Browsing by Subject "Stochastic programming"

Now showing 1 - 17 of 17

Open Access
A stochastic programming approach to surgery scheduling under parallel processing principle
(Elsevier Ltd, 2023-11-06) Çelik, Batuhan; Gül, Serhat; Çelik, Melih
Parallel processing is a principle which enables simultaneous implementation of anesthesia induction and operating room (OR) turnover with the aim of improving OR utilization. In this article, we study the problem of scheduling surgeries for multiple ORs and induction rooms (IR) that function based on the parallel processing principle under uncertainty. We propose a two-stage stochastic mixed-integer programming model considering the uncertainty in induction, surgery and turnover durations. We sequence patients and set appointment times for surgeries in the first stage and assign patients to IRs at the second stage of the model. We show that an optimal myopic policy can be used for IR assignment decisions due to the special structure of the model. We minimize the expected total cost of patient waiting time, OR idle time and IR idle time in the objective function. We enhance the model formulation using bounds on variables and symmetry-breaking constraints. We implement a novel progressive hedging algorithm by proposing a penalty update method and a variable fixing mechanism. Based on real data of a large academic hospital, we compare our solution approach with several scheduling heuristics from the literature. We assess the additional benefits and costs associated with the implementation of parallel processing using near-optimal schedules. We examine how the benefits are inflated by increasing the number of IRs. Finally, we estimate the value of stochastic solution to underline the importance of considering uncertainty in durations. © 2022 Elsevier Ltd
Open Access
Allocating vaccines under scarce supply
(2023-08) Kılınç, Onur
We consider the vaccine allocation problem under scarce supply. We formulate the problem as a two stage stochastic programming model, considering the uncertain factors such as vaccine efficacy, disease spread dynamics and the amount of future supply. We discuss two variants of the model that could be used under different preferences. We demonstrate the usability of our formulations on two case study examples that are generated based on real-life data. The results demonstrate that incorporating the uncertainty in these factors into the decision making process would allow the policy makers to use more effective strategies with an adaptive nature. This is also indicated by the value of stochastic solution, which shows a significant enhancement in disease control gained by the stochastic programming solution compared to a plan based on expected figures.
Open Access
A Benders decomposition approach for the charging station location problem with plug-in hybrid electric vehicles
(Elsevier, 2016) Arslan, O.; Karaşan, O. E.
The flow refueling location problem (FRLP) locates p stations in order to maximize the flow volume that can be accommodated in a road network respecting the range limitations of the vehicles. This paper introduces the charging station location problem with plug-in hybrid electric vehicles (CSLP-PHEV) as a generalization of the FRLP. We consider not only the electric vehicles but also the plug-in hybrid electric vehicles when locating the stations. Furthermore, we accommodate multiple types of these vehicles with different ranges. Our objective is to maximize the vehicle-miles-traveled using electricity and thereby minimize the total cost of transportation under the existing cost structure between electricity and gasoline. This is also indirectly equivalent to maximizing the environmental benefits. We present an arc-cover formulation and a Benders decomposition algorithm as exact solution methodologies to solve the CSLP-PHEV. The decomposition algorithm is accelerated using Pareto-optimal cut generation schemes. The structure of the formulation allows us to construct the subproblem solutions, dual solutions and nondominated Pareto-optimal cuts as closed form expressions without having to solve any linear programs. This increases the efficiency of the decomposition algorithm by orders of magnitude and the results of the computational studies show that the proposed algorithm both accelerates the solution process and effectively handles instances of realistic size for both CSLP-PHEV and FRLP.
Open Access
Bounds on risk-averse mixed-integer multi-stage stochastic programming problems with mean-CVaR
(Elsevier B.V., 2018) Mahmutoğulları, Ali İrfan; Çavuş, Özlem; Aktürk, M. Selim
Risk-averse mixed-integer multi-stage stochastic programming forms a class of extremely challenging problems since the problem size grows exponentially with the number of stages, the problem is non-convex due to integrality restrictions, and the objective function is nonlinear in general. We propose a scenario tree decomposition approach, namely group subproblem approach, to obtain bounds for such problems with an objective of dynamic mean conditional value-at-risk (mean-CVaR). Our approach does not require any special problem structure such as convexity and linearity, therefore it can be applied to a wide range of problems. We obtain lower bounds by using different convolution of mean-CVaR risk measures and different scenario partition strategies. The upper bounds are obtained through the use of optimal solutions of group subproblems. Using these lower and upper bounds, we propose a solution algorithm for risk-averse mixed-integer multi-stage stochastic problems with mean-CVaR risk measures. We test the performance of the proposed algorithm on a multi-stage stochastic lot sizing problem and compare different choices of lower bounds and partition strategies. Comparison of the proposed algorithm to a commercial solver revealed that, on the average, the proposed algorithm yields 1.13% stronger bounds. The commercial solver requires additional running time more than a factor of five, on the average, to reach the same optimality gap obtained by the proposed algorithm.
