Line Blander Reinhardt

Multi-objective and multi-constrained non-additive shortest path problems

Shortest path problems appear as subproblems in numerous optimization problems. In most papers concerning multiple objective shortest path problems, additivity of the objective is a de-facto assumption, but in many real-life situations objectives and criteria, can be non-additive. The purpose of this paper is to give a general framework for dominance tests for problems involving a number of non-additive criteria. These dominance tests can help to eliminate paths in a dynamic programming framework when using multiple objectives. Results on real-life multi-objective problems containing non-additive criteria are reported. We show that in many cases the framework can be used to efficiently reduce the number of generated paths.

Synchronized dial-a-ride transportation of disabled passengers at airports

The largest airports have a daily average throughput of more than 500 passengers with reduced mobility. The problem of transporting these passengers is in some cases a multi-modal transportation problem with synchronization constraints. A description of the problem together with a mathematical model is presented. The objective is to schedule as many of the passengers as possible, while ensuring a smooth transport with short waiting times. A simulated annealing based heuristic for solving the problem is presented. The algorithm makes use of an abstract representation of a candidate solution which in each step is transformed to an actual schedule by use of a greedy heuristic. Local search is performed on the abstract representation using advanced neighborhoods which modify large parts of the candidate solution. Computational results show that the algorithm is able to find good solutions within a couple of minutes, making the algorithm applicable for dynamic scheduling. Moreover high-quality solutions can be obtained by running the algorithm for 10minutes.

Optimization of hospital ward resources with patient relocation using Markov chain modeling

Overcrowding of hospital wards is a well-known and often revisited problem in the literature, yet it appears in many different variations. In this study, we present a mathematical model to solve the problem of ensuring sufficient beds to hospital wards by re-distributing beds that are already available to the hospital. Patient flow is modeled using a homogeneous continuous-time Markov chain and optimization is conducted using a local search heuristic. Our model accounts for patient relocation, which has not been done analytically in literature with similar scope. The study objective is to ensure that patient occupancy is reflected by our Markov chain model, and that a local optimum can be derived within a reasonable runtime.

Solving vehicle routing with full container load and time windows

A service provided by the liner shipping companies is the transport of containers by truck between the terminal and customers. These transports consist of import orders and export orders. Even though these transports concern containers and, therefore, each order is a full load, an import and an export order can be combined in one trip where the container is emptied at an import customer and taken to an export customer to be filled. Finding a set of optimal vehicle routes allowing these combinations is NP-hard. However, exploring the fact that the number of possible routes is small in the problem presented, we in this report show a model which can within seconds solve the problem to optimality. The model is tested on real-life data sets and additional constraints to the problem are considered.

Bounding component sizes of two-connected Steiner networks

Abstract We consider the problem of constructing a shortest Euclidean 2-connected Steiner network in the plane (SMN) for a set of n terminals. This problem has natural applications in the design of survivable communication networks. In [P. Winter, M. Zachariasen, Two-connected Steiner networks: Structural properties, OR Letters 33 (2005) 395–402] we proved that all cycles in SMNs with Steiner points must have pairs of consecutive terminals of degree 2. We use this result and the notion of reduced block-bridge trees suggested by Luebke [E.L. Luebke, k-connected Steiner network problems, PhD thesis, University of North Carolina, USA, 2002] to show that no full Steiner tree in a SMN spans more than ⌊ n / 3 ⌋ + 1 terminals.

Optimization of the drayage problem using exact methods

Abstract Major liner shipping companies offer pre- and end-haulage as part of a door-to-door service, but unfortunately pre- and end-haulage is frequently one of the major bottlenecks in efficient liner shipping due to the lack of coordination between customers. In this paper, we apply techniques from vehicle routing problems to schedule pre- and end-haulage of containers, and perform tests on data from a major liner shipping company. The paper considers several versions of the scheduling problem such as having multiple empty container depots, and having to balance the empty container depot levels. The influence of the side constraints on the overall cost is analysed. By exploring the fact that the number of possible routes in the considered case is quite limited, we show that the model can be solved within a minute by use of column enumeration. Alternative constraints and problem formulations, such as balancing empty container storage level at depots, are considered. Computational results are reported on real-life data from a major liner shipping company.

Staff optimization for time-dependent acute patient flow

Abstract The emergency department is a key element of acute patient flow, but due to high demand and an alternating rate of arriving patients, the department is often challenged by insufficient capacity. Proper allocation of resources to match demand is, therefore, a vital task for many emergency departments. Constrained by targets on patient waiting time, we consider the problem of minimizing the total amount of staff-resources allocated to an emergency department. We test a matheuristic approach to this problem, accounting for both patient flow and staff scheduling restrictions. Using a continuous-time Markov chain, patient flow is modeled as a time-dependent queueing network where inhomogeneous behavior is evaluated using the uniformization method. Based on this modeling approach, we recursively evaluate and allocate staff to the system using integer linear programming until the waiting time targets are respected in all queues of the network. By comparing to discrete-event simulations of the associated system, we show that this approach is adequate for both modeling and optimizing the patient flow. In addition, we demonstrate robustness to the service time distribution and the associated system with multiple classes of patients.

Exact Methods and Heuristics for the Liner Shipping Crew Scheduling Problem

In this paper the liner shipping crew scheduling problem is described and modelled. Three different models have been formulated and tested for the scheduling problem. A mixed integer formulation and a set covering formulation are constructed and solved using exact methods. A mat-heuristic based on column generation has been implemented and tested. Moreover, a simple heuristic is implemented as a benchmark value. The models and methods were tested on smaller instances of the problem. The results show that good results can be achieved within 5 min using the heuristic and around an hour using the set partitioning formulation.

The Liner Shipping Routing and Scheduling Problem Under Environmental Considerations: The Case of Emissions Control Areas

This paper deals with the Liner Shipping Routing and Scheduling Problem (LSRSP), which consists of designing the time schedule for a vessel to visit a fixed set of ports while minimizing costs. We extend the classical problem to include the external cost of ship air emissions and we present some results of our work investigating the impact of Emission Control Areas in the routing and scheduling of liner vessels.