Title: Fairness-driven mid term scheduling of medical staff at a hospital network

Authors:  Marco Roma (University of Florence, Italy), Maddalena Nonato (University of Ferrara, Italy), Paola Cappanera (University of Florence, Italy), Marco Gavanelli (University of Ferrara, Italy) and Niccolò Fabbri(Ospedale del Delta, Ferrara, Italy)

Abstract: This study deals with a staff scheduling problem concerning physicians working at the surgical department of a four hospital local area network. The problem shares some features of classical scheduling problems, i.e., a set of tasks, which repeat on a weekly basis, must be assigned to a set of workers according to a set of rules, possibly meeting a few criteria. However, staff members present different professional profiles, while tasks differ in required skills, duration, frequency, and location. In addition, this problem differs from a classic scheduling problem because of articulated staff preferences. In fact, although the main objective is to cover all tasks, some physician-shift assignment should be avoided whenever possible, while some working patterns are highly desirable. Beside the challenges posed by feasibility constraints, fairness related issues sharply arise in the mid term. Indeed, each physician may accumulate different overtime hours, according to specific rules, and different working hours, possibly leading to different remuneration. Therefore, working time should be fairly balanced in a mid term horizon among the different physicians. Moreover, differences arise because of the variety of tasks and physicians skills, and achieving fairness by simply rotating tasks among different people is not viable. Moreover, because of this diversity, a priori there is no ideal workload threshold whose distance from may return a measure of fairness. In our proposal, fairness can be improved by trying to bring all the workers to the same level of satisfied preferences over a mid term time period. Besides, in addition to compulsory requirements, many soft preferences are present. We propose to tackle the problem by Answer Set Programming, as it easily handles preferences and soft constraints and we use the Clingo solver. The aim of the project is to provide the administration of the hospital network with a flexible and customizable tool, able to deal with staff preferences and handling fairness related issues over a mid term period. Computational results on real data will be provided

Title: The 'Healthcare Access and Quality Index' revisited: A fuzzy Data Envelopment Analysis approach

Authors : Miguel Pereira (IST, ULisboa)

Abstract: Nowadays, health systems comprise a series of resources structured to provide healthcare services to meet our health needs. However, premature deaths still occur. To quantify and understand personal healthcare conditions affecting such amenable mortality, the Healthcare Access and Quality Index (HAQI) was put forward, evaluating 195 countries and territories since 1990. Nevertheless, the literature acknowledges a series of limitations of this framework, such as the drawbacks of using principal component analysis to aggregate individual indicators, the absence of control for financing and environmental conditions, and the presence of a substantial degree of data uncertainty. Accordingly, we propose a methodological alternative to the computation of the HAQI using a novel fuzzy Data Envelopment Analysis model to handle the aforementioned shortcomings. We also propose its extension towards the quantification of efficiency (E-HAQI) - in the sense of value for money - by incorporating financial aspects as modelling inputs. This way, we contribute with innovative modelling approaches that can also deal with the high degree of data uncertainty. Furthermore, in a second-stage analysis, the impact of key exogenous factors on healthcare access and quality is assessed via non-parametric hypothesis testing. Our results show positive and significant correlations of both the revisited HAQI and E-HAQI with the original HAQI 2016 dataset. They also reveal a better use of resources by European and Oceanian countries and territories than by Sub-Saharan African ones. Concerning contextual determinants, socio-demographic development, human development, and the type of health system were found to be statistically significant drivers of healthcare access and quality efficiency.

Title: Last-Mile Logistics in London

Authors:Tolga Bektaş (Management School, University of Liverpool)

Abstract: Freight shipped on light and heavy goods vehicles makes up 23% of all road vehicle activity in the UK, with commercial van traffic increasing year-on-year. In the UK alone, the volume of the parcel market reached 3.8 billion items in 2021-22, giving rise to significant operational challenges in delivering the 'last-mile'. In this talk, I will present findings of the research project FTC2050: Freight Traffic Control 2050, that looked at the impact of current 'business-as-usual' carrier activities in London. I will describe the modus operandi and the practical issues faced by last-mile logistics providers, present alternative distribution strategies to help improve the efficiency of the operations, discuss the associated mathematical modelling challenges, and present some results. This talk is based on joint work with co-authors from the Universities of Lancaster, Southampton, Westminster and UCL.

Title: Node based compact formulations for the Hamiltonian p-Median Problem

Authors: Francisco Canas (DEIO, Ciências, ULisboa), Michele Barbato (Dipartimento di Informatica “Giovanni Degli Antoni”, Università degli Studi di Milano, Italy), Luís Gouveia (CMAFcIO, Ciências, ULisboa), and Pierre Pesneau (Université Bordeaux, CNRS, INRIA)

Abstract: We introduce and study new compact models for the symmetric Hamiltonian p-Median Problem (HpMP), and compare these with other compact models known from the literature (see [1], [2]). Given a weighted undirected graph G=(V,E) with weights on the edges and a positive integer p, the HpMP on G is to find a minimum weight set of p elementary cycles partitioning the vertices of G. Compact models have the advantage of being convenient and easily used in combination with off-the-shelf optimization software, unlike other types of models. We focus on models for eliminating solutions with less than p cycles, as such models are less well known than ones which prevent solutions with more than p cycles. The new models consider variables that assign labels to nodes, using these labels to prevent solutions with less than p cycles. They are partitioned into two classes - node-depot assignment models (the label corresponds to the index of the depot of the cycle the node belongs to, similar to models from [3] and [4]) and node-cycle assignment models (the label corresponds to the number of the cycle the node belongs to). We also present enhancements for each class of models. The main conclusions of this study are: i) most of the proposed enhancements result in lower computational times; ii) the new compact models are more effective than the other compact models from the literature; iii) the new node-depot assignment models result in the lowest computational times.

[1] Gollowitzer S., Lucas Pereira D., Wojciechowski A. “New Models for and Numerical Tests of the Hamiltonian p-Median Problem”, Network Optimization, 385–394 (2011)

[2] Gollowitzer S., Gouveia L., Laporte G., Lucas Pereira D., Wojciechowski A. “A Comparison of Several Models for the Hamiltonian p-Median Problem”, Networks, 63, No. 4, 350–363 (2014)

[3] Burger M., Su Z., De Schutter B. “A node currentbased 2-index formulation for the fixed-destination multi-depot travelling salesman problem”, European Journal of Operational Research, 265, No. 2, 463– 477 (2018).

[4] Bektaş T., Gouveia L., Santos D. “Compact formulations for multi-depot routing problems: Theoretical and computational comparisons”, Computers & Operations Research, 124, No. 2, 105084 (2020).