Many operational decisions of a company or an organization can be captured as a combinatorial optimization problem and, when the problem is clearly defined and appropriately formulated, it can be handled by a decision maker with the help of a suitable computerized algorithm. However, in a practical situation, it is often the case that the information required for clearly defining the problem is not fully available for a single decision maker but is dispersed among multiple stakeholders. This makes the problematic situation ill-defined and difficult to be dealt with properly by the decision maker alone. Thus, this paper takes up an undefinable shortest path problem as an example and proposes a prediction market approach for collectively solving it with a team of stakeholders. The approach aggregates the dispersed information on the problematic situation from the stakeholders through the market mechanism. After modeling the ill-defined situation by a shortest path problem with uncertainties in arc lengths, the paper discusses how to design the prediction security and market institution for collectively resolving the situation. Then, it conducts laboratory experiments to investigate how the proposed approach actually works. It further discusses how to generalize the approach to the case where the topology of the network is also uncertain.