A Novel and Efficient Exact Technique for Integrated Staffing, Assignment, Routing, and Scheduling of Home Care Services Under Uncertainty

40 Pages Posted: 5 May 2021

See all articles by Bahman Naderi

Bahman Naderi

University of Windsor - Mechanical, Automotive & Materials Engineering

Mehmet A. Begen

Ivey Business School, University of Western Ontario

Gregory S. Zaric

University of Western Ontario - Richard Ivey School of Business

Vahid Rroshanaei

University of Toronto - Operations Management

Date Written: April 27, 2021

Abstract

We model and solve an integrated multi-period staffing, assignment, routing, and scheduling for home care services under uncertainty. The goal is to construct a weekly schedule that adheres to related operational considerations and determines optimal staffing of caregivers by minimizing caregivers’ fixed- and overtime costs. For tractability, we incorporate a priori generated visit patterns—an existing practical approach that deals effectively with hard assignment decisions in. First, we propose a novel mixed-integer program (MIP) for the nominal problem. We then incorporate uncertainty in service and travel times and develop a robust counterpart by hybridizing interval and polyhedral uncertainty sets. Second, we show that there is a special mathematical structure within the model that allows us to develop a novel logic-based Benders branching-decomposition algorithm that systematically delays the resolution of difficult routing/ scheduling problems and efficiently solves both the nominal and robust MIP models. Using a dataset from the literature, we show that CPLEX can solve our nominal and robust models with an average optimality gaps of 44.56% and 45.53%, respectively. Using the same dataset, we demonstrate that our new exact technique can solve our nominal and robust mixed-integer models to an average optimality gap of 2.8% and 4.5%, respectively. Third, we provide practical insights into (i) the price of robustness and (ii) the impacts of nurse flexibility and overtime. The average total cost does not increase beyond 12.7% than the nominal solution and the cost-savings of nurse flexibility is approximately five times higher than that of overtime.

Keywords: Combinatorial Optimization, Home Health Care Planning and Scheduling, Multi period, Logic-Based Benders, New Exact Branching-Decomposition.

Suggested Citation

Naderi, Bahman and Begen, Mehmet A. and Zaric, Gregory S. and Roshanaei, Vahid, A Novel and Efficient Exact Technique for Integrated Staffing, Assignment, Routing, and Scheduling of Home Care Services Under Uncertainty (April 27, 2021). Available at SSRN: https://ssrn.com/abstract=3836827 or http://dx.doi.org/10.2139/ssrn.3836827

Bahman Naderi

University of Windsor - Mechanical, Automotive & Materials Engineering ( email )

OR
Canada

Mehmet A. Begen (Contact Author)

Ivey Business School, University of Western Ontario ( email )

1255 Western Road
London, Ontario N6G 0N1
Canada

HOME PAGE: http://www.ivey.uwo.ca/faculty/MBegen

Gregory S. Zaric

University of Western Ontario - Richard Ivey School of Business ( email )

London, Ontario
Canada

Vahid Roshanaei

University of Toronto - Operations Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada

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