The restaurant delivery problem with uncertain cooking time and travel time

Abstract

Eliminating delays under uncertain delivery conditions presents a formidable challenge for meal delivery platforms. Nevertheless, by implementing effective measures, these platforms can successfully mitigate the impacts of uncertainties on delays. This paper introduces a scenario-based chance-constrained programming model tailored for meal delivery services with uncertain cooking time and travel time, ensuring a more accurate representation of real-world scenarios. The objective is to minimize the delivery cost while considering the decision preferences of a platform. To generate high-quality solutions, this work proposes a novel island harmony search algorithm that incorporates several key components, including greedy search, harmony selection, neighborhood reduction, island migration, and scenario-based simulation. Additionally, a matheuristic is introduced for the purpose of comparison. Comparative evaluation against a set of adopted benchmarks reveals the superior performance of both algorithms. A series of sensitivity analyses are conducted to explore the advantages of considering uncertainty, and investigate how decision preference values influence the feasibility of solutions for meal delivery platforms. The proposed formulation and algorithm yield high-quality solutions for delivery platforms with various preferences, facilitating decision-making that aligns with their operational context.