Open Access
A capacitated hub location problem under hose demand uncertainty
(Elsevier, 2017) Meraklı, M.; Yaman, H.
In this study, we consider a capacitated multiple allocation hub location problem with hose demand uncertainty. Since the routing cost is a function of demand and capacity constraints are imposed on hubs, demand uncertainty has an impact on both the total cost and the feasibility of the solutions. We present a mathematical formulation of the problem and devise two different Benders decomposition algorithms. We develop an algorithm to solve the dual subproblem using complementary slackness. In our computational experiments, we test the efficiency of our approaches and we analyze the effects of uncertainty. The results show that we obtain robust solutions with significant cost savings by incorporating uncertainty into our problem.
Embargo
Drones for relief logistics under uncertainty after an earthquake
(Elsevier BV, 2023-03-03) Dükkancı, Okan; Koberstein, Achim; Kara, Bahar Y.
This study presents a post-disaster delivery problem called the relief distribution problem using drones under uncertainty, in which critical relief items are distributed to disaster victims gathered at assembly points after a disaster, particularly an earthquake. Because roads may be obstructed by debris after an earthquake, drones can be used as the primary transportation mode. As the impact of an earthquake cannot be easily predicted, the demand and road network uncertainties are considered. Additionally, the objective is to minimize the total unsatisfied demand subject to a time-bound constraint on the deliveries, as well as the range and capacity limitations of drones. A two-stage stochastic programming and its deterministic equivalent problem formulations are presented. The scenario decomposition algorithm is implemented as an exact solution approach. To apply this study to real-life applications, a case study is conducted based on the western (European) side of Istanbul, Turkey. The computational results are used to evaluate the performance of the scenario decomposition algorithm and analyze the value of stochasticity and the expected value of perfect information under different parametric settings. We additionally conduct sensitivity analyses by varying the key parameters of the problem, such as the time-bound and capacities of the drones.
Open Access
Gain-loss pricing under ambiguity of measure
(E D P Sciences, 2010) Pınar, M. Ç.
Motivated by the observation that the gain-loss criterion, while offering economically meaningful prices of contingent claims, is sensitive to the reference measure governing the underlying stock price process (a situation referred to as ambiguity of measure), we propose a gain-loss pricing model robust to shifts in the reference measure. Using a dual representation property of polyhedral risk measures we obtain a one-step, gain-loss criterion based theorem of asset pricing under ambiguity of measure, and illustrate its use.
Embargo
Index policy for multiarmed bandit problem with dynamic risk measures
(Elsevier BV, 2023-08-06) Malekipirbazari, Milad; Çavus, Özlem
The multiarmed bandit problem (MAB) is a classic problem in which a finite amount of resources must be allocated among competing choices with the aim of identifying a policy that maximizes the expected total reward. MAB has a wide range of applications including clinical trials, portfolio design, tuning parameters, internet advertisement, auction mechanisms, adaptive routing in networks, and project management. The classical MAB makes the strong assumption that the decision maker is risk-neutral and indifferent to the variability of the outcome. However, in many real life applications, these assumptions are not met and decision makers are risk-averse. Motivated to resolve this, we study risk-averse control of the multiarmed bandit problem in regard to the concept of dynamic coherent risk measures to determine a policy with the best risk-adjusted total discounted return. In respect of this specific setting, we present a theoretical analysis based on Whittle’s retirement problem and propose a priority-index policy that reduces to the Gittins index when the level of risk-aversion converges to zero. We generalize the restart formulation of the Gittins index to effectively compute these risk-averse allocation indices. Numerical results exhibit the excellent performance of this heuristic approach for two well-known coherent risk measures of first-order mean-semideviation and mean-AVaR. Our experimental studies suggest that there is no guarantee that an index-based optimal policy exists for the risk-averse problem. Nonetheless, our risk-averse allocation indices can achieve optimal or near-optimal policies which in some instances are easier to interpret compared to the exact optimal policy.
Embargo
Maintaining fairness in stochastic chemotherapy scheduling
(2024-06) Çelik, Batuhan
Chemotherapy scheduling is hard to manage under uncertainty in infusion durations, and focusing on expected performance measure values may lead to unfavorable outcomes for some patients. We aim to design daily patient appointment schedules considering fairness regarding patient waiting times. We propose using a metric that encourages fairness and efficiency in waiting time allocations. To optimize this metric, we formulate a two-stage stochastic mixed-integer nonlinear programming model. We employ a binary search algorithm to identify an optimal schedule, and then propose a modified binary search algorithm (MBSA) to enhance computational capability. Moreover, to address stochastic feasibility problems at each MBSA iteration, we introduce a novel reduce-and-augment algorithm that utilizes scenario set reduction and augmentation methods. We use real data from a major oncology hospital to show the efficacy of MBSA. We compare the schedules identified by MBSA with both the baseline schedules from the oncology hospital and those generated by commonly employed scheduling heuristics. We also compare our metric with a well-known inequity metric (the Gini coefficient) and a Rawlsian-type welfare function. Finally, we highlight the significance of considering uncertainty in infusion durations to maintain fairness while creating appointment schedules.
