling. The breakdown of facts was made by R-Statistical computing (version 3.3.2) whereas the findings were depicted using graphs and tables. The statistical estimates like percentage, mean and variance were also used. In line with SPCA, PCA and Robust PCA were also fitted for comparison purpose. Results showed 19 variables were condensed to six components explaining 63.7 per cent variations under PCA. Contrary to these findings, there were great improvements of the loadings, consistent and easier to interpret in each PC of the modified model (SPCA). However, the paper discovered that the Robust PCA condensed the p-variable to two PCs such that PC1 explained (81.0 per cent) variances. The study recommends the Sparse and Robustness as the best filtering techniques with reliable results as contrasted to the ordinary PCA.
Optimal portfolio management when stocks are driven by Mean-Reverting Processes
(University of Dar es Salaam, 2012) Mbigili, Lusungu Julius
In this work, we present and solve the problem of portfolio optimization within the context of continuous-time stochastic model of financial variables. We consider an investment problem where an investor has two assets, namely, risk-free assets (e.g. bonds) and risky assets (e.g. stocks) to invest on and tries to maximize the expected utility of the wealth at some future time. The evolution of the risk-free asset is described deterministically while the dynamics of the risky asset is described by the geometric mean reversion (GMR) model. The controlled wealth stochastic deferential equation (SDE) and the portfolio problem are formulated. The portfolio optimization problem is then successfully formulated and solved with the help of the theory of stochastic control technique where the dynamic programming principle (DPP) and the HJB theory were used. We obtained very interesting results which are the solution of the non-linear second order partial deferential equation and the optimal policy which is the optimal control strategy for the investment process. So far we have considered utility functions which are members of hyperbolic absolute risk aversion (HARA) family, called power and exponential utility. In both cases, the optimal control (investment strategy) has explicit form and is wealth dependent, in the sense that, as the investor becomes more rich, the less he invests on the risky assets. Linearization of the logarithmic term in the portfolio problem was necessary to be undertaken for making the work of obtaining the explicit form of the optimal control much simple than it was expected.
Optimization model for solid waste management at Ilala Municipal, Tanzania
(Journal of Informatics and Virtual Education, 2011) Lyeme, Halidi A; Mujuni, Egbert; Mushi, Allen R.
The existing solid waste management system at Ilala Municipal suffers from the lack of a real plan for collection centre locations and vehicle routes. In this study, a proposed mathematical model for municipal solid waste management process for Ilala municipality is presented. It includes the use of the concept of collection centres. Operational research methodology particularly Mixed Integer Programming is used to model the problem. The problem is solved to optimality which provides the best distribution of collection centres and their capacities. The solution shows a leastcost transportation plan with a cost saving of 38.3% per day compared to the current system.
Pricing barrier options when the dynamics of the prices are driven by the Mean Reverting Process
(University of Dar es Salaam, 2013) Komunte, Masoud
This dissertation considers a problem of pricing barrier options when the dynamics of the asset prices (X(t)) are driven by the mean reverting process, the market/asset price X(t) is obtain from mean reversion model and a Black-Scholes PDE model for pricing barrier options under mean reversion model is obtained upon using It ˆ o formula. Through the Homotopy Analysis Method (HAM) the price of the chosen barrier option (up􀀀and􀀀out European call) that satisfies the Black-Scholes PDE model was determined. Thus, through HAM we can determine approximated prices of barrier options when the dynamics of the prices are driven by the mean reverting process (Liao, 2004). Lastly the analysis is conducted to observe the behaviour of the option price when value of one parameter increases while the value of the other two parameters remain constant. The analysis shows that the option price tends to increase with the increase of the value of the parameter for the case of volatility and degree of mean reversion while for interest rate the option price decreases when interest rate increases. In all cases it is observed that early exercise is better than late exercise to owner of the option since the option price tends to decrease as time increases also to minimize risk owner of the option should exercise the option when the volatility of the market become large. It is recommended that in future, areas of interest for research related to this study are; first, finding the option price by using direct integration after obtaining a reflection principle which is useful in determining the joint distribution of the It ˆ o integral and secondly, finding the price which is a closed form solution by using Laplace transform.
Probabilistic weather forecasting using Bayesian Model averaging: the case of Sagcot Regions
(Mzumbe University, 2018) Joel, Emmanuel
Over the past decade Tanzania has experienced spontaneous population increase (1.556 mil annual). But the number is estimated to further increase by 2050 to 2.982 mil annual, thus Tanzania is estimated to have population of 137 million people in 2050 (UN, 2015). The fast growing population is mainly depending on rainfed agriculture, which contribute 29 percent of the country GDP and providing employment to 65.5 percent of Tanzanians (Deloitte, 2016). The diversity in climatic and weather activities has posed a challenge in rainfed agriculture especially on when to plant seeds. Therefore, in order to promote agricultural activities, stable and reliable weather information are crucial in order for production to match with population increase. This study explores the challenge facing the Numerical Weather Prediction (NWP) namely WRF-ARW, by creating the system of equation (ensembles) from WRF-ARW resulting from the use of different initial conditions. Ensemble allow for probabilistic forecast to take the form of predictive probability function (PDF). But, raw ensemble forecast system are finite hence they only capture some of the uncertainty of the NWP. Thus, this study used Bayesian Model Averaging (BMA) methods of post processing ensemble forecast to maximize the sharpness of the parameter and calibration. The findings show BMA method successively removes most of under disersion showed by raw ensembles. Thus, calibrated and sharp results of BMA approach resolves a number of the weaknesses of the ensemble forecasts including their under dispersion and the discrepancy between forecasts and observations. Therefore, BMA can be used to attain higher consistency in the probabilistic forecasts of an operational model.
Projecting Tanzania pension fund system
(Statistics and Probability African Society, 2017) John, Andongwisye; Torbjörn, Larsson; Singull, Martin; Mushi, Allen R.
A mandatory Tanzania pension fund with a final salary defined benefit is analyzed. This fund is a contributory pay-as-you-go defined benefit pension system which is much affected by the change in demography. Two kinds of pension benefit, a commuted (at retirement) and a monthly (old age) pension are considered. A decisive factor in the analysis is the increased life expectancy of members of the fund. The projection of the fund's future members and retirees is done using expected mortality rates of working population and expected longevity. The future contributions, benefits, asset values and liabilities are analyzed. The projection shows that the fund will not be fully sustainable on a long term due to the increase in life expectancy of its members. The contributions will not cover the benefit payouts and the asset value will not fully cover liabilities. Evaluation of some possible reforms of the fund shows that they cannot guarantee a long-term sustainability. Higher returns on asset value will improve the funding ratio, but contributions are still insufficient to cover benefit payouts. Un fonds de pension obligataire en Tanzanie avec un salaire final défini est défini. Ce fonds est un système de retraite à prestations déterminées contributif et payant qui est très affecté par les changements démographiques. Deux types de prestations de retraite, une retraite de rachat (à la retraite) et une pension mensuelle (vieillesse) sont considérés. Un facteur décisif dans l'analyse est l'augmentation de l'espérance de vie des participants au fonds. La projection des futurs membres et des retraités du fonds se fait à l'aide des taux de mortalité attendus de la population active et de la longévité espérée. Les contributions futures, les avantages, la valeur de l'actif et du passif sont analysés. Nos projections montrent que le fonds ne sera pas pleinement durable à long terme, en raison de l'augmentation de l'espérance de vie de membres. Les contributions ne couvriront pas les paiements de prestations et la valeur de l'actif ne couvrira pas entièrement le passif. Une évaluation de certaines réformes possibles du fonds montre qu'ils ne peuvent garantir une viabilité à long terme. Un rendement plus élevé de la valeur de l'actif améliorera le ratio de financement, mais les contributions restent insuffisantes pour couvrir les paiements des prestations.

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