Probabilistic programming models for traffic incident management operations planning

This paper proposes mathematical programming models with probabilistic constraints in order to address incident response and resource allocation problems for the planning of traffic incident management operations. For the incident response planning, we introduce the concept of quality of service during a potential incident to give the decision-maker the flexibility to determine the optimal policy in response to various possible situations. An integer programming model with probabilistic constraints is proposed to address the incident response problem with consideration given to the stochastic resource requirements at the sites of incidents. For the resource allocation planning, assuming that the stochastic distribution of incidents over a network is given, we introduce a mathematical model to determine the number of service vehicles allocated to each depot to meet the requirements of the incidents by taking into account the stochastic nature of the resource requirement and incident occurrence probabilities. Several examples are included to demonstrate the applications of these models to real-world problems. This paper concludes with a summary of results and recommendations for future research. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 Probabilistic Programming Models for Traffic Incident Management Operations Planning Kaan Ozbay, Ph.D., Professor, Department of Civil and Environment Engineering, Rutgers University, 623 Bowser Road, Piscataway, NJ 08854-8014 [email protected], (732)445-2792, fax (732)445-0544 Cem Iyigun, Ph.D., Assistant Professor, Department of Industrial Engineering, Middle East Technical University, Ankara, TURKEY [email protected] Melike Baykal-Gursoy, Ph.D., Associate Professor, Department of Industrial and Systems Engineering, Rutgers University, 96 Frelinghuysen Road, Piscataway, NJ 08854-8018 [email protected], (732)445-5465, fax (732)445-5465 Weihua Xiao, Ph.D. Capital One [email protected] Manuscript Click here to download Manuscript: Iyigun-etal-IndicentManagament.doc Click here to view linked References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 1 ABSTRACT This paper proposes mathematical programming models with probabilistic constraints in order to address incident response and resource allocation problems for the planning of traffic incident management operations. For the incident response planning, we introduce the concept of quality of service during a potential incident to give the decision-maker the flexibility to determine the optimal policy in response to various possible situations. An integer programming model with probabilistic constraints is proposed to address the incident response problem with consideration given to the stochastic resource requirements at the sites of incidents. For the resource allocation planning, assuming that the stochastic distribution of incidents over a network is given, we introduce a mathematical model to determine the number of service vehicles allocated to each depot to meet the requirements of the incidents by taking into account the stochastic nature of the resource requirement and incident occurrence probabilities. Several examples are included to demonstrate the applications of these models to real-world problems. This paper concludes with a summary of results and recommendations for future research.