Integrated column generation for volunteer-based delivery assignment and route optimization

Abstract

This study develops an integrated delivery assignment and route planning strategy for food banking operations, considering food supply and demand constraints, food item restrictions, and vehicle capacity constraints. A mixed-integer linear model is formulated to maximize the total demand served and minimize the total travel cost imposed on delivery volunteers. An integrated solution algorithm is developed that includes Lagrangian relaxation and column generation. The algorithm decomposes the problem into assignment and routing components and solves each iteratively. The proposed methodology is applied to a case study in Wake County, NC. A series of sensitivity analyses are conducted to draw insights. The numerical results demonstrate the proposed methodology's capacity to solve complex problems in food delivery operations efficiently.