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Consider a generalization of the inventory model of Sec. 3.2 in which unfilled orders may be...

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Basic Math

Consider a generalization of the inventory model of Sec. 3.2 inwhich unfilled orders may be backlogged indefinitely with a cost ofb(u) if u units are backlogged for one period. Assume revenue isreceived at the end of the period in which orders are placed andthat backlogging costs are charged only if a unit is backlogged foran entire month, in which case the backlogging cost is incurred atthe beginning of that month. a. Identify the state space and derivetransition probabilities and expected rewards.

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The modified model can be formulated as a MDP as followsDecision epochs T 1 2 NStates S 1 0 1 Mwhere st 0 if there are unfilled orders at the beginning ofthe tth period and    See Answer
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