Questions tagged [inventory]

For questions about mathematical models and algorithms for optimizing inventories.

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13
votes
4answers
205 views

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?
12
votes
4answers
911 views

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

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 ...
10
votes
4answers
332 views

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), $h$ ...
10
votes
3answers
1k 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 ...
10
votes
1answer
632 views

Loss functions for specific probability distributions?

For a random variable $X$ with pdf $f(x)$, the loss function* is defined as $$n(x) = \mathbb{E}[(X-x)^+] = \int_{x}^\infty (y-x)f(y)dy,$$ where $a^+ = \max\{a,0\}$. Or, for a discrete distribution, $...
10
votes
1answer
123 views

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

I'm working on an Inventory Optimization (Allocation) problem. The decision variable is the amount of inventory budget to allocate for each product, from a set of products. My objective is to ...
8
votes
1answer
282 views

Safety stock when there is uncertainty in order completion

Safety stocks account for uncertainty both on demand and provider lead times, but never mention how to include the effect of incomplete orders. For example, what would happen if a provider always ...
8
votes
1answer
85 views

Can I use an MDP for a stochastic inventory model when my demand distribution is non-stationary?

Most formulations of Markov Decision Processes for stochastic inventory models I've come across assume a fixed demand distribution. But in my case I have a time series forecast with a non stationary ...
8
votes
0answers
82 views

Is a base-stock policy optimal for a serial inventory system with upstream stockout costs?

In a serial inventory system without fixed costs, an echelon base-stock policy is known to be optimal if there is no stockout cost at any stage except the last stage. (This was proved for finite-...
7
votes
1answer
64 views

An upper-bound on the value of $S$ in $(s,S)$ policy

I recently have come across a problem which can be categorized as a stochastic optimization. The problem seems simple, but I haven't been able to solve it yet. It has a major impact on algorithm ...
7
votes
0answers
73 views

Can demand be modeled by a limited amount of probability distributions?

In stochastic inventory control, it is very important to model the demand appropriate to set e.g. order levels. Demand can be fit to a certain probability distribution via many means (e.g. a goodness ...
7
votes
0answers
63 views

Modelling a simple ordering problem to have balanced delivery days

Assuming that I should buy 50 items from 25 different vendors with pre-known delivery duration between 2-7 day for each, which day of a week should I place each order so that the delivery days be even ...
6
votes
2answers
143 views

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

Here is a typical setup for the newsvendor problem: The newsvendor buys newspapers for $c$ each, sells them for $r$ each, and salvages unsold newspapers for $v$ each. The demand distribution has ...
6
votes
1answer
171 views

Lead time longer than cycle time

I am trying to calculate the reorder point and safety stock for a pharmaceutical product. I am using this formula $$r = \mu_{LTD} + z_\alpha\sigma_{LTD}. $$ $$SS = z_\alpha\sigma_{LTD}. $$ where, $$...
5
votes
2answers
495 views

Monte-Carlo Simulations in inventory management

I am using Monte-Carlo simulations in Microsoft Excel to determine optimum reorder points and safety stock levels. I have the demand patterns of the last one year of the product. Using that I can ...
5
votes
1answer
62 views

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

There are two common approximations for the $(r,Q)$ inventory optimization problem that use the EOQ model. It is well known that one of them has a fixed worst-case error bound, but there is confusion ...
5
votes
2answers
85 views

Estimating optimal inventory in times of high uncertainty due to coronavirus

I'm trying to help out a relative of mine who runs a small highly seasonal business in the clothing/textiles industry. 80% of sales are in Q1 of every year, and the purchasing and manufacturing ...
5
votes
1answer
218 views

Safety stock for log-normal distribution demand

I came across this example on how to model your lead time demand as a log-normal distribution and calculate the safety stock. https://www.linkedin.com/pulse/why-you-keep-missing-your-service-level-...
5
votes
1answer
175 views

Safety stock for lumpy demand

I have a product for which the monthly demand pattern for the last year looks like the following. The product is ordered only 22 days out of 366 days in batch sizes of 272 kgs. Since there are so many ...
4
votes
1answer
105 views

One and two period policy for inventory situation

The following exercise is in the book Operational Research by Hillier, 7th edition, page 978. In this exercise $p$ and $p$ are the stockout and holding cost parameters, respectively. $𝑦^0_i$ is the ...
4
votes
1answer
34 views

(Q,R) inventory policy with supplier disruptions

I am trying to understand the (Q,R) inventory policy with a type 1 service level and demand and lead time modelled as normal distributions. As far as I have understood, the assumption is that the ...
3
votes
2answers
102 views

Inventory Theory

I've been doing a bit of inventory theory, and just wanted to know if I could interpret: "Tim has decided to keep enough safety stock to prevent a shortage before the delivery arrives during 95 ...
2
votes
1answer
70 views

How to calculate Cycle & Safety Stock

I have been asked to calculate cycle and safety stock levels for one of our business units. I have very little/no knowledge on the subject of inventory theory so would like to ask what a reasonable ...
2
votes
1answer
87 views

Safety stock calculation with production forecast variance

I am trying to find an safety stock calculation where the expression incorporates: Lead time variance Sales demand variance & Production forecast variance My calculation so far is based on the ...
2
votes
1answer
47 views

Reorder point and safety stock for very long lead times

I have previously asked this problem here-Lead time longer than cycle time, but I keep getting more confused the more I think about it. Using the Q,R inventory model, suppose my mean monthly demand $\...
0
votes
1answer
154 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 ...
-8
votes
1answer
129 views

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 ...