作者cheersbk (Miss B)
看板Math
标题[其他] 动态规划的问题
时间Wed Jun 8 17:49:54 2011
您好,手边有一提动态规划的问题解不出来想请大家帮我看一下,题目如下:
Jack sells and manufactures smart phones. Every period, he can manufacture
new phones using brand new components or he can manufacture refurbished
phones using recycled components.Every period, Jack has to determine how many
new phones to produce (Q3), how many refurbished phone to produce (Q2), and
how many components to recycle (Q1). The quality of recycled component
varies a lot. 60% of the chance all the components acquired is usable, and
40% of the chance 100 components out of total components acquired are not
usable.
The market price of the phone depends on how many phones are available to
sell (Q) and is evaluated as following:
The phones will be manufactured and recycled in a batch of 100 and the total
capacity Jack have is 300 phones per period new and refurbished combined.
The space of component inventory can only store 400 units of components.
The unit cost of brand new component is $120, the unit cost to acquire a
recycled component is $50, and the holding cost to hold a recycled component
for one period is $0.25. The unit remanufacturing cost to produce a
refurbished phone is $50. The unit manufacturing cost to produce a brand new
phone is $20.
(a) Formulate this problem as stochastic optimization problem. Clearly
define the stages, decision variables, states, state transition, and
recursive function.
(b) If the planning horizon is 3 period, list all necessary tables used in
calculation. Report your decisions and optimal profit.
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