Robust Optimization for Age-friendly Facility Location Problem

Abstract

Optimizing age-friendly community facilities has become crucial for enhancing elderly well-being. This study proposes a distributionally robust optimization (DRO) framework for public seating facility planning, addressing the limitations of conventional models in handling multidimensional uncertainties. We construct Wasserstein metric-based ambiguity sets to characterize stochastic interactions among individual physiological traits (e.g., balance capacity), environmental factors (e.g., terrain irregularity), and fatigue-induced risk accumulation. A dual-layer constraint system synergizes safety assurance (fall probability control) and functional adequacy (demand-responsive coverage) under budget limits. To address computational challenges in large-scale networks, we develop a Two-stage Greedy-deterministic (TSGD) algorithm with dynamic candidate screening and dual-variable correction, achieving high computational efficiency and scalability for large-scale networks. For small-scale validation, we further propose a Distributionally Robust Simulated Annealing (DRSA) algorithm. Numerical experiments demonstrate the following facts: 1) TSGD reduces computation time by 66% compared to Gurobi in 200-node scenarios with < 3% optimality gap; 2) The Wasserstein-DRO formulation ensures 89.3% risk compliance under worst-case uncertainty. Theoretically, this work integrates safety-functionality synergy into stochastic facility location models. Practically, it provides a decision-making paradigm for spatial optimization in aging communities, with algorithmic innovations enabling scalable implementation.

Keywords

Age-friendly retrofit / facility location problem / distributionally robust optimization / wasserstein metric / heuristic algorithm

References

[1] American Geriatrics Society. Summary of the updated American Geriatrics Society/British Geriatrics Society clinical practice guideline for prevention of falls in older persons. Journal of the American Geriatrics Society, 2011, 59(1): 148-157

[2] Anderson SP, Coate S. Market provision of broadcasting: A welfare analysis. Review of Economic Studies, 2005, 72(4): 947-972

[3] Anderson SP, de Palma A. The logit as a model of product differentiation. Oxford Economic Papers, 1992, 44(1): 51-67

[4] Anderson S, Gabszewicz J. The media and advertising: A tale of two-sided markets. Handbook of the Economics of Art and Culture, 2006, 1: 567-614

[5] Baron O, Milner J, Naseraldin H. Facility location: A robust optimization approach. Production and Operations Management, 2011, 20(5): 772-785

[6] Ben-Tal A, Den Hertog D, De Waegenaere A, Melenberg B, Rennen G. Robust solutions of optimization problems affected by uncertain probabilities. Management Science, 2013, 59(2): 341-357

[7] Benedict JThree hierarchical objective models which incorporate the concept of excess coverage for locating EMS vehicles or hospital, 1983Evanston IINorthwestern University

[8] Boswell DAElder-friendly plans and planner’s effort to involve older citizens in the plan-making process, 2001New OrleansUniversity of New Orleans

[9] Carlson T, York S, Primomo J. The utilization of geographic information systems to create a site selection strategy to disseminate an older adult fall prevention program. The Social Science Journal, 2011, 48(1): 159-174

[10] Daskin MS. What you should know about location modeling. Naval Research Logistics, 2008, 55(4): 283-294

[11] Delage E, Ye Y. Distributionally robust optimization under moment uncertainty with application to data-driven problems. Operations Research, 2010, 58: 595-612

[12] Drezner Z. On the conditional p-median problem. Computers & Operations Research, 1995, 22(5): 525-530

[13] Eiselt HA, Marianov VFoundations of Location Analysis, 2011

[14] Esfahani PM, Kuhn D. Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations. Mathematical Programming, 2018, 171(1): 115-166

[15] Gao R, Kleywegt A. Distributionally robust stochastic optimization with Wasserstein distance. Mathematics of Operations Research, 2016, 48(2): 603-655

[16] Gergin Z, et al.. Clustering approach using artificial bee colony algorithm for healthcare waste disposal facility location problem. International Journal of Operations Research and Information Systems, 2019, 10(1): 56-75

