Scheduling and co-ordination of multi-suppliers single-warehouse-operator single-manufacturer supply chains with variable production rates and storage costs

We study a supply chain scheduling and co-ordination problem comprising multiple suppliers, a single warehouse operator, a single manufacturer, and multiple retailers, where the supply chain has limited production capacity that can take only some of the orders from the retailers. For a decentralised supply chain, the manufacturer is a decision maker that selects the orders and aims to maximise its own profit, where the profit is a function of the order storage time and storage quantity, order sequence-dependent weighted storage costs, and idle time of the orders. On the other hand, for a centralised supply chain, a supply chain co-ordinator exists that aims to maximise the profit of the whole supply chain and allocates the profit among the supply chain members. We first formulate the problem as a two-machine common-due-window flow shop scheduling problem. We then develop a theorem and two algorithms to solve the optimal scheduling problems in both the decentralised and centralised supply chains. With these results, we develop a method that can achieve channel co-ordination based on a profit sharing rule, together with an increase in the production rates and a decrease in the storage costs.