# Questions tagged [inventory]

For questions about mathematical models and algorithms for optimizing inventories.

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112 views

### Alternate formulation for modeling inventory constraints

I'm working on a inventory optimization problem where inventory used at a time-period is computed based on price-bucket that is selected for an item. Problem contains multiple items (around 10K), 15-...
110 views

### Scheduling of planned orders while respecting certain stock levels

I am searching for the academic name of the problem of computing a valid schedule for planned order. More precisely, The problem consists of: list of orders O, available vehicle per day K, and the ...
55 views

### Confusion about how to account for leadtimes with a fixed-review period base stock(S,T) inventory policy

So we're using a fixed review period model with base stock $S$, and review period $T$ of 1 month - the period is not chosen optimally to minimise ordering cost like in an EOQ model, it's just a nice ...
84 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 ...
148 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,...
588 views

### Recommendations for OM blogs

Could someone suggest good blogs to follow for researchers in Operations Management/ Supply Chain Management /Operations Research?
32 views

### 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 ...
20 views

### 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 ...
89 views

### inventory control for vending machine like mini store

Let's say we have a kiosk inside gas station selling cigarettes and snacks outside a supermarket. There are limited space for each product. The kiosk only allows to get restocked from the supermarket, ...
102 views

### Safety Stock with Fill Rate Criterion

When applying the base stock inventory policy, assuming the daily demands are normally distributed with parameter $(\mu, \sigma)$, we can find the optimal parameter $S$ (the base stock level) in ...
43 views

### 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 ...
139 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 ...
101 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 ...
109 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 ...
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 $\... 2answers 768 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 ... 1answer 281 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 ... 1answer 441 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, $$... 1answer 46 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 ... 2answers 94 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 ... 1answer 365 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-... 2answers 122 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 ... 1answer 175 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 ... 1answer 72 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 ... 1answer 285 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 ... 0answers 81 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 ... 0answers 73 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 ... 1answer 116 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 ... 3answers 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 ... 1answer 136 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 ... 4answers 310 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? 0answers 93 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-... 1answer 85 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 ... 1answer 139 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 ... 4answers 405 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 ... 1answer 132 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 ... 2answers 168 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 ... 1answer 2k 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,$...
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 ...