combinatorial auctions in logistics under stochastic travel times and stochastic clearing prices

We are dealing with a situation of a firm in which multiple trucks with known locations are to be routed to serve full truckload demands called loads with known origin and destination points. on the other hand, in order to avoid empty maneuvers of the trucks and to gain profit, firm tries to get loads from spot market by the help of a combinatorial auction in which more than one load can be bided on simultaneously. loads are assumed to have known time windows limitations, i.e., loads have to be served within specific time frames. in this study, we take travel times of the trucks as stochastic which makes complying with time window constraints a difficult problem. we also consider that the clearing price of each auctioned load to be a stochastic random variable. a mathematical programming with chance constraints are developed first, and then it is linearized and solved for extensive numerical instances.