Abstract:

The rapid changes of supply chain environment make it difficult for firms to predict future demands or obtain a full knowledge of raw material supplies， resulting in low efficiency of production and operation. How to cope with market demand and raw material supply uncertainties and ensure ideal operational performance has become an urgent issue for firms.A production-inventory planning problem is explored for a three-stage supply chain consisting of a raw material supplier， a manufacturer， a third-party logistics company， and customers. The raw materials used to produce products are supplied and distributed by the supplier to the manufacturer. The output of each product is influenced by the inventory levels of raw materials， the production capacity and the market demands. The total production time is subject to maintenance， holidays and other factors. The end products are supplied by the manufacturer to the customers. In particular， any unsold products will be stored by the third-party logistics company. Considering demand and raw material lead time uncertainties， a multi-product multi-period production-inventory planning robust optimization model is developed by minimizing the total production-inventory cost with production capacity， quantities of raw materials， product inventories and logistics as constraints， and order quantities of raw materials， production time， number of orders signed by the manufacturers and the third-party logistics companies and lost sales as decision variables. Furthermore， an affinely adjustable robust optimization model is developed based on the realized demands. With the definitions of the uncertain sets to which the uncertain demands and the lead times belong， the proposed robust optimization models are transformed into tractable linear programming models by dual approach. Finally， numerical studies are conducted to verify the proposed models， especially to illustrate the effectiveness and advantages of the affinely adjustable robust optimization model in coping with demand and lead time uncertainties.The main findings reveal that the affinely adjustable robust optimization model outperforms the traditional static robust optimization model in terms of the total costs and operational decisions. The total production-planning costs under the two robust optimization methods increase with the increase of the demand and lead time uncertainties， indicating that decision-makers should strengthen the management of uncertainties in practice and reduce the uncertainty levels to reduce costs.

Key words: supply chain, production-inventory planning, affinely adjustable robust optimization, demand uncertainties, lead time uncertaintie