I'm solving a multi-period inventory/price optimization where inventory used at a time-period is to be computed based on price-bucket that is selected for the item. Problem contains multiple items (around 10K), 15-20 time-periods and 10-15 price buckets. Inventory consumed at a time-period (t) is minimum of available inventory and demand (which is dependent on price selected). This particular constraint is making problem harder (not able to obtain optimal solution even in 30 mins for above scale) and i tried modeling it as shown below:
Big-M's are chosen as tight as possible. Can you please suggest any other way to model the same? .Any reference's would help!!
Also, would like to know if any modeling constructs like indicator improve performance?
Thanks & regards, Anjani Kumar.
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