Determining order size in the newsvendor problem with a second order option and transportation costs

In this study, we consider a single period problem, where seasonal products can sold by a supplier to a risk-neutral buyer. The demand exists in the system is stochastic and the objective is to maximize expected profit of the buyer. Since the demand met by order given by the buyer at the beginning of the season and is stochastic, there may be a back-ordering or shortage cost for the difference between the actual demand and the order quantity. In real world, there may be freight cost affecting the expected profit. For our problem, we consider a truck load freight cost structure. In addition to these, we assumed that there is a second order option at the end of the season for the demand which is not met by the first order quantity. For the second order, it is assumed that the buyer accepts a higher transportation cost and ordering cost which includes back-ordering cost. Therefore the second order is used only if it is profitable. In this manner, some algorithms for different cases of the problems are developed in order to maximize the expected profit of the risk-neutral buyer. Besides, a sensitivity analysis is made for the system parameters.