A Two-Stage Stochastic Optimization Model for Cruise Ship Food Provisioning with Substitution

Weilin Sun, Ying Yang () and Shuaian Wang
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Weilin Sun: School of Management, Huazhong University of Science and Technology, Wuhan 430070, China
Ying Yang: Department of Logistics and Maritime Studies, Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 999077, China
Shuaian Wang: Department of Logistics and Maritime Studies, Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 999077, China

Mathematics, 2025, vol. 13, issue 23, 1-25

Abstract: The global cruise industry has demonstrated remarkable growth, with modern ships functioning as large-scale floating resorts. Effective food provisioning is a critical operational function that directly impacts both cost efficiency and passenger satisfaction. This task is characterized by massive consumption scales and high demand uncertainty. To address these challenges, this paper develops a two-stage stochastic optimization model for cruise ship food provisioning. The first-stage decisions involve procurement quantities made before the voyage under demand uncertainty, subject to the volumetric constraints of different storage types. The second-stage decisions determine the optimal substitution plan after the actual demand is realized, mitigating shortages by utilizing alternative available items. Solving stochastic programs with continuous distributions is computationally challenging. Therefore, we employ the sample average approximation (SAA) method to obtain tractable solutions, complemented by a full statistical evaluation of solution quality. Numerical experiments using real-world data confirm that a scenario size of 80 achieves an optimal balance with an optimality gap of 0.78%. Sensitivity analysis demonstrates the model’s robust performance and provides valuable managerial insights: higher shortage penalty coefficients significantly reduce stockouts; two-way substitution structures enhance system flexibility; appropriate salvage value accounting reduces total costs; and implementing a service level constraint of λ i = 0 . 80 optimally balances operational resilience with economic efficiency. These findings support the development of more resilient and cost-effective provisioning strategies, offering cruise operators a practical decision-support tool for managing food provisioning under uncertainty.

Keywords: two-stage stochastic optimization model; sample average approximation; cruise operations; food provisioning; product substitution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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