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Here, we consider single vendor-buyer model with multi-product and multi-customer and multi-facility location-production-distribution problem. It is assumed that the players of the supply chain are coordinated by sharing information. Vendor manufactures produce different products at different plants with limited capacities and then distribute the products to the consumers according to deterministic demands. A mixed integer linear fractional programming (MILFP) model is formulated and a solution approach for MILFP is discussed. Product distribution and allocation of different customers along with sensitivity of the key parameters and performance of the model are discussed through a numerical example. The results illustrate that profit achieved by the MILFP model is slightly higher than mixed integer programming (MIP) model. It is observed that increase in the opening cost decreases the profit obtained by both MILFP and MIP models. If the opening cost of a location decreases or increases, the demand and capacity of the location changes accordingly. The opening cost dramatically changes the demand rather than the capacity of the product. Finally, a conclusion is drawn in favor of the MILFP model as a relevant approach in a logistic model searching for the optimum solution.

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Coordination is a critical factor in optimizing supply chain performance. Given the pervasive uncertainties in supply chain management, it is essential to develop decisions that are robust against these uncertainties while preserving operational efficiency. This paper aims to determine an optimal supply chain policy that ensures the total system cost remains robust against correlated uncertainties in demand and lead time. To address the correlation among demand data and avoid overly conservative solutions, a novel robust optimization model is proposed based on a correlated polyhedral uncertainty set. This approach explicitly accounts for demand correlation, thereby reducing the price of robustness. Numerical results demonstrate that integrating coordination as a strategic decision and employing robust optimization as a tactical tool significantly enhances supply chain performance. Moreover, incorporating demand correlation in the proposed model leads to a substantial reduction in the price of robustness and, consequently, higher supply chain profitability. Extending this framework to more complex supply chain models with multiple sources of uncertainty holds great potential for further improving the robustness and practical applicability of supply chain decision-making.