A two-stage stochastic programming model for phlebotomist scheduling in hospital laboratories

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.

In this paper, the uncertain duration of the section blockade is considered for the high-speed railway train timetable rescheduling problem with the entire section blockade. The objective is to minimize the conditional value-at-risk of the train delay by retiming, reordering, etc. A two-stage stochastic mixed-integer linear programming model is established for the train rescheduling problem in a macroscopic view. Some model approximation methods with scenarios are applied to speed up the solution process. The proposed models are solved by the GUROBI commercial solver. Numerical experiments are performed based on the Beijing-Tianjin intercity railway to show the effectiveness of the proposed stochastic programming model. The experimental results showed that the proposed model with scenario reduction and order scenario reduction could get a high- quality solution with a shorter computation time.

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.

How should water resources be allocated for shale gas development? An exploratory study in China

To mitigate outpatient care delivery inefficiencies induced by resource shortages and demand heterogeneity, this paper focuses on the problem of allocating and sequencing multiple medical resources so that patients scheduled for clinical care can experience efficient and coordinated care with minimum total waiting time. We leverage highly granular location data on people and medical resources collected via Real-Time Location System technologies to identify dominant patient care pathways. A novel two-stage Stochastic Mixed Integer Linear Programming model is proposed to determine the optimal patient sequence based on the available resources according to the care pathways that minimize patients’ expected total waiting time. The model incorporates the uncertainty in care activity duration via sample average approximation.We employ a Monte Carlo Optimization procedure to determine the appropriate sample size to obtain solutions that provide a good trade-off between approximation accuracy and computational time. Compared to the conventional deterministic model, our proposed model would significantly reduce waiting time for patients in the clinic by 60%, on average, with acceptable computational resource requirements and time complexity. In summary, this paper proposes a computationally efficient formulation for the multi-resource allocation and care sequence assignment optimization problem under uncertainty. It uses continuous assignment decision variables without timestamp and position indices, enabling the data-driven solution of problems with real-time allocation adjustment in a dynamic outpatient environment with complex clinical coordination constraints.

Risk management optimization framework for the optimal deployment of carbon capture and storage system under uncertainty

This work presents the formulation of a two-stage stochastic mixed-integer linear programming (MILP) model to include uncertainty in the design of renewable-based utility plants. The model is based on a superstructure that integrates technologies to process biomass, waste, solar radiation, and wind and considers uncertainty in availability of the renewable resources and on the utility demands. The uncertain parameter space is calculated based on a monthly probability density function for each uncertain parameter and discretized into different levels. It is shown that as uncertainty is considered in the model formulation, design flexibility improves with respect to the deterministic-based designs, although the flexibility is achieved at the expense of higher underused facilities and therefore unused investment cost.

A stochastic linear programming model for maximizing generation and firm output at a reliability in long-term hydropower reservoir operation

Whole blood or apheresis donations? A multi-objective stochastic optimization approach

We develop a two-stage stochastic integer programming model for the simultaneous optimization of power production and day-ahead power trading in a hydro-thermal system. The model rests on mixed-integer linear formulations for the unit commitment problem and for the price clearing mechanism at the power exchange. Foreign bids enter as random components into the model. We solve the stochastic integer program by a decomposition method combining Lagrangian relaxation of nonanticipativity with branch-and-bound in the spirit of global optimization. Finally, we report some first computational experiences.

Islanding in distribution systems considering wind power and storage

The high cost of flight delays for airlines has motivated scientific research in air traffic flow management (ATFM). The majority of ATFM models in the literature are deterministic and do not take into account stochastic factors such as weather. In this paper, new stochastic programming models for ATFM are proposed. The models include as tactical control options: ground holding, airborne holding and rerouting. To solve the models, a new heuristic method that takes advantage of the problem structure is derived and illustrated. Computational results show that the heuristic method provides practical computation times. Furthermore, the value of the stochastic solution is up to 14% for cases where adverse weather affects a significant part of the network. This implies that using the proposed approach to make air traffic flow decisions can lead to tangible monetary benefits for airlines.

Supply chains are vulnerable to disruptions at any stage of the distribution system. These disruptions can be caused by natural disasters, production problems, or labor defects. The consequences of these disruptions may result in significant economic losses or even human deaths. Therefore, it is important to consider any disruption as an important factor in strategic supply chain design. Consequently, the primary outputs of this dissertation include insights for designing robust supply chains that are neither significantly nor adversely impacted by disruptions. The impact of correlated supplier failures is examined and how this problem can be modeled as a variant of a facility location problem is described. Two main problems are defined, the first being the design of a robust supply chain, and the second being the optimization of operational inspection schedules to maintain the quality of an already established supply chain. In this regard, both strategic and operational decisions are considered in the model and (1) a two-stage stochastic programming model; (2) a multi-objective stochastic programming model; and (3) a dynamic programming model are developed to explore the tradeoffs between cost and risk. Three methods are developed to identify optimal and robust solutions: an integer L-shaped method; a hybrid genetic algorithm using Data Envelopment Analysis; and an approximate dynamic programming method. Several sensitivity analyses are performed on the model to see how the model output would be affected by uncertainty. The findings from this dissertation will be able to help both practitioners designing supply chains, as well as policy makers who need to understand the impact of different disruption mitigation strategies on cost and risk in the supply chain.

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

A stochastic programming winner determination model for truckload procurement under shipment uncertainty