Choosing a transport contract over multiple periods

We offer a shipper and a carrier the choice among three contracts in which to frame their relationship. Both can also take recourse in the transport spot market. Demand and price on the spot market are dependent exogenous stochastic processes. We model the outcome of this endogenous choice of contract. The results, given in closed form, are different from those presented in the literature. Using numeric instances, we show how a choice is made and which contract would be preferred. Comparison on the variance of the economic returns are offered. The conclusions are applicable when the carrier is not capacity constrained.