# Questions tagged [inventory]

For questions about mathematical models and algorithms for optimizing inventories.

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### Optimizing Safety Stock in a Multi Echelon Optimization

In general the relationship between safety stock and service level is non-convex. As it contains often a Normal distribution or simulation. If one considers now optimization the supply chain by ...
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### relationship between safetystock and service level

How is the relationship between safetystock and service level correctly simulated and what data do you need if you don't assume any distribution? EOQ Lead time Demand forecast ...?
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### Seeking Help: Algorithm Recommendations for Inventory Data Adjustment

I am currently working with inventory fluctuation data for a company and facing some issues. The raw data is stored in an xls file, recorded on a monthly basis. According to the logic, the sum of the ...
1 vote
178 views

### Multi-period Inventory Balance in Gurobipy

I would like to get the inventory balance in the oponed facility $\text{C}$ such that, the Inventory at time $t$ is equal to the previous one, plus the inflow minus the outflow. I have tried to create ...
• 81
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### use Forecast distribution width in inventory optimization

I have a demand forecast that gives me a distribution for future demand, for each time period in percentiles (e.g. demand for period 1 will be between 6 and 25 (zero and 100th percentiles, and i know ...
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### To maintain safe order level from a customer

A telecommunication company (CALLME TEL Co., Ltd) receives and processes customers’ orders. Orange Co., Ltd is an important customer, who mostly places orders every 2 months. Medium quantity of ...
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206 views

### How to model not-met demand to next period?

I am trying to include to my model a demand shift. That is, I am having a fixed demand for each period (t), but because of capacity constraints I am not able to serve the whole demand for each period. ...
• 79
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### Inventory Continuity Equation

I have to minimize