Consider the following one-period problem: a certain item is produced centrally in a factory and…
Consider the following one-period problem: a certain item is produced centrally in a factory and distributed to four warehouses. The factory can produce up to 12 thousand pieces of the item. The transportation cost from the factory to warehouse n is tn dollars per thousand pieces.
From historical data, it is known that the demand per period from warehouse n for the item is governed by a Poisson distribution† with mean λn (in thousands of pieces). If demand exceeds available stock a penalty of πn dollars per thousand units out of stock is charged at warehouse n. The current inventory on hand at warehouse n is qn thousand units.
a) Formulate a dynamic program for determining the amount to be produced and the optimal allocation to each warehouse, in order to minimize transportation and expected stockout costs.
b) Solve the problem for a four-warehouse system with the data given in Table.
The Poisson distribution is given by Prob.