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help: eoq model with backlogging with different demand rates
Consider the following modification of the EOQ model with backlogging. When the inventory is positive, demand arrives at rate lamda1; when the inventory is negative, demand arrives at rate lamda2. Suppose that, there are parameters
k; b; h > 0 associated with the problem as well. Compute the optimal (Q,r)
policy in this setting, showing all work / steps and providing informal justication for each step. Hint : break each relevant interval up into what happens before the inventory reaches 0, and what happens between the
time it reaches 0 and the time it reaches r. If done this way, there is no need to differentiate under the integral sign, as all integrals can be computed explicitly. Also, although your answer cannot involve any integrals or
derivatives or anything like that, you do not need to simplify all algebraic expressions, and can (if appropriate) define intermediate algebraic quantities / expressions which your final answer can be stated in terms of.