Open Access
A multi-stage stochastic programming approach in master production scheduling
(Elsevier, 2011) Körpeoğlu, E.; Yaman, H.; Aktürk, M. S.
Master Production Schedules (MPS) are widely used in industry, especially within Enterprise Resource Planning (ERP) software. The classical approach for generating MPS assumes infinite capacity, fixed processing times, and a single scenario for demand forecasts. In this paper, we question these assumptions and consider a problem with finite capacity, controllable processing times, and several demand scenarios instead of just one. We use a multi-stage stochastic programming approach in order to come up with the maximum expected profit given the demand scenarios. Controllable processing times enlarge the solution space so that the limited capacity of production resources are utilized more effectively. We propose an effective formulation that enables an extensive computational study. Our computational results clearly indicate that instead of relying on relatively simple heuristic methods, multi-stage stochastic programming can be used effectively to solve MPS problems, and that controllability increases the performance of multi-stage solutions.
Embargo
Optimization of pumped hydro energy storage systems under uncertainty: A review
(Elsevier, 2023-12-20) Toufani, P.; Karakoyun, E. Ç.; Nadar, Emre; Fasso, O. B.; Kocaman, Ayşe Selin
This paper provides an overview of the research dealing with optimization of pumped hydro energy storage (PHES) systems under uncertainty. This overview can potentially stimulate the scientific community’s interest and facilitate future research on this topic. We review the literature from various perspectives, including the optimization problem type, objective function, physical characteristics of the PHES facility, paradigm used to capture uncertainty, and solution method adopted. We then identify several research gaps and future research directions for energy researchers. This review highlights the need for developing optimization models such as Markov decision processes that can represent uncertainties in renewable energy sources and electricity markets more accurately, constructing multi-objective models that consider not only economic but also environmental impacts, investigating underrepresented solar-PHES systems and PHES sizing problems, addressing nonlinear characteristics of PHES facilities, and optimizing bidding strategies in sequential or coordinated electricity markets.
Open Access
Optimizing airline operations under uncertainty
(2019-06) Aydıner, Özge Şafak
Fluctuations in passenger demand, airport congestion, and high fuel costs are the main threats to airlines' profit, thereby need to be carefully addressed in airline scheduling problems. This study takes an advantage of aircraft cruise speed control in several scheduling problems to keep the cost of fuel manageable. We first generate a flight schedule by integrating strategic departure time decisions, tactical eeting and routing decisions and more operational flight timing decisions under stochastic demand and non-cruise times. Our model differs from the existing studies by including aircraft cruise speed decisions to compensate for increase in non-cruise time variations due to the airport congestion. To e ciently solve the problem, we provide a scenario group-wise decomposition algorithm. Then, we consider a new problem which aims to accommodate new flights into an existing flight schedule in a short time. We suggest some operational changes such as controlling the aircraft cruise speed, re-timing flight departures and swapping aircraft to open up time for new flights. However, nonlinear fuel cost function, and binary assignment and swapping decisions significantly increase the computational burden of solving scheduling problems. In this thesis, we propose strong mixed integer conic quadratic formulations. Finally, we extend the problem by including a strategic decision to lease an aircraft for introducing new flights. More importantly, we consider the effects of departure time decisions on the probability distribution of random demand. We propose a bounding method based on scenario group-wise decomposition for stochastic programs with decision dependent probabilities.
Open Access
Renewable energy system design and operational planning for demand fulfillment
(2024-08) Yurter, Gülin
Renewable energy sources have gained prominence in reducing the dependency on fossil fuels and minimizing their negative environmental impacts. Considering renewables' uncertain and variable nature, an effective design and operational planning of hybrid energy systems is key to success in clean energy transition. We study the optimal design and operational planning problem of hybrid energy systems involving a renewable energy source and a storage unit. We first develop two-stage stochastic mixed-integer programming models to determine the optimal sizing and investment decisions for solar/wind farms co-operated with pumped hydro energy storage facilities in decentralized areas. We then utilize a Markov decision process to find the optimal energy generation and storage decisions for decentralized grid-connected wind farm-battery systems with demand-fulfillment obligations. This is a novel study that compares several pumped hydro energy storage configurations with respect to optimal sizing decisions for system components and allows for uncertainties in electricity price, wind speed, and electricity demand for optimal operational planning. Using real-life data and considering economic benefits, we demonstrate how the renewable energy systems should be designed and managed to mitigate the adverse effects of uncertainties in matching supply with demand.
Open Access
Robust scenario optimization based on downside-risk measure for multi-period portfolio selection
(Springer, 2007) Pınar, M. Ç.
We develop and test multistage portfolio selection models maximizing expected end-of-horizon wealth while minimizing one-sided deviation from a target wealth level. The trade-off between two objectives is controlled by means of a non-negative parameter as in Markowitz Mean-Variance portfolio theory. We use a piecewise-linear penalty function, leading to linear programming models and ensuring optimality of subsequent stage decisions. We adopt a simulated market model to randomly generate scenarios approximating the market stochasticity. We report results of rolling horizon simulation with two variants of the proposed models depending on the inclusion of transaction costs, and under different simulated stock market conditions. We compare our results with the usual stochastic programming models maximizing expected end-of-horizon portfolio value. The results indicate that the robust investment policies are indeed quite stable in the face of market risk while ensuring expected wealth levels quite similar to the competing expected value maximizing stochastic programming model at the expense of solving larger linear programs.
Open Access
A two-stage decision dependent stochastic approach for airline flight network expansion
(Elsevier Ltd, 2022-02-28) Şafak, Ö.; Çavuş, Özlem; Aktürk, M. Selim
Airlines need to expand their flight networks with developing new routes and introducing more flights to increase their market share. In this work, we propose a two-stage stochastic mixed integer nonlinear program (MINLP), which expands an existing flight schedule by operating new flights either with existing fleet resources or a leased aircraft while considering the impact of departure time decisions on the probability distribution of random demand. Moreover, our study helps an airline to link a strategic decision of leasing an aircraft to the tactical aircraft assignment decisions by considering fuel efficiency and seat capacity of the aircraft alternatives in response to new passenger demand. However, the large number of scenarios, nonlinear fuel burn function and nonlinearities due to the decision dependent probabilities become main challenges of solving the problem. In order to deal with the computational requirements of a two-stage stochastic MINLP with decision dependent probabilities, we propose strong conic quadratic and McCormick inequalities, and an exact scenario group wise decomposition algorithm along with a new bounding method. In our computational results, we clearly demonstrate the effectiveness of proposed decomposition algorithm and the strength of the reformulations.
Open Access
A two-stage stochastic programming approach for reliability constrained power system expansion planning
(Elsevier, 2018) Peker, Meltem; Kocaman, Ayşe Selin; Kara, Bahar Yetiş
Probabilistic realizations of outages and their effects on the operational costs are highly overlooked aspects in power system expansion planning. Since the effect of randomness in contingencies can be more prominent especially when transmission switching is considered, in this paper we introduce contingency-dependent transmission switching concept to ensure N-1 criterion. To include randomness of outages and the outputs (i.e. flow on the lines/generation amounts) during the outages, we represent each contingency by a single scenario. Status of transmission lines, generation amounts and power flow decisions are defined as recourse actions of our two-stage stochastic model, therefore, expected operational cost during the contingencies are taken into account in a more accurate manner. A solution methodology with a filtering technique is also proposed to overcome the computational burden. The model and the solution methodology are tested on the IEEE Reliability Test System and IEEE 118-bus power system and the results show that the solution method finds the solutions for these power systems in significantly shorter solution times. The solution method is also tested on a new data set for the 380-kV Turkish transmission network. Suggestions for possible extensions of the problem and the modifications of the solution approach to handle these extensions are also discussed.
Open Access
The value of multi-stage stochastic programming in risk-averse unit commitment under uncertainty
(IEEE, 2019) Mahmutoğulları, Ali İrfan; Ahmed, S.; Çavuş, Özlem; Aktürk, M. Selim
Day-ahead scheduling of electricity generation or unit commitment is an important and challenging optimization problem in power systems. Variability in net load arising from the increasing penetration of renewable technologies has motivated study of various classes of stochastic unit commitment models. In two-stage models, the generation schedule for the entire day is fixed while the dispatch is adapted to the uncertainty, whereas in multi-stage models the generation schedule is also allowed to dynamically adapt to the uncertainty realization. Multi-stage models provide more flexibility in the generation schedule; however, they require significantly higher computational effort than two-stage models. To justify this additional computational effort, we provide theoretical and empirical analyses of the value of multi-stage solution for risk-averse multi-stage stochastic unit commitment models. The value of multi-stage solution measures the relative advantage of multi-stage solutions over their two-stage counterparts. Our results indicate that, for unit commitment models, the value of multi-stage solution increases with the level of uncertainty and number of periods, and decreases with the degree of risk aversion of the decision maker.