# Questions tagged [inventory]

For questions about mathematical models and algorithms for optimizing inventories.

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### Good distribution assumptions for customer demand in a supply chain

Why do we normally assume normal distribution/Poisson distribution for customer demand in a supply chain? Are there other good distribution assumptions?
1k views

In a continuous-review $(r,Q)$ inventory system under a type-1 service level constraint, if the demand per unit time is distributed as $N(\mu,\sigma^2)$ and the lead time, $L$, is a constant, then the ...
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### Units in the EOQ problem

This is a very basic question about a very basic model, but I can't come up with a satisfactory answer. In the economic order quantity (EOQ) model, let $\lambda$ be the demand rate (items/year), $h$ ...
2k views

### Holding cost vs carrying cost vs storage cost

I was reading an article on supply chain management and encountered a number of inventory costs like ordering, carrying, shortage, holding, storage costs. I cannot understand the difference between ...
1k views

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### If $F$ is MHR (log-concave), can the monopoly reserve price exceed the mean?

Let $V\sim F$ be some positive valued random variable such that $F$ has a monotone hazard rate (alternatively $F$ is log-concave). Let $p = \operatorname{argmax}q(1-F(q))$. We call $p$ the monopoly ...
145 views

### Generating numbers that should add up to a fixed value while they follow a known distribution

Suppose a perishable item that is associated with a shelf life $m\in \mathcal{M} = \{1,\dots,M\}$. We have a periodic review system with stock level $S$, i.e., based on the inventory level of the item,...
80 views

### Relation between order quantity and average cycle stock

Annual demand: $1000$ units Unit cost: $5$ dollars Company replenishes the inventory two times per year. Average Cycle Stock: $300$ I am asked to compare average cycle stock with number of ...
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### Lead time higher than cycle time in static EOQ model

All the examples I saw so far were for the case when lead time is smaller than the cycle period. What should the reorder point be if lead time is higher than the cycle time? Should I just simply order ...
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### Concepts for managing inventory and orders with specific fulfillment date

I'm modeling a fairly basic order and inventory management system but with a use case that doesn't seem very common (or at least hard to look up online and in books about operations): the order ...
172 views

### How to form math model to solve this problem using cplex

Hiring company has the following requirement within a year; week 1 to 5: 20 week 6 to 20: 40 week 21 to 40: 35 week 41 to 60: 55 week 61 to 80:75 week 81 to 100: 60 Training time for an ...
131 views

### Scaling of standard deviation for forecast error

I am doing inventory optimization for my firm and need to compute the safety stock for a couple of products. I have learned that the correct quantity to consider in calculating the safety stock is the ...
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### Why the optimal value that minimizes a function does not satisfy condition?

I have found a solved example of A Stochastic Two-Period Model with No Setup Cost in the book Operational Research by Hillier, 7th edition, that has a lot of complicated calculations to arrive to the ...