13 votes
Accepted

Normal demand and normal lead time; is lead-time demand normal?

I had the same doubt, and I arrived at the conclusion that the formula given in the textbooks is, at best, a practical approximation. The lead-time demand, in fact, is not normally distributed. Let $...
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13 votes

Recommendations for OM blogs

Here is the list of blogs and social media that I regularly check [in no particular order]: https://www.zverovich.net/ https://yetanothermathprogrammingconsultant.blogspot.com/ https://orinanobworld....
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  • 3,034
10 votes
Accepted

Loss functions for specific probability distributions?

There is indeed a paper titled Loss Distributions that provides the limited expected value functions $L(x)$ for several probability distributions (on page 15). It is directly related to the first-...
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  • 5,185
10 votes

Good distribution assumptions for customer demand in a supply chain

I agree with @QianZhang's answer (nice theoretical properties, easy to implement), and I would add that there is some theoretical justification too. If demands come from customer arrivals, then ...
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9 votes

Safety stock when there is uncertainty in order completion

What you’re describing is known as inventory optimization under yield uncertainty. There is quite a bit of literature on it. Two relevant literature reviews are Yano and Lee (OR 1995) and Grosfeld-Nir ...
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9 votes

Good distribution assumptions for customer demand in a supply chain

In my understanding, using normal/Poisson distribution for customer demand is mainly for two reasons. These distributions have nice properties for theoretical analysis in supply chain models These ...
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8 votes

Which EOQ-based $(r,Q)$ approximation has a fixed worst-case error bound?

Only the EOQB approximation (approximation 2) has a fixed worst-case error bound. Zheng (1992) proved an error bound of $\frac18$, and Axsäter (1996) proved a stronger bound of $(\sqrt{5}-2)/2 \approx ...
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7 votes

Holding cost vs carrying cost vs storage cost

According to a buddy of mine who was a faculty member in the area of purchasing / sourcing / procurement (they change their name every few years), "holding cost" and "carrying cost" are used pretty ...
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  • 29.7k
7 votes

One and two period policy for inventory situation

I think you simply made a mistake in the sign of one expression. You already figured out that: $$\Phi(y_2^0) = \frac{p-c}{p+h}.$$ So: $$\begin{align} &1 - e^{-\frac{1}{25}y_2^0} &&\hspace{-...
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7 votes

Three newsvendor functions, three optimal solutions—which is correct?

This question provides a good example about a common problem we have when teaching newsvendor concepts. In some of the most useful problem settings, it can be tricky for students to properly specify ...
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  • 1,502
7 votes

Holding cost vs carrying cost vs storage cost

I agree that holding cost, carrying cost, and storage cost all sound like the same thing. The only thing I will add to the answer by @prubin is that often holding costs are expressed as a percentage ...
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7 votes
Accepted

Monte-Carlo Simulations in inventory management

I'm in general agreement with Larry's answer, but with one qualification. If you are generating random demand quantities from the sample CDF for a year, your demands will not conform to any trends or ...
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  • 29.7k
7 votes

Recommendations for OM blogs

For OM, you might like Jay, Barry and Chuck's OM Blog. For OR, I like OR in Devon, UK as well as many of the entries in Richard's excellent answer. I had a few other OR blogs that I liked, but sadly ...
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6 votes
Accepted

How to form math model to solve this problem using cplex

In general it's good to write some equations before. But when you rely on an algebraic modeling language like OPL you may also directly try your ideas. Disclosure: I am the author of the linked ...
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6 votes
Accepted

Units in the EOQ problem

In the EOQ setting, the total cost incurred during one order cycle is: $$TC = K + \frac{hQ^2}{2 \lambda} \;\;,$$ where the units of $K$ must be only \$ and $Q$ measures the inventory count in items ...
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  • 1,502
6 votes
Accepted

Safety stock for log-normal distribution demand

To calculate the base-stock to meet a 99% type-1 service level, we need the 0.99 fractile of the demand distribution. The safety stock level is the base-stock level minus the mean demand. For the ...
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6 votes

Monte-Carlo Simulations in inventory management

Why not build the forecasting directly into your simulation? So, in each period $t$, you generate a forecast $y_t$ using whatever method you want (moving average, exponential smoothing, etc.), and ...
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6 votes

Recommendations for OM blogs

Our blog might be useful too: https://www.optaplanner.org/blog/ We cover OR use cases (just did an article on Covid Appointment Scheduling), our technology and general insights.
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6 votes

Minimizing cost of transportation and storage of items

I would approach this as a mixed integer linear programming (MILP) problem. There are a number of MILP solvers, some open source, some commercial (with some of the commercial solvers providing free ...
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  • 29.7k
5 votes

Units in the EOQ problem

The coefficient $2$ in the first equation has unit $1/\text{order}$, so the second approach is the right one, and $Q^*$ has units $\text{item}/\text{order}$. The unit comes from the holding cost $hQ/...
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  • 2,665
5 votes
Accepted

Three newsvendor functions, three optimal solutions—which is correct?

Only approach 1 is correct! The other two approaches double-count one of the costs. In particular, approach 2 double-counts the cost of purchasing units. The cost of purchasing units is already "...
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5 votes
Accepted

Safety stock for lumpy demand

Just like any other demand distribution (e.g., this one), you want to set the base-stock level ($S$) equal to $F^{-1}(\alpha)$, where $F(\cdot)$ is the cdf of the lead-time demand distribution and $\...
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5 votes
Accepted

Minimizing cost of transportation and storage of items

I won't write a python solution as i am not familiar with any python modeling language but i can describe the approach i took in the past to solve problems like this. I would solve this problem using ...
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4 votes

Normal demand and normal lead time; is lead-time demand normal?

I tried simulating lots of normally distributed lead times and the normally distributed demand in each. The lead time demand sure looks normal: But a normality test gives $p = 0$ to at least 9 ...
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4 votes

Approaches for choosing a "risk" factor in an Inventory Optimization problem?

Here's an approach that might be close to what you are looking for. Suppose that we have $n$ products, and for each product $i$ we know: $c_i$ = purchase cost per unit (i.e., cost to order inventory ...
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4 votes

Good distribution assumptions for customer demand in a supply chain

Question: Why do we normally assume normal distribution/Poisson distribution for customer demand in a supply chain? Answer : Based on my experience in the industry, I have seen that generally, ...
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  • 81
4 votes

Estimating optimal inventory in times of high uncertainty due to coronavirus

This is indeed a newsvendor problem. The fact that D is very uncertain only makes it more so. If we were in normal times, the standard approach would be: Use your historical data to calculate $\hat{\...
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4 votes

Units in the EOQ problem

It is an interesting question. EOQ model starts from that the minimum point of the total cost (Inventory holding + Ordering cost). At the minimum point, the Inventory holding cost equals to the ...
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4 votes
Accepted

(Q,R) inventory policy with supplier disruptions

Yes, there are such models. On (Q,R) specifically, see Gupta (1996), Parlar (1997), Mohebbi (2003), and others. There are many papers on other inventory models (not necessarily (Q,R)) under ...
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4 votes

Recommendations for OM blogs

SAS has several blogs. Here are two relevant tags: https://blogs.sas.com/content/tag/optimization/ https://blogs.sas.com/content/tag/operations-research/
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