A stochastic program approach for path reconstruction oriented sensor location model

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

Stochastic optimization models have been extensively applied to financial portfolios and have proven their effectiveness in asset and asset-liability management; hardly however they have been applied to decision universe including not only financial but also derivatives written on the underlying, derivatives such as options or futures with their dedicated risk profiles and associated modeling complexities. Including options in the portfolio gives us the opportunity to hedge the underlying and to speculate on them to increase the profit potential given a certain risk level. The modeling of options in multistage stochastic programming framework would have many advantages, for instance, a put option can be used for insuring a portfolio against any downside movement in the market, high volatility in options prices is risky but rewarding if captured accurately, in-the-money call/put options at maturity can be used to buy/sell the underlying security at a price lower/higher than the market price, optimally increasing and reducing inventory. We present here multistage models to include cash and physical settled call and put options in a portfolio along with other asset classes.

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.

Strong seasonality at high latitudes represents a major challenge for many endotherms as they must balance survival and reproduction in an environment that varies widely in food availability and temperature. To avoid energetic mismatches caused by limited foraging time and stochastic weather conditions, bats employ the energy-saving state of torpor during summer to save accumulated energy reserves. However, at high-latitude small-bats-in-summer face a particular challenge: as nocturnal foragers, they rely on the darkness at night to avoid predators and/or interspecific competition, but live in an environment with short, light summer nights, and even a lack of true night at the northernmost distributions of some bat species. To predict optimal behaviour in relation to latitudinal variation in diurnal cycles, we constructed a stochastic dynamic programming model of bats living at high latitudes. Using a stochastic dynamic programming framework with values that are representative for our study system, we show that individual energetic reserves are a strong driver of daytime use of torpor and night-time foraging behaviour alike, with these linked effects being both temperature- and photoperiod-dependent. We further used the model to predict survival probabilities at five locations across a latitudinal gradient (60.1° N to 70.9° N), finding that combinations of photoperiod and temperature conditions limited population distributions in the model. To verify our model results, we compared predictions for optimal decisions with our own empirical data collected on northern bats (Eptesicus nilssonii) from two latitudes in Norway. The similarities between our predictions and observations provide strong evidence that this model framework incorporates the most important drivers of diurnal decision-making in bat physiology and behaviour. Comparing empirical data and model predictions also revealed that bats facing lighter night conditions further north restrict their mass gain, which strengthens the hypothesis that predation threat is a main driver of bat nocturnality. Our model findings regarding state-dependent decisions in bats should contribute to the understanding of how bats cope with the summer challenges at high latitudes.

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.

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.

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.

Two stage stochastic programming is an important part in the whole area of stochastic programming, and is widely spread in multiple disciplines, such as financial management, risk management, and logistics. The two stage stochastic programming is a natural extension of linear programming by incorporating uncertainty into the model. This thesis solves the two stage stochastic programming using a novel approach. For most two stage stochastic programming model instances, both the objective function and constraints are convex but non-differentiable, e.g. piecewise-linear, and thereby solved by the first gradient-type methods. When encountering large scale problems, the performance of known methods, such as the stochastic decomposition (SD) and stochastic approximation (SA), is poor in practice. This thesis replaces the objective function and constraints with their polynomial approximations. That is because polynomial counterpart has the following benefits: first, the polynomial approximation will preserve the convexity; Second, the polynomial approximation will uniformly converge to the original objective/constraints with arbitrary accuracy; and third, the polynomial approximation will not only provide good estimation on the original objectives/functions but also their gradients/sub-gradients. All these features enable us to apply convex optimization techniques for large scale problems. Hence, the thesis applies SAA, polynomial approximation method and then steepest descent method in combination to solve the large-scale problems effectively and efficiently.

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.

This paper develops a mathematical model for post-disaster planning with human casualties, which can be considered as operational guidance for the proper use of emergency resources. For this purpose, a stochastic mixed-integer programming model is provided to formulate the problem. The objective functions of the model are (1) maximizing the survival probability of patients, (2) minimizing the maximum of completion time of treatment of all patients, and (3) minimizing the total cost of operations. The model is solved with the ϵ-constraint method. Due to the NP-hardness of the problem which is a significant challenge in the literature, two innovative meta-heuristic algorithms are proposed, i.e. a non-dominated sorting genetic algorithm (NSGA-II) and a multi-objective simulated annealing (MOSA). Finally, a comprehensive computational analysis is performed for evaluation purposes. Also, a case study is made on the earthquake in Iran, which illustrates the real-world application of the model. Highlights A stochastic multi-objective mathematical programming model to allocate patients to hospitals and treat them. NSGA-II and MOSA are proposed, in addition to ϵ-constraint method as solution methods. Performance of two meta-heuristic algorithms is measured with five evaluation metrics. The study showed that NSGA-II is more effective than MOSA. The model was implemented on a real-world case, Tabriz earthquake in Iran.

The integration of natural gas and electricity sectors has increased sharply in the last decade as a consequence of combined cycle natural gas thermal power plants. In some countries such as Brazil, gas-fired generation has been a major factor in the overall growth of natural gas consumption. When related to the operations planning, in some hydrothermal systems, a national system operator dispatches these gas-fired plants (along with other thermal sources such as coal, oil, and nuclear) in conjunction with the country’s hydroelectric plants by using a production-costing model based on stochastic programming. The algorithm determines the optimal hydro-to-thermal energy production ratio on the basis of the expected benefit of reducing thermal plant generation over a large number of hydrological scenarios, along a planning horizon of some years. This means that the optimal scheduling decision today depends on the assumptions about future load growth and future entrance of new generation capacity. Stochastic dynamic programming models are extensively used. However, the hydrothermal scheduling models usually do not take into account the possibility of future fuel supply constraints, either in production or in transportation. The assumption of fuel supply adequacy is felt to be reasonable for the more mature markets such as coal and oil. However, because of the fast growth of the natural gas market, it is possible that demand outpaces supply or transportation investments. Indications that gas-related constraints could be relevant were observed in New England, in the US, and in Brazil in 2004, where several megawatt of combined-cycle generation could not be dispatched when needed due to constraints in pipeline capacity. The objective of this work is to present a methodology for representing the natural gas supply, demand, and transportation network in the stochastic hydrothermal power scheduling model. Application of the integrated electricity–gas scheduling model is illustrated in case studies, with realistic configurations of the 90GW Brazilian system.KeywordsHydroelectric-thermal power generationNatural gas industryStochastic dual dynamic programming

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.

Effects of higher order moments on the newsvendor problem