Workforce planning for meal deliveries with Ad-Hoc drivers: A distributionally robust contextual optimization approach

Meal delivery with a mix of in-house and ad-hoc drivers has been prevalent in recent years, in which the workforce constitutes about 30%–60% of the total expenses. In this work, we study a tactical workforce planning problem to minimize the total costs for meal delivery platforms. This problem determines the number of in-house drivers to hire as tactical-level decisions, who would fulfill the uncertain and feature-dependent customer orders together with ad-hoc drivers in the subsequent operational phase. The objective is to minimize the sum of fixed costs for hiring in-house drivers, variable costs for delivering goods by both in-house and ad-hoc drivers, and penalty costs for unfulfilled orders. We account for uncertain customer orders and availability of ad-hoc drivers, which are affected by uncertain contextual feature information such as weather. To address the challenges caused by the complex interplay of in-house and ad-hoc drivers, the feature-dependent uncertainty and the limited historical data, we propose a two-stage distributionally robust contextual optimization (DRCO) model. We reveal a hidden network flow structure for the operational-level delivery problem, which enables us to relax the integer decision variables to continuous ones and further allows us to propose a Benders decomposition algorithm to solve the DRCO. Our numerical tests based on real-world data demonstrate the effectiveness and efficiency of the proposed models and algorithms.