Introduction to stochastic programming

http://www.optimization-online.org/DB_FILE/2012/07/3537.pdf

Recent advances in robust optimization: An overview☆

Transportation Networks. Optimality. Cost Functions. Deterministic User Equilibrium Assignment. Stochastic User Equilibrium Assignment. Trip Table Estimation. Network Reliability. Network Design. Conclusions. References. Index.

Transportation network analysis

One-way station-based carsharing systems provide short term car rentals in which users can take a car from the initial station and return it to any other station. They are more flexible than round-trip carsharing, where the vehicle can only be returned to the station where it was picked up, and can be used for daily commuting trips as well. This flexibility, however, comes at a cost of vehicle stock imbalance within the network. Several solutions and strategies have been suggested to counter this problem, one of which is variable trip pricing. By charging high prices for the trips that increase imbalance and lowering prices for trips that help improve the balance, it has been hypothesized, but never demonstrated, that the clients’ behavior could be used to balance the vehicle stocks and thus make carsharing systems more manageable and profitable. In this paper, we develop a mixed integer non-linear programming (MINLP) model, defined as the Trip Pricing Problem for One-Way Carsharing Systems (TPPOCS), which sets these prices in order to maximize profit. An iterated local search (ILS) metaheuristic is proposed for solving it. The method is applied to the theoretical case-study of a network of 75 stations distributed across the city of Lisbon (Portugal). Although the implemented metaheuristic is tuned for the Lisbon example, the generic nature of its operators makes the model applicable elsewhere. The results demonstrate that the trip pricing strategy can be used to increase profit through a more balanced system. If no price-based balancing strategies are applied, operating this service results in a daily deficit of €1161. When the trip pricing policy is applied, profits of 2068 €/day are possible. The optimal prices are on average 23% higher than the base price, and 18% less demand is served, but the enhanced performance leads to lower expenses with the fleet of vehicles and number of parking spaces.

Trip pricing of one-way station-based carsharing networks with zone and time of day price variations

The fact that road transportation negatively affects the quality of the environment and deteriorates its bearing capacity has drawn a wide range of concerns among researchers. In order to provide more realistic traffic data for estimations of environmental impacts, dynamic traffic assignment (DTA) models have been adopted in transportation planning and traffic management models concerning environmental sustainability. This review summarizes and examines the recent methodological advances of DTA models in environmentally sustainable road transportation applications including traffic signal control concerning vehicular emissions and emission pricing. A classification of emission estimation models and their integration with DTA models are accordingly reviewed as supplementary to the existing reviews. Finally, a variety of future research prospects of DTA for environmentally sustainable road transportation research are discussed. In particular, this review also points out that at present the research about DTA models in conjunction with noise predictive models is relatively deficient.

/pdf/dynamic-traffic-assignment-a-review-of-the-methodological-3bvlfuxoae.pdf

Dynamic traffic assignment: A review of the methodological advances for environmentally sustainable road transportation applications

This paper provides a chance-constrained programming approach for transportation planning and operations under uncertainty. The major contribution of this paper is to approximate a joint chance-constrained Cell Transmission Model based System Optimum Dynamic Traffic Assignment with only partial distributional information about uncertainty as a linear program which is computationally efficient. Numerical experiments have been conducted to show the performance of the proposed approach compared with other two workable approaches based on a cumulative distribution function and a sampling method. This new approach can be used as a pragmatic tool for system optimum dynamic traffic control and management.

Dynamic Traffic Assignment under Uncertainty: A Distributional Robust Chance-Constrained Approach

Production planning is basically concerned with determining the production and inventory level over a finite planning horizon to satisfy customer demand in the most efficient way. Such a decision has long been an important issue in manufacturing since it leads higher utilization of resources and customer satisfaction, and eventually, more profit for a company. So far, several mathematical optimization models have been proposed, including linear programming, mixed integer programming, and goal programming (Nam and Logendran, 1992; Pochet and Wolsey, 2006). When researchers and practitioners develop mathematical models, dealing with uncertainty is recognized as a critical concern, since models without consideration of uncertainty can be expected to perform worse than the models accounting for the uncertainty (Mula et al., 2006). Ho (1989) classified several types of uncertainty affecting production processes into two groups: environmental uncertainty beyond the production processes, and system uncertainty within the production processes. Similarly, Ravindran and Warsing (2012) divided the sources of uncertainty into internal and external sources. Examples of system uncertainty are production lead time, yield, and quality. Environmental uncertainty includes demand uncertainty and supply uncertainty. Typically, environmental uncertainty is less manageable than system uncertainty, since it arises outside of a manufacturing system. Therefore, determining a robust production planning and inventory management policy that is less sensitive to environmental uncertainty may be one of the most effective ways to mitigate loss for a company. There have been several approaches to optimization under uncertainty, such as stochastic optimization (Birge and Louveaux, 1997; Shimizu et al, 2011) and robust optimization (RO) (Ben-Tal et al., 2009; Seo and Chung, 2014). In traditional stochastic optimization, it is assumed that an uncertain parameter follows a certain probability distribution, and an optimal solution minimizes the average objective value. In contrast, discrete scenarios or a continuous range is assumed in RO to find an optimal solution that minimizes the worst-case objective value. The use of discrete scenarios Kwang-Kyu SEO*, Jun KIM** and Byung Do CHUNG** *Department of Management Engineering, Sangmyung University 31, Sangmyungdea-gil, Dongnam-gu, Cheonan, Chungnam 330-720, Republic of Korea **Department of Industrial Engineering, Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon 440-746, Republic of Korea E-mail: bd.chung@skku.edu

https://www.jstage.jst.go.jp/article/jamdsm/9/5/9_2015jamdsm0067/_pdf

A minimax p-robust optimization approach for planning under uncertainty

This paper addresses certain misconceptions regarding what is known and what may be expected when performing sensitivity analyses of network user equilibrium flow patterns. Our presentation relies on a simple observation: any given user equilibrium sensitivity analysis technique should be employed only when the regularity conditions on which it is based are satisfied. Violating regularity, as we show through previously published numerical examples, as well as new examples presented here for the first time, may well lead to incorrect results when the Tobin-Friesz sensitivity analysis method is applied. This is especially so when the most critical regularity assumption of the Tobin-Friesz method, namely that the unperturbed solution must be a nondegenerate extreme point, is violated. We also illustrate how a degenerate unperturbed solution may sometimes be modified to obtain an appropriate nondegenerate solution, thereby allowing the Tobin-Friesz method to be applied.

/pdf/sensitivity-analysis-of-user-equilibrium-flows-revisited-54e1po9k7b.pdf

Sensitivity Analysis of User Equilibrium Flows Revisited

The spread of emerging devices such as smartphone and Tablet PC enables people to experience an unprecedented technology innovation. However, some smartphone users show their intentions to reuse the feature phone due to the increased stress and pressure caused by a lot of functions of the smartphone. This study explores that the technology innovation doesn't provide all the people with the same level of values and satisfactions. A paper and pencil survey is employed with 3,798 mobile users randomly selected from 10's to 60's in Korea and asks them to answer the devices, ICT services, and applications in use, and the degree of their satisfactions as well as their perceived values and reuse intentions. Results show that the effects of technology innovation are different depending on mobile users' perceived value of technology innovation and price-value scheme, satisfaction of mobile service in use, and ages.

Do All People Enjoy the Benefits from Technology Innovation

and Nemirovski (1999, 2000) and Bertsimas and Sim (2003, 2004). RO differs from stochastic programming in that the objective is to find the best worst-case solution, which is a solution that performs well even in a worst case scenario. RO has several advantages. First, RO does not require probability distribution information or scenarios to

Robust optimization for identical parallel machine scheduling with uncertain processing time

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Byung Do Chung

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