A Deterministic Optimization Framework for O2O Supply Chains under Manufacturing Unreliability, Transportation Hazards, and SSMUID Delivery Structures
Soumya Kanti Hota1∗
1Department of Mathematics, Debra Thana Sahid Kshudiram Smriti Mahavidyalaya, Debra, Paschim Medinipur, West Bengal 721124, India
Abstract: This paper presents a deterministic optimization framework for a two-echelon Online-toOffline (O2O) supply chain composed of an unreliable manufacturer and a reliable retailer. Customer demand is modeled as a function of selling price, green investment, and serviceimprovement investment. The manufacturer produces at a controllable rate but only a fraction of output is usable due to unreliability; shipments are further subject to transportation hazards that damage a fraction of each delivery. The retailer employs a single-setup–multi-unequalincreasing-delivery (SSMUID) policy, parameterized by a geometric ratio, to reduce average inventory at the expense of increased shipment frequency, emission and transport costs. We derive closed-form expressions for SSMUID shipment sizes and average inventory, present the joint total cost (manufacturer + retailer), and reduce the decision problem via substitution. First-order optimality conditions for price, investments, shipment shape and cycle time are obtained and a full 5×5 Hessian matrix is constructed to provide a sufficient Hessian-based global-optimality certificate under interpretable parameter conditions. Numerical experiments compare single-delivery, equal-multi-delivery and SSMUID policies and provide sensitivity analysis on reliability and hazard parameters. Results show that SSMUID reduces joint cost under typical ranges and that manufacturing reliability and transportation hazards are the dominant cost drivers.
Key Words: Online-to-Offline (O2O) supply chain; unreliable manufacturer; transportation hazard; SSMUID delivery policy; green investment; deterministic optimization