Approximating multiple class queueing models with loss models

Multiple class queueing models arise in situations where some flexibility is sought through pooling of demands for different services. Earlier research has shown that most of the benefits of flexibility can be obtained with only a small proportion of cross-trained operators. Predicting the performance of a system with different types of demands and operator pools with different skills is very difficult. We present an approximation method that is based on equivalent loss systems. We successively develop approximations for the waiting probability, The average waiting time and the service level. Our approximations are validated using a series of simulations. Along the way we present some interesting insights into some similarities between queueing systems and equivalent loss systems that have to our knowledge never been reported in the literature.

Resource constrained routing and scheduling: Review and research prospects

In the service industry, it is crucial to efficiently allocate scarce resources to perform tasks and meet particular service requirements. What considerably complicates matters is when these resources, for example skilled technicians, nurses, and home carers have to visit different customer locations. This paper provides a comprehensive survey on resource constrained routing and scheduling that unveils the problem characteristics with respect to resource qualifications, service requirements and problem objectives. It also identifies the most effective exact and heuristic algorithms for this class of problems. The paper closes with several research prospects

Pattern-based decompositions for human resource planning in home health care services

Home health care services play acrucial role in reducing the hospitalization costs due to the increase of chronic diseases of elderly people. At the same time, they allow us to improve the quality of life for those patients that receive treatments at their home. Optimization tools are therefore necessary to plan service delivery at patients' homes. Recently, solution methods that jointly address the assignment of the patient to the caregiver (assignment), the definition of the days (pattern) in which caregivers visit the assigned patients (scheduling), and the sequence of visits for each caregiver (routing) have been proposed in the scientific literature. However, the joint consideration of these three level of decisions may be not affordable for large providers, due to the required computational time. In order to combine the strength and the flexibility guaranteed by a joint assignment, scheduling and routing solution approach with the computational efficiency required for large providers, in this study we propose a new family of two-phase methods that decompose the joint approach by incrementally incorporating some decisions into the first phase.The concept of pattern is crucial to perform such a decomposition in a clever way. Several scenarios are analyzed by changing the way in which resource skills are managed and the optimization criteria adopted to guide the provider decisions. The proposed methods are tested on realistic instances. The numerical experiments help us to identify the combinations of decomposition techniques, skill management policies and optimization criteria that best fit with problem instances of different size

Integrating passenger and freight transportation : model formulation and insights

Integrating passenger and freight flows creates attractive business opportunities because the same transportation needs can be met with fewer vehicles and emissions. This paper seeks an integrated solution for the transportation of passenger and freight simultaneously, so that fewer vehicles are required. The newly introduced problem concerns scheduling a set of vehicles to serve the requests such that a part of the journey can be carried out on a scheduled passenger transportation service. We propose an arc-based mixed integer programming formulation for the integrated transportation system. Computational results on a set of instances provide a clear understanding on the benefits of integrating passenger and freight transportation in the current networks, considering multi-modality of traditional passenger-oriented transportation modes, such as taxi, bus, train or tram

Exact Models, Heuristics, and Supervised Learning Approaches for Vehicle Routing Problems

This dissertation presents contributions to the field of vehicle routing problems by utilizing exact methods, heuristic approaches, and the integration of machine learning with traditional algorithms. The research is organized into three main chapters, each dedicated to a specific routing problem and a unique methodology. The first chapter addresses the Pickup and Delivery Problem with Transshipments and Time Windows, a variant that permits product transfers between vehicles to enhance logistics flexibility and reduce costs. To solve this problem, we propose an efficient mixed-integer linear programming model that has been shown to outperform existing ones. The second chapter discusses a practical workforce scheduling problem, formulated as a specific type of vehicle routing problem. The objective here is to efficiently assign consultants to various clients and plan their trips. This computational challenge is addressed by using a two-stage approach: the first stage employs a mathematical model, while the second stage refines the solution with a heuristic algorithm. In the final chapter, we explore methods that integrate machine learning with traditional approaches to address the Traveling Salesman Problem, a foundational routing challenge. Our goal is to utilize supervised learning to predict information that boosts the efficiency of existing algorithms. Taken together, these three chapters offer a comprehensive overview of methodologies for addressing vehicle routing problems

Shortest Expected Delay Routing for Erlang Servers

The queueing problem with a Poisson arrival stream and two identical Erlang servers is analysed for the queueing discipline based on shortest expected delay. This queueing problem may be represented as a random walk on the integer grid in the first quadrant of the plane. In the paper it is shown that the equilibrium distribution of this random walk can be written as a countable linear combination of product forms. This linear combination is constructed in a compensation procedure. In this case the compensation procedure is essentially more complicated than in other cases where the same idea was exploited. The reason for the complications is that in this case the boundary consists of several layers which in turn is caused by the fact that transitions starting in inner states are not restricted to end in neighbouring states. Good starting solutions for the compensation procedure are found by solving the shortest expected delay problem with the same service distributions but with instantaneous jockeying. It is also shown that the results can be used for an efficient computation of relevant performance criteria

Personaneinsatz- und Tourenplanung für Mitarbeiter mit Mehrfachqualifikationen

In workforce routing and scheduling there are many applications in which differently skilled workers must perform jobs that occur at different locations, where each job requires a particular combination of skills. In many such applications, a group of workers must be sent out to provide all skills required by a job. Examples are found in maintenance operations, the construction sector, health care operations, or consultancies. In this thesis, we analyze the combined problem of composing worker groups (teams) and routing these teams under goals expressing service-, fairness-, and cost-objectives. We develop mathematical optimization models and heuristic solution methods for an integrated solution and a sequential solution of the teaming- and routing-subproblems . Computational experiments are conducted to identify the tradeoff of better solution quality and computational effort