Markov Decision Process

There are two locations (location A and location B).Shipments of inventory are sent from A to B. There is a discount on the cost of the shipment if a certain amount is reached. However, there is a holding cost per kilogram per day. Look for a policy where you can combine orders to minimize shipping and holding costs. Px is the probability that the total weight of orders arriving in a day equals x.You can accumulate orders or ship them each evening.The parameter for discount is W which is the minimum weight for a discount. Shipments that weigh less than W have a cost c_n per kg. Shipments for weights greater or equal to W cost c_d per kg. Therefore c_d is less than c_n. Assume the cost of delaying a shipment of an order is E per kg per day.

Formulate the Markov Decision Process (determine transition probabilities, decision epochs, state space, action set, reward function).

Determine an optimality equation as if there was a finite amount of days. State assumptions