Integrated Production–Distribution Scheduling for E-Grocery Fulfillment and Outbound Distribution under Demand Uncertainty

Abstract

Rapid expansion of the e-grocery sector has intensified the need for integrated scheduling of production and distribution under operational uncertainty. This study introduces the first exact solution to the e-grocery integrated production and distribution scheduling problem (IPDSP), specifically designed for fulfillment-center operations and decentralized-hub distribution under demand uncertainty. The IPDSP model simultaneously optimizes single-machine order batching, homogeneous single-trip vehicle routing with delivery time windows, demand splitting, and multi-hub routing. Separate models—a mixed-integer linear programming (MILP) formulation and a genetic algorithm (GA)—are each formulated, presented, and evaluated for solving the IPDSP within realistic runtime constraints. The deterministic MILP is further extended into a stochastic formulation to capture demand variability by generating multiple demand scenarios, incorporating the maximum demand across those scenarios, and allowing the model to optionally exclude certain scenarios. Computational experiments on real-world fulfillment center (FC) data demonstrate that the MILP finds feasible solutions to the deterministic case in 44% of instances (100% for the two smallest FCs) and proves optimality in 7.6% of runs within a one-hour limit. The GA reduces average runtime by 99.6% while incurring only a 3.4% increase in objective value and yields feasible schedules in all cases. The stochastic MILP shows that increasing driving time by 21.3% achieves full scenario coverage, with 80%–90% coverage offering the best cost–robustness trade-off. For large or time-sensitive problems, the GA is recommended; the MILP remains suitable for small instances requiring strict optimality. Overall, these findings advance resilient and efficient e grocery scheduling under uncertainty.