[17] Hakimi S. Optimum locations of switching centers and the absolute centers and medians of a graph. Operations Research, 1964, 12(3): 450-459

[18] Hausdorff JM, Rios DA, Edelberg HK. Gait variability and fall risk in community-living older adults: A 1-year prospective study. Archives of Physical Medicine and Rehabilitation, 2001, 82(8): 1050-1056

[19] Jung BS, Kyung CY, Lee S. Demand estimation of public rental housing for the elderly. SH Urban Research & Insight, 2018, 8(1): 37-52

[20] Karp RM. Complexity of computer computations: Reducibility among combinatorial problems. Proceedings of a Symposium on the Complexity of Computer Computations, 1972, 23(1): 85-103

[21] Kuhn D, Esfahani PM, Nguyen VA, Shafieezadeh-Abadeh S. Wasserstein distributionally robust optimization: Theory and applications in machine learning. INFORMS TutORials in Operations Research, 2019130-166

[22] Kwan MM, Close JC, Wong AK, et al.. Falls incidence, risk factors, and consequences in Chinese older people: A systematic review. Journal of the American Geriatrics Society, 2011, 59(3): 536-543

[23] Liu K, Li Q, Zhang ZH. Distributionally robust optimization of an emergency medical service station location and sizing problem with joint chance constraints. TransportationResearchPartB:Methodological, 2019, 119: 79-101

[24] National Center for Injury Prevention and Control (U.S.). Preventing falls: A guide to implementing effective community-based fall prevention programs (2ed). Division of Unintentional Injury Prevention, 2015

[25] Park J, Choi B. Factors affecting the intention of multi-family house residents to age in place in a potential naturally occurring retirement community of Seoul in South Korea. Sustainability, 2021, 13(16): 8922-8922

[26] Revelle CS, Eiselt HA, Daskin MS. A bibliography for some fundamental problem categories in discrete location science. European Journal of Operational Research, 2008, 184(3): 817-848

[27] Scarf HE, Arrow KJ, Karlin SA min-max solution of an inventory problem (No. P910), 1957Santa MonicaRand Corporation

[28] Schultz GP. The logic of health care facility planning. Socio-Economic Planning Sciences, 1970, 4(3): 383-393

[29] Shehadeh KS, Sanci E. Distributionally robust facility location with bimodal random demand. Computers & Operations Research, 2021, 134: 105-127

[30] Teitz MB. Toward a theory of urban public facility location. Papers of the Regional Science Association, 1968, 21(1): 35-51

[31] Wang L, Wang X, Song P, Han P, Fu L, Chen X, Yu H, Hou L, Yu X, Zhang Y, Zhang W. Combined depression and malnutrition as an effective predictor of first fall onset in a Chinese community-dwelling population: A 2-year prospective cohort study. Rejuvenation Research, 2020, 23(6): 498-507

[32] Weber A. On the location of industries. Progress in Human Geography, 1982, 6(1): 120-128

[33] Wiesemann W. Distributionally robust convex optimization. Operations Research, 2014, 62: 1358-1376

[34] World Health OrganizationWHO global report on falls prevention in older age, 2008

[35] Xie W. On distributionally robust chance constrained programs with Wasserstein distance. Mathematical Programming, 2021, 186(1–2): 115-155

[36] Zhou M, Wang H, Zeng X, et al.. Mortality, morbidity, and risk factors in China and its provinces, 1990–2017: A systematic analysis for the global burden of disease study 2017. The Lancet, 2019, 394(10204): 1145-1158

[37] Zhu N, Fu CY, Ma S. Data-driven distributionally robust optimization approach for reliable travel-time-information-gain-oriented traffic sensor location model. Transportation Research Part B:Methodological, 2018, 113: 91-120

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Systems Engineering Society of China and Springer-Verlag GmbH Germany