Questions tagged [inventory]

For questions about mathematical models and algorithms for optimizing inventories.

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7
votes
1answer
58 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 ...
8
votes
1answer
272 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 ...
7
votes
0answers
52 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 ...
6
votes
0answers
56 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 ...
8
votes
1answer
62 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 ...
10
votes
3answers
760 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
102 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 ...
13
votes
4answers
127 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?
8
votes
0answers
67 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-...
4
votes
1answer
48 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 ...
-8
votes
1answer
116 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 ...
10
votes
4answers
267 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), $h$ ...
5
votes
1answer
96 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 ...
6
votes
2answers
127 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 ...
9
votes
1answer
124 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, $...
12
votes
4answers
467 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 ...