A Study on Optimization using Stochastic Linear Programming

Using different dominance criteria in stochastic fuzzy linear multiobjective programming: A case of fuzzy weighted objective function

Many planning problems involve choosing a set of optimal decisions for a system in the face of uncertainty of elements that may play a central role in the way the system is analyzed and operated. During the past decade, there has been a renewed interest in the modelling, analysis, and solution of such problems due to a remarkable development of both new theoretical results and novel computational techniques in stochastic optimization. A prominent approach is to develop upper and lower bounding approximations to the problem along with procedures to sharpen bounds until an acceptable tolerance is satisfied. The contributions of this dissertation are concerned with the latter approach. The thesis first studies the stochastic linear programming problem with randomness in both the objective coefficients and the constraints. A convex concave saddle property of the value function is utilized to derive new bounding techniques which generalize previously known results. These approximations require discretizing bounded domains of the random variables in such a way that tight upper and lower bounds result. Such techniques will prove attractive with the recent advances in large scale linear programming. The above results are also extended to obtain new upper and lower bounds when the domains of random variables are unbounded. While these bounds are tight, the approximating models are large-scale deterministic linear programs. In particular, with a proposed order-cone decomposition for the domains, these linear programs are well-structured, thus enabling one to use efficient techniques for solution, such as parallel computation. The thesis next considers convex stochastic programs. Using aggregation concepts from the deterministic literature, new bounds are developed for the problem which are computable using standard convex programming algorithms. Finally, the discussion is focused on a stochastic convex program arising in a certain resource allocation problem. Exploiting the problem structure, bounds are developed via the Karush-Kuhn-Tucker conditions. Rather than discretizing domains, these approximations advocate replacing difficult multidimensional integrals by a series of simple univariate integrals. Such practice allows one to preserve differentiability properties so that smooth convex programming methods can be applied for solution.

SEWA (Self Employed Women Association) was formed by Ela Bhatt with the objective of enhancing their incomes. Therefore, NABARD in 1992 formed the SHG (Self Help Group) Bank linkage project, which is today the world's largest micro finance project. In India with 1.38 billion people, the majority of population (70% roughly) is engaged in Agricultural activities where people coming from rural areas often find difficulties to save and do not have the access to credit and other finances. Women often faced difficulties in their daily lives, where there is an absolute necessity for them to adopt certain measures to step forward for their finances. This concept was well known as Self Help Group or in short women SHGs which is regarded as the unique notion in this direction. The SHGBLP (Self Help Group Bank Linkage Programme) had a modest beginning in 1992-93 with 255 credit-linked groups and a loan amount of Rs. 29 lakhs. India’s Self Help Group (SHG) movement has emerged as the world’s largest and most successful network of Community Based Organizations (CBOs). The main foresight for joining the SHG is not simply to get just credit but it is an empowerment process having with motivational attributes encouraging women to join the job. An attempt has been made to analyze such motivational, influential factors which encouraged women to join the SHGs and main motives for them to carry on in the groups for long periods. Therefore, the present paper discusses the major roles of working women in the present era of Self-Help Groups in Telangana. Since women empowerment plays a key role in socio economic development. It mainly throws light on women who are now entrepreneurs and are playing vital roles through SHG. It also focuses on the women contribution to the nation and various established parameters through SHG (Self Help Group). Key Words - SEWA (Self-employed women association), Self-help Groups (SHGs), Community based organizations (CBO), BPL (Below poverty line), SHGBLP (Self-help group Bank linkage programme).

A technique is developed for finding a closed form expression for the cumulative distribution function of the maximum value of the objective function in a stochastic linear programming problem, where either the objective function coefficients or the right hand side coefficients are continuous random vectors with known probability distributions. This is the “wait and see” problem of stochastic linear programming. Explicit results for the distribution problem are extremely difficult to obtain; indeed, previous results are known only if the right hand side coefficients have an exponential distribution [1]. To date, no explicit results have been obtained for stochastic c, and no new results of any form have appeared since the 1970’s. In this paper, we obtain the first results for stochastic c, and new explicit results if b an c are stochastic vectors with an exponential, gamma, uniform, or triangle distribution. A transformation is utilized that greatly reduces computational time.

For a class of stochastic linear bilevel programming problem, we firstly transform it into a deterministic linear bilevel covariance programming problem. Then, the deterministic bilevel covariance programming problem is solved by backpropagation artificial neural network based on elite particle swam optimization algorithm (BPANN-PSO). Finally, we perform the simulation experiments and the results show that the computational efficiency of the proposed algorithm has a potential upside compared with the classical algorithm.

Most of the studies on ageing in Kerala, India were centered on the health aspects, old age homes, socio-economic problems and quality of life of the elderly. But studies on the extent of food availability and accessibility of the elderly living Below Poverty Line (BPL) in Kerala, India have not been undertaken till date. The present study aims at examining the food availability and accessibility of the elderly living Below Poverty Line. The study is conducted not only to access their food availability and accessibility but also to see how they consume with their own income, pension or family income, or to see how much they depend on their children, relatives or others and to analyze whether their income is sufficient or not to meet their requirements. Keywords: Ageing, Food availability, Food accessibility, Below Poverty Line (BPL), Elderly

It is now difficult for an agricultural-labour household to get employment as agricultural labourers throughout the year. So, this type of household for survival purposes has to depend on diversified occupations when sometimes only the household head participates and sometimes more than one able-bodied household member participate. Based on a village-level field investigation in West Bengal, the article explores that possibility to keep an agricultural labour household above the poverty line will be more effective if more than one adult member participates in different types of occupations throughout the year. Except this, other possible determinants which can play an effective role to keep an agricultural-labour household above the poverty line are higher operational land among the marginal farmer household who are also working as hired agricultural labour in others’ land and accessibility of microcredit for income-generating activity for the female member(s) of a household from self-help groups (SHGs).

We present a parallelization of the revised simplex method for large extensive forms of two-stage stochastic linear programming (LP) problems. These problems have been considered too large to solve with the simplex method; instead, decomposition approaches based on Benders decomposition or, more recently, interior-point methods are generally used. However, these approaches do not provide optimal basic solutions, which allow for efficient hot-starts (e.g., in a branch-and-bound context) and can provide important sensitivity information. Our approach exploits the dual block-angular structure of these problems inside the linear algebra of the revised simplex method in a manner suitable for high-performance distributed-memory clusters or supercomputers. While this paper focuses on stochastic LPs, the work is applicable to all problems with a dual block-angular structure. Our implementation is competitive in serial with highly efficient sparsity-exploiting simplex codes and achieves significant relative speed-ups when run in parallel. Additionally, very large problems with hundreds of millions of variables have been successfully solved to optimality. This is the largest-scale parallel sparsity-exploiting revised simplex implementation that has been developed to date and the first truly distributed solver. It is built on novel analysis of the linear algebra for dual block-angular LP problems when solved by using the revised simplex method and a novel parallel scheme for applying product-form updates.

A novel microgrid support management system based on stochastic mixed-integer linear programming

We formulate and discuss a model of two-period stochastic optimization which allows for the possibility of the probability distribution over a non-empty finite set of states of nature-exactly one member of which will be realized in the future period- to depend on the control variable chosen in the initial period. In the second and terminal period, the decision maker chooses the value of a control variable vector which along with the control variable vector chosen in the initial period, solve a linear programming problem. The parameters of the linear programming are determined by an uncertain state of nature that is realized at the beginning of the terminal period. In order to obtain specific results, we assume that in the initial period, the decision maker can choose any one alternative from a finite set of alternatives, each such alternative being “a system of linear inequality constraints.” It is further assumed that solution sets of any two different systems are mutually disjoint and the probability distribution of the uncertain components of the state variables that is realized in the second period is determined by the system of linear inequalities chosen in the initial period. We refer to the overall problem as a “two-period stochastic linear programming game”. Our first result for a two-period stochastic linear programming game is that the optimal value for such a game as well as the optimal solutions for each of the finite number of stochastic linear programs can be found by solving a linear programming problem and our second result in this context says that the (optimal) solution for the dual of this linear programming contains a component that determines “at least one” stochastic linear programming problem any solution of which when substituted in its objective function, yields the optimal value of the two-period stochastic linear programming game. There is no need to solve any other subproblem or the primal problem to derive the optimal value of the game. AMS Classifications: 90C05, 90C15, 90C39, 90C46, 91A65 JEL Classifications: C61, C79, D81

The aim of this paper is to derive a method for solving a stochastic linear programming problem with Cauchy distribution. Assuming that the coefficients are distributed as Cauchy random variables, the stochastic linear programming is converted to a deterministic non-linear programming problem by a suitable transformation. Then an algorithm can be used to solve the resulting deterministic problem .A numerical example can be considered to illustrate the above methodology.

Pisciculture is an important source of livelihood for resource poor farmers as well as Self Help Group (SHGs) member of West Bengal. Fish culture generating regular flow of income helps SHGs to meet their food and nutritional security. The present paper examined the performance of the fishery groups and impact of earning of Self Help Groups on their households and threats related to this economic activity as well as social & economic empowerment of the women members of SHG. The study is based on primary as well as secondary data, which was collected with the help of semi-structured interview survey schedule from 19 rural blocks of Birbhum district of West Bengal. This study has focused on the functioning of 93 SHGs of Birbhum district comprising of 1001 members belonging to Below Poverty Line families under Swarnjayanti Gram Swarojgar Yojana. Totally 93 SHGs included 45 male, 38 female and 10 mixed SHGs respectively. Focus group discussions were conducted to crosscheck the collected data. The survey revealed that cash credit and project loan was used for better sustainability and enhancement of income from pisciculture. Most of the cultural water bodies i.e. ponds were under lease condition. SHG members practice composite fish culture/ poly culture and some of them were involved in integrating fish farming. Male SHGs increased their income in comparison to female & mixed SHGs. Family income increased per member after repayment of bank loan and other expenses. Empowerment of SHG women through training and other assistance have positive impact on the SHG members; increase in self-confidence, leadership qualities and enhanced income to improve their nutrition.

Background: Development can be inclusive and reduce poverty- only if all groups of people contribute to creating opportunities, share the benefits of the developmental processes and participate effectively in decision- making at all levels of governance. There is significant scope to build an enabling environment that can ensure the inclusion of people with disabilities in national development processes. Objectives: The main objective was to explore the changing status of Persons with disabilities, their problems and difficulties in the delivery of services in Bakliya village, Ladnun Block of Rajasthan. Sample: The study is purely qualitative in nature. Three different types of case studies have been selected which reflect different causes for disabilities, types and number of differently abled in family and benefits of financial assistance. Six in-depth interviews were also conducted. Design: It is explorative in nature and purposive sampling was used for this study. Tool: Guideline for case studies, Focused Group Discussion and interview schedule was used. Results: It was found that welfare schemes were helpful for the persons with disabilities to improve their livelihood, education, health care, respect and starting of new business. Recreational facilities and special services were not provided in the school to manage these children. Panchayat did not take any interest for their development except providing financial assistance. Indira Awaas Yojna and toilet facility helped these children and their mother for living in a safe and secure manner without any fear. Conclusion: Panchayat needs to be proactive to develop community based services for these children of special needs. Government officials of panchayat samiti may intervene to conduct research studies regarding their types of problems and provide support services to their families with proper planning and management. Early detection and identification of such cases needs to be done in priority basis. Keywords: Person with Disabilities, Below Poverty Line (BPL) families, Case Studies

This paper derives a mathematical structure for investment decisions of a profit-maximising and strategic producer in liberalised electricity markets. The paper assumes a Cournot producer in an energy market with nodal pricing regime. The Cournot producer is assumed to have revenue from selling energy to the pool. The investment problem of the strategic producer is modelled through a leader-follower game in applied mathematics. The leader is the strategic producer seeking the optimal mix of its investment technologies and the follower is a stochastic estimator. The stochastic estimator forecasts the reactions of other producers in the market in response to the investment decisions of the producer in question. The stochastic estimator takes the investment decisions of the producer and it calculates the stochastic prices. The mathematical structure is a stochastic linear bilevel programming problem. This problem is reformulated as a stochastic MILP problem which can be solved using the commercially available software packages. Finally, the developed mathematical structure is applied to a six-node example system to highlight the strengths of the whole approach.

We study qualitative properties of a stochastic linear programming problem with quantile criterion for a wide class of distributions. We show convexity conditions for the criterion function with respect to the strategy, and continuity conditions with respect to the strategy and reliability level. We give sufficient conditions for the existence of a solution. We present a new algorithm for finding a guaranteeing solution of the problem, i.e., an admissible solution for which the quantile criterion function's value turns out to be close to optimal.