Abstract: With the rise of inter-firm cooperation, capacity outsourcing appears not only in the manufacturing industry, but also in the service industry. In this paper, logistics service system in which a retailer (she) outsources the activity of order delivery to a logistics service provider (LSP, he) is considered. The retailer faces random demands and is allowed to make capacity reservation before order arriving. The LSP has fixed amount of logistics capacity and aside from the retailer, has another external cooperation opportunity. The LSP would get external revenue if he allocates logistics capacity to the external cooperator. We assume that the retailer doesn't always have the perfect information about the LSP's external revenue. In such case, how to design a coordination mechanism to assure the system-wide optimization by encouraging the LSP to tell the truth and the retailer to make the right decision on capacity reservation is highly needed.From the perspective of the retailer, a mechanism of compensation contracts, in which besides the service fee, the retailer gives the LSP a compensation fee for each left-over capacity due to over-reservation, is proposed. By using game theory and the apparatus of mechanism design, the retailer's optimal compensation contracts under the LSP's external revenue information being symmetric and asymmetric are solved. Then, these contracts are analyzed and they are compared between the two different information conditions.It is found that thecompensation contract mechanism works out perfectly. Both the logistics reservation quantity and the expected profit of the whole system in each of the information conditions reach the same values as in the centralized decision-making condition. In optimal contracts, the compensation fee should be increased with LSP's external revenue index; Under the information asymmetric condition, the LSP has the motivation to understate the external revenue if he pursues for unchangeable retained profit while he has the motivation to overstate the external revenue if he pursues for changeable retained profit; In order to induce the LSP to disclose his real external revenue information, the retailer should increase the service price and at the same decrease the compensation fee compared to the information symmetric condition. In the end, numerical examples are used to verify the compensation contracts as well as to analyze how external revenue and its degree of asymmetry affecting the contracts and the two parties' expected profits. Our work extends the research of logistics capacity coordination to consider asymmetric information. The results show that optimal logistics outsourcing contracts should incorporate the LSP's external revenue and the form of his retained profit into different information conditions.

Key words: external revenue, asymmetric information, compensation contract, logistics capacity