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What is the optimal of inventory optimization (one inventory in serial system) when considering fixed ordering cost, and (holding/units)cost and (shortage/units)cost

user10296606
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1 Answers1

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There are several optimization strategies. the 's,S' orderstrategy is the one that can be seen as optimal. This strategy means that there is an order point 's' and when inventory reaches this point, one orders up to an amount 'S'. Determining s and S are pretty difficult and exhaustive in computation. There are numerical methods that can be used, but an algebraic expression isn't present.

A good approximation where we don't deviate more than 1% in total cost is determining 's' as the simple calculation of a re-order point (demand durling lead time + safety stock) and 'S' as this re-orderpoint plus the EOQ (economic order quantity).

I don't know your level of knowledge, but the EOQ and the safety stock also require some computations, as it is a trade-off of costs and some other mathematical manipulations. A good resource book is the following:

https://www.amazon.com/Inventory-Management-Production-Planning-Scheduling/dp/0471119474

This post describes the calculation of the safety stock

Derivation of the Safety Stock Formula on Wikipedia

Steven

Steven01123581321
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  • The OP didn't specify whether it's continuous or periodic review. Your answer is correct if it's periodic review, but if it's continuous review, then (r,Q) is optimal. One other minor note: I'm not sure if you're saying there's a provable bound of 1% error for that approximation, but there's not. In fact, the EOQ+SS approximation has no fixed worst-case bound. But the approximation that uses the EOQ w/Backorders does have a fixed worst-case error bound, of ~12%. – LarrySnyder610 May 03 '19 at 02:35
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    Hi Larry. Your comments are definitely valid, but I've never seen a true continuous review in practice. Even in supermarkets, they have a periodic review of half a day. And with the orderpoint-undershoot I see in practice, the, s, S-strategy seems to have the advantage. But from a computational and practical point of view, a r, Q is the best solution.I'm not saying there is a provable bound of 1%. I regularly do research on real-life customer databases and this bound is from what I've found. Steven – Steven01123581321 May 03 '19 at 07:52
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    That's true. I was interpreting the question as referring to a theoretical model rather than a practical system. Reflects my own bias. :-) – LarrySnyder610 May 03 '19 at 13:08
  • @LarrySnyder610 I came across this old question and I saw you say that with a continuous review system, the (r, Q) policy is optimal. But in all sources I have, i see that a r, S policy is optimal under quite general conditions. Can you share the resource that you use ? – Steven01123581321 Dec 11 '22 at 17:13
  • @ Steven01123581321 Lots of sources claim an (r,Q) policy is optimal, including Zheng 1992, Federgruen and Zheng 1992, and my own book. There are situations in which (r,Q) and (r,S) (or I would call it (s,S)) policies are equivalent -- maybe that's where the confusion is? – LarrySnyder610 Dec 15 '22 at 17:43