Tree Model

In Exercise 5.14, suppose that the owner wishes to consider her decision problem over a 2- day period. Her alternatives for the second day are determined as follows. If the demand in day 1 is equal to the amount stocked, then she will continue to order the same quantity on the second day. Otherwise, if the demand exceeds the amount stocked, then she will have the options to order higher levels of stock on the second day. Finally, if day 1’s demand is less than the amount stocked, then she will have the options to order any of the lower levels of stock for the second day. Express the problem as a decision tree, and find the optimal solution using the cost data given in Exercise 5.14.

***(Exercise 5.14 – The daily demand for a particular type of printed circuit board in an assembly shop can assume one of the following values: 100, 120, or 130 with probabilities 0.2, 0.3, and 0.5. The manager of the shop thus is limiting her alternatives to stocking one of the three levels indicated. If she prepares more boards that are needed in the same day, the she must reprocess those remaining at a cost of 55 cents/board. Assuming that it costs 60 cents to prepare a board for assembly and the each board produces $1.05 in revenue, find the optimal stocking level by using a decision tree model)***