Measuring and rewarding flexibility in collaborative distribution, including two-partner coalitions

• Collaborating partners can have an asymmetric effort or flexibility to reduce costs.
• This difference in flexibility should be rejected in the cost allocation.
• Flexibility is best rewarded by a cost allocation mechanism based on (marginal) costs.
• These methods are unable to give incentives to be flexible in two-partner coalitions.
• We suggest incorporating situations where a partner remains rigid.

Horizontal collaboration among shippers is gaining traction as a way to increase logistic efficiency. The total distribution cost of a logistic coalition is generally between 9% and 30% lower than the sum of costs of each partner distributing separately. However, the coalition gain is highly dependent on the flexibility that each partner allows in its delivery terms. Flexible delivery dates, flexible order sizes, order splitting rules, etc., allow the coalition to exploit more opportunities for optimization and create better and cheaper distribution plans.An important challenge in a logistic coalition is the division (or sharing) of the coalition gain. Several methods have been proposed for this purpose, often stemming from the field of game theory. This paper states that an adequate gain sharing method should not only be fair, but should also reward flexibility in order to persuade companies to relax their delivery terms. Methods that limit the criteria for cost allocation to the marginal costs and the values of the subcoalitions are found to be able to generate adequate incentives for companies to adopt a flexible position. In a coalition of two partners however, we show that these methods are not able to correctly evaluate an asymmetric effort to be more flexible. For this situation, we suggest an alternative approach to better measure and reward the value of flexibility.