Аннотация
This study addresses the joint formation of group purchases and allocation of orders to capacity-constrained delivery slots when users may participate in several groups. A mixed-integer optimization model is developed to represent order-slot assignment, group activation, delivery time windows, courier capacity, seller service requirements, and limits on concurrent user participation. The objective minimizes total delivery cost and penalties for unmet seller service levels while preserving feasibility of hard logistical constraints. The model was evaluated on a reproducible synthetic instance comprising 200 users, 40 purchase groups, 300 orders, 10 sellers, and 15 courier slots, each with a capacity of 50 units. Its performance was compared with a baseline assignment procedure that does not jointly enforce the stated restrictions. The proposed model increased average slot utilization from 69% to 85%, reduced average delivery cost from 12.1 to 9.7 conventional units, raised the share of orders delivered within their time windows from 78% to 92%, reduced assignment conflicts from 31 to 11, and shortened average delivery time from 96 to 70 minutes. A two-proportion test confirmed the increase in timely deliveries (z = 4.802, p < 0.001); 95% Wilson intervals were 72.97-82.32% and 88.37-94.57%. An exact conditional test showed a reduction in conflicts (p = 0.0029). Optimality follows from the finite binary feasible set and the branch-and-bound certificate: when the incumbent objective equals the lower bound, no feasible assignment can improve the reported solution. These findings support optimization as a practical basis for robust, reliable, resource-efficient group-purchase delivery planning under competing operational constraints.