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.Consider the following one-period problem: a certain item is produced centrally in a factory and...-1

Consider the following one-period problem: a certain item is produced centrally in a factory and...-2

Consider the following one-period problem: a certain item is produced centrally in a factory and...-3

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