Two-stage Stochastic Integer Linear Programming Research Articles

An optimization model for express delivery with high-speed railway

With the expansion of the high-speed railway (HSR) network in China, high-speed rail express delivery (HSReD) is being used to satisfy the increasing demand for express cargo. The decisions on transportation resources arrangement and freight flow allocation are two of the key issues for practical implementation of HSReD. In this study, we examine the above key issues by developing a two-stage stochastic integer linear programming model to maximize the expected net operation profit of HSReD. A meta-heuristic solution approach introduced some tailored tactics is proposed to speed up the process of solving the above model in the large-scale instances. Numerical experiments based on different sizes and practical investigation on China Railway Nanchang Group are conducted to validate the effectiveness of the proposed model and solution approach. Some managerial implications are also obtained based on the sensitivity analysis, which may be potentially useful for optimizing the daily operation management of HSReD.

A robust multiobjective integrated master surgery schedule and surgical case assignment model at a publicly funded hospital

This paper considers an integrated operating room (OR) planning and advanced scheduling problem in a surgery department comprising several specialties that share a fixed number of ORs and post-surgery beds. It jointly considers the allocation of surgical specialties to OR blocks together with the assignment of the subsets of patients from each specialty’s waiting list to the OR blocks over a one-week planning horizon. By integrating the master surgical schedule problem (MSSP) and surgical case assignment problem (SCAP), we extend the stability of the scheduling process. We consider both uncertain surgery durations and emergency arrivals. The aim of this study is to maximize both patient service levels and hospital efficiency. A multi-objective integer linear programming (MOILP) model is developed to minimize patient waiting times as well as to maximize the OR utilization rates. An Lp-metric methodology is applied to solve the final integrated objective function. The MOILP is transformed into a robust optimization model using a transformation framework. In addition, we develop a two-stage stochastic integer linear programming model. The effectiveness of three models is compared and demonstrated through an extensive numerical experiment carried out on a large set of instances based on real data.

A Multi-Depot Vehicle Routing Problem with Stochastic Road Capacity and Reduced Two-Stage Stochastic Integer Linear Programming Models for Rollout Algorithm

A matheuristic approach based on a reduced two-stage Stochastic Integer Linear Programming (SILP) model is presented. The proposed approach is suitable for obtaining a policy constructed dynamically on the go during the rollout algorithm. The rollout algorithm is part of the Approximate Dynamic Programming (ADP) lookahead solution approach for a Markov Decision Processes (MDP) framed Multi-Depot Dynamic Vehicle Routing Problem with Stochastic Road Capacity (MDDVRPSRC). First, a Deterministic Multi-Depot VRP with Road Capacity (D-MDVRPRC) is presented. Then an extension, MDVRPSRC-2S, is presented as an offline two-stage SILP model of the MDDVRPSRC. These models are validated using small simulated instances with CPLEX. Next, two reduced versions of the MDVRPSRC-2S model (MDVRPSRC-2S1 and MDVRPSRC-2S2) are derived. They have a specific task in routing: replenishment and delivering supplies. These reduced models are to be utilised interchangeably depending on the capacity of the vehicle, and repeatedly during the execution of rollout in reinforcement learning. As a result, it is shown that a base policy consisting of an exact optimal decision at each decision epoch can be obtained constructively through these reduced two-stage stochastic integer linear programming models. The results obtained from the resulting rollout policy with CPLEX execution during rollout are also presented to validate the reduced model and the matheuristic algorithm. This approach is proposed as a simple implementation when performing rollout for the lookahead approach in ADP.

An efficient stochastic programming for optimal allocation of combined heat and power systems for commercial buildings using

Advantages of combined heat and power system such as high efficiency, low environmental pollution, reliability and controllable output result in its widely application in commercial and residential buildings. Finding the optimal number and capacity of combined heat and power (CHP) units in commercial buildings is a challengeable issue. In this paper, an optimization method based on constrained index of reliability is used for optimal allocation of these systems. Hence, the value of lost load is considered as the reliability index. The random prediction errors of load and energy in CHP systems are modelled as a scenario based on Monte Carlo sampling procedure. Optimization is formulated by using a two-stage stochastic integer linear programming. To reduce the computation time, the number of scenarios has been reduced. Finally, the proposed model is used in a commercial building as a case study.

Locating unmanned aircraft systems for multiple missions under different weather conditions

Motivated by the increasing civilian use of Unmanned Aerial Vehicles (UAVs), this paper considers the simultaneous location and routing of UAVs for multiple missions and different weather conditions. We include modeling and computational experience inspired by requirements for air surveillance by the Turkish government’s public agencies. We model these demands in multiple mission areas and consider the impact of different weather conditions on the ability to employ UAVs from different geographic locations. We formulate the problem as a two-stage stochastic integer linear program with recourse and get an optimal solution for realistic test instances in a reasonable amount of time using decomposition by weather and mission combinations. We also introduce an optimization-based heuristic with bounds based on our decomposition for larger test instances.

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

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.

Proactive on-call scheduling during a seasonal epidemic

Overcrowding in Emergency Departments (EDs) is particularly problematic during seasonal epidemic crises. Each year during this period, EDs set off recourse actions to cope with the increase in workload. Uncertainty in the length and amplitude of epidemics make managerial decisions difficult. We propose in this study a staff allocation model to manage the situation using on-calls. An on-call scheduling policy is proposed to best balance between demand coverage and labor cost under legal constraints of working time. The problem is modeled as a two-stage stochastic Integer Linear Program (ILP) and solved using a Sample Average Approximation (SAA) method. Several epidemic scenarios are defined with data from an ED in Lille, France.