Stochastic Programming Models for Optimal Risk Control with Financial Derivatives

Stochastic programming models have been proposed for capacity planning problems in different environments, including energy, telecommunication networks, distribution networks, and manufacturing systems. In this chapter we give an introductory tutorial to stochastic linear programming models, with emphasis on modeling techniques, rather than specialized solution methods. We consider two-stage and multi-stage stochastic programming models with recourse for manufacturing related applications, such as production planning and capacity planning with uncertainty on demand. We stress the importance of proper model formulation from two points of view: the first one is building strong mixed-integer formulations; the second one is generating scenario trees in order to suitably represent uncertainty while keeping them to a manageable size. We also compare the stochastic programming approach to traditional dynamic programming and to robust optimization.

Multiperiod stochastic programming for biomass supply chain design under spatiotemporal variability of feedstock supply

Chapter 13 - Stochastic programming models for strategic and tactical asset allocation—A study from Norwegian life insurance

We present a long-term model 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

: The main interest is in investigating several kinds of implications of stochastic programming models and their uses to provide several types of dialogues between formal models and the decision maker himself under risk-taking situations. First, some stochastic programming models which are often discussed in the literature are presented and parametric evaluations using dual evaluators are attempted. Second, we see a close relationship between these models and the mean-standard deviation analysis mainly developed in the context of portfolio selection theory. Third, we explore utility implications of these models in connection with the expected utility maximization principle. Finally, attempts are made to impute the value(s) of key parameters in each of these models and some other utility models from the actual decision made in the mean-standard devication analysis of framework. (Author)

A stochastic program approach for path reconstruction oriented sensor location model

This paper proposes a stochastic dependent-chance programming model for vendor selection problem under the condition that the capacity, quality level, service level and lead time of each vendor are considered to be stochastic. Since stochastic programming is hard to solve by traditional methods, a hybrid adaptive genetic algorithm, which embeds the neutral network and stochastic simulation, is presented. To improve the performance of the algorithm, the probability of crossover and mutation will be adjusted according to the stage of evolution and fitness of the population. The solution procedure is tested on several randomly generated problems with varying parameters. The experimental results demonstrate that the hybrid adaptive genetic algorithm has strong adaptability.

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.

ABSTRACTThis paper introduces a two-stage stochastic integer linear programming model to improve phlebotomist scheduling in laboratory facilities of healthcare delivery systems. The model developed enables laboratory management to determine optimal scheduling policies that minimize work overload. The stochastic programming model considers the uncertainty associated with the blood collection demand in laboratory environments when optimizing phlebotomist scheduling. The paper presents an application of the model to a hospital laboratory in urban North Carolina as a case study discussing the implications for hospital laboratory management.

With the complications of modern agricultural production, how to formulate scientific and reasonable planting strategies in the limited land resources and highly uncertain market environment has become a key research topic in the agricultural field. The diversity of land types (such as terraced fields, sloping fields, and irrigated land) and the variety of crops in North China make the problem of planting optimization more complicated and practical. In this paper, a bi-level optimization model combining mixed integer programming (MIP) and stochastic programming (SP) is proposed to solve the problems of resource allocation and income maximization in crop planting. Under certain conditions, the planting scheme is constructed by a mixed integer programming model, and the effects of two over-processing strategies, namely “slow sales” and “lower price sales”, are analyzed. Under the condition of uncertainty, various random scenarios are generated by Monte Carlo simulation, and the influence of market demand and yield fluctuation per mu on planting strategy is explored by combining with a stochastic programming model.The experimental results show that the stochastic programming model is superior to the deterministic model in key indicators such as average income, land utilization rate, and income stability. Specifically, compared with the deterministic model, the land utilization rate of the stochastic programming model is increased by about 15% on average, the average income is increased by about 8%, and the fluctuation range of income is reduced by more than 50%. Sensitivity analysis further reveals the significant influence of market demand and the fluctuation range of yield per mu on income, and the stochastic programming model shows strong flexibility and robustness in adapting to uncertainty. At the same time, this study provides multi-dimensional decision support for agricultural operators by introducing multi-scenario weight optimization, which not only performs well in improving economic benefits but also provides an effective reference in resource allocation efficiency and risk management.This paper provides a new theoretical framework for agricultural planting optimization and has important practical value. The stochastic programming method can effectively deal with extreme market conditions and environmental uncertainties, and provide a decision-making basis for agricultural policy makers in subsidy distribution and market regulation. In addition, the research results provide technical support for the digital transformation and intelligent management of agricultural production and promote the development of precision agriculture. The optimization model proposed in this study also provides a reference for resource allocation and optimization in other fields.

Multi-period stochastic optimization models for dynamic asset allocation

For the companies adopting assemble-to-order (ATO) production strategy, providing accurate and reliable order promising is an important issue especially subject to the uncertainty. The ATO production system has the following characteristics. There are no finished goods in the strict sense. Inventory is holding at component level. The material and capacity planning is driven by the sales forecasting. Assembly scheduling is driven by the customer orders. We reviewed the existing order-promising researches which are mostly determined by the environment. In the base of analysis the influence mechanism of uncertainty and available-to-promise/capable-to-promise (ATP/CTP) allocation approach, we establish a stochastic dependent-chance programming model considering the available resources which are fluctuant. The objective is to maximise the chance of acceptance of the orders as much as possible. This means higher utilisation of assembly capacity. The available amount of resources obeyed some kind of common distribution. We develop a hybrid genetic algorithm (HGA) for solving the stochastic programming model; the main steps are chance function construction, Monte Carlo simulation, neural network approach and genetic algorithm (GA). We implement the model and algorithm in an automobile manufacturer, the uncertainty variables are fitted using historical data. The experiment result verified that the model and solver are valid.

The increasing shares of stochastic renewables bring higher uncertainty in power system operation and underline the need for optimal utilization of flexibility. However, the European market structure that separates energy and reserve capacity trading is prone to inefficient utilization of flexible assets, such as the HVDC interconnections, since their capacity has to be ex-ante allocated between these services. Stochastic programming models that co-optimize day-ahead energy schedules with reserve procurement and dispatch, provide endogenously the optimal transmission allocation in terms of minimum expected system cost. However, this perfect temporal coordination of trading floors cannot be attained in practice under the existing market design. To this end, we propose a decision-support tool that enables an implicit temporal coupling of the different trading floors using as control parameters the inter-regional transmission capacity allocation between energy and reserves and the area reserve requirements. The proposed method is formulated as a stochastic bilevel program and cast as mixed-integer linear programming problem, which can be efficiently solved using a Benders decomposition approach that improves computational tractability. This model bears the anticipativity features of a transmission allocation model based on a pure stochastic programming formulation, while being compatible with the current market structure. Our analysis shows that the proposed mechanism reduces the expected system cost and thus can facilitate the large-scale integration of intermittent renewables.

We present StochasticPrograms.jl, a user-friendly and powerful open-source framework for stochastic programming written in the Julia language. The framework includes both modeling tools and structure-exploiting optimization algorithms. Stochastic programming models can be efficiently formulated using an expressive syntax, and models can be instantiated, inspected, and analyzed interactively. The framework scales seamlessly to distributed environments. Small instances of a model can be run locally to ensure correctness, whereas larger instances are automatically distributed in a memory-efficient way onto supercomputers or clouds and solved using parallel optimization algorithms. These structure-exploiting solvers are based on variations of the classical L-shaped, progressive-hedging, and quasi-gradient algorithms. We provide a concise mathematical background for the various tools and constructs available in the framework along with code listings exemplifying their usage. Both software innovations related to the implementation of the framework and algorithmic innovations related to the structured solvers are highlighted. We conclude by demonstrating strong scaling properties of the distributed algorithms on numerical benchmarks in a multinode setup. Summary of Contribution: This paper presents StochasticPrograms.jl, an open-source framework for stochastic programming implemented in the Julia programming language. The framework includes an expressive syntax for formulating stochastic programming models as well as versatile analysis tools and parallel optimization algorithms. The framework will prove useful to researchers, educators, and industrial users alike. Researchers will benefit from the readily extensible open-source framework, in which they can formulate complex stochastic models or quickly typeset and test novel optimization algorithms. Educators of stochastic programming will benefit from the clean and expressive syntax. Moreover, the framework supports analysis tools and stochastic programming constructs from classical theory and leading textbooks. We strongly believe that the StochasticPrograms.jl framework can reduce the barrier to entry for incoming practitioners of stochastic programming. Industrial practitioners can make use of StochasticPrograms.jl to rapidly formulate complex models, analyze small instances locally, and then run large-scale instances in production. In doing so, they get distributed capabilities for free without changing the code and access to well-tested state-of-the-art implementations of parallel structure-exploiting solvers. As the framework is open-source, anyone from these target audiences can contribute with new functionality to the framework. In conclusion, by providing both an intuitive interface for new users and an extensive development environment for expert users, StochasticPrograms.jl has strong potential to further the field of stochastic programming.

In a telecommunication network, routing and wavelength assignment (RWA) is the problem of finding lightpaths for incoming connection requests. When facing a dynamic traffic, greedy assignment of lightpaths to incoming requests based on predefined deterministic policies leads to a fragmented network that cannot make use of its full capacity because of stranded bandwidth. At this point, service providers try to recover the capacity via a defragmentation process. We study this setting from two perspectives: (i) while granting the connection requests via the RWA problem and (ii) during the defragmentation process by lightpath rerouting. For both problems, we present the first two-stage stochastic integer programming model incorporating incoming request uncertainty to maximize the expected grade of service. We develop a decomposition-based solution approach, which uses various relaxations of the problem and a newly developed problem-specific cut family. Simulation of two-stage policies for a variety of instances in a rolling-horizon framework of 52 stages shows that our stochastic models provide high-quality solutions when compared with traditionally used deterministic ones. Specifically, the proposed provisioning policies yield improvements of up to 19% in overall grade of service and 20% in spectrum saving, while the stochastic lightpath rerouting policies grant up to 36% more requests, using up to just 4% more bandwidth spectrum.Summary of Contribution: For handling the intrinsic uncertainty of demand in the telecommunications industry, this paper proposes novel stochastic models and solution methodology for two fundamental problems in telecommunications at operational level: (i) routing and wavelength assignment (RWA) and (ii) lightpath rerouting problem. Despite the vast literature on the RWA problem, stochastic optimization has not been considered as a viable solution for resource allocation in optical networks. We propose two-stage stochastic programming models for both problems and design efficient decomposition-based solution methods that use various relaxations of the models and a new family of cutting planes. Our extensive and rigorous numerical experiments show the significant merit of incorporating uncertainty into decision making, as well as the effectiveness of the decomposition framework and our newly designed family of cuts in enhancing the solvability of both models. This work opens new avenues to explore where the powerful stochastic programming literature can be leveraged to make operational decisions in telecommunications problems, a field that currently relies mostly on deterministic and heuristic solution methods.