Because the demand is uncertain and it is impossible to expand capacity immediately, suppliers in supply chains are faced with insufficient capacity. As a result, they are unable to satisfy fully the demand from many retailers. Sometimes the use of additional shifts or outsourcing may resolve the problem, but many times, suppliers have to seek ways to appropriately allocate their limited capacity to the retailers. A non-cooperative coordinative mechanism is often required which has to be acceptable and beneficial for all members of the supply chain. This study considers a supply chain with a single supplier and multiple retailers in which the retailers are categorized into two types: ordinary and privileged, according to the steadiness of their partnership with the supplier. The primary concern is to coordinate the capacity allocation within the supply chain with the uses of quantity discount and strategic price-quantity auction with consideration of maintaining fairness and a long-term steady partnership. Our analytical results show that both parties benefit from these coordination mechanisms since the supplier's profit increases because the retailers are incentivized to place orders with higher quantities, lowering the cost of idle capacity and increasing revenues. In the meantime, retailers are able to trim down their ordering costs and fairly compete for limited capacity, which reduces the transaction risks and shortage costs for uncertain demands, and thus increases their profits.
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