I am looking for MILP modeling code with stochastic/deterministic demand for Inventory ordering policy (e.g. (q,r) or (s,S) policy) with pyomo or gurobi or cplex or GAMS. Any link?
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3$\begingroup$ What have you tried already? $\endgroup$– RichardCommented Aug 4, 2022 at 1:11
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$\begingroup$ Well, I tried with cplex and gurobi but it didn't work for me... $\endgroup$– PeterCommented Aug 4, 2022 at 16:05
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$\begingroup$ More details on the nature of the model would be helpful. I don't normally associate (Q,R) or (s,S) inventory models with integer programming. $\endgroup$– prubin ♦Commented Aug 4, 2022 at 21:01
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2 Answers
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One example I know of: https://yetanothermathprogrammingconsultant.blogspot.com/2020/11/optimal-qr-inventory-policy-as-mip.html (and its Pyomo version: https://sysid.github.io/inventory_management/).
answered Aug 4, 2022 at 9:54
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$\begingroup$ Thanks Kalv... It's absolutely helpful for me. $\endgroup$– PeterCommented Aug 4, 2022 at 15:33
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$\begingroup$ Hey Kalv... thank you again for the link. I believe GAMS was used to program the first link. doesn't it? do you know any further link of that program? TIA... $\endgroup$– PeterCommented Aug 4, 2022 at 16:02
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$\begingroup$ Yes, that was based on a GAMS model. I don't think that was ever made public (it needs probably a bit of clean-up). I was hoping that the math description should be enough to reproduce the results (the math is just a transcribed GAMS model). $\endgroup$ Commented Aug 4, 2022 at 18:08
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$\begingroup$ Yeah! you are absolutely correct!... math description is very clear!. I'm new to GAMS (I use gurobi mostly) so, I wanted to check how the command line interacts with equations. $\endgroup$– PeterCommented Aug 5, 2022 at 1:01
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$\begingroup$ I don't know what that means, but it should be easy to implement this in Gurobi. $\endgroup$ Commented Aug 5, 2022 at 2:16
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You may find some useful ideas in this paper on s,S policies.
IYER, A. V. AND L. SCHRAGE (1992)
ANALYSIS OF THE DETERMINISTIC (s, S) INVENTORY PROBLEM
MANAGEMENT SCIENCE Vol. 38, No. 9,
Part of the abstract is:
The traditional or textbook approach for finding an (s, S) inventory policy is to take a demand distribution as given and then find a reorder point s and order up to point S that are optimal for this demand distribution. In contrast, the deterministic (s, S) inventory problem is to directly determine the (s, S) pair that would have been optimal for the original demand stream, bypassing the distribution fitting step. The deterministic (s, S) inventory problem thus chooses parameters s and S which minimize setup, holding and backorder costs when the corresponding (s, S) policy is implemented over n periods with known demands d1, d2, . . ., d,,. Our contributions are two: (a) a polynomial time algorithm for finding an optimal (s, S) for the deterministic problem, and (b) an empirical comparison of the two approaches. In (b) we compare the long term average costs of the two approaches as a function of the amount of data available, distributional assumptions, and order lead time.
