Joint replenishment and pricing decisions with different freight modes considerations for a supply chain under a composite incentive contract

Companies often offer incentive contracts to persuade buyers to order more to increase their sales volume and to decrease their setup and freight costs. More sales volume means an increase in profits, market power, and market shares. This investigation analyzes optimal pricing and replenishment decisions of a single-manufacturer/multiple-retailer supply chain where a composite contract combines quantity and freight discounts, and a free shipping contract is incorporated into the model. Here, the transportation modes of raw materials and finished products are subject to a limited capacity. The manufacturer, who faces geographically dispersed retailers, ships the ordered shipments under three different modes classified in three scenarios. In the first scenario, the shipments are shipped by identical transport modes to the retailers. In the second one, they are delivered by different transport modes in terms of their capacities regarding distance from the manufacturing site. In the third scenario, products are sent to a central warehouse for fast ship to the retailers. Demand depends on selling price and shortage is not permitted. The leader-follower game is considered between the members of the chain so that the manufacturer is a follower and the retailers are the leaders. This research aims to optimize the chain total profit concerning the selling prices and order quantities of the manufacturer and the retailers under different transport methods and a composite incentive contract. To clarify the applicability of the model, some numerical samples are presented and the effects of optimal decision policies of the chain's partners are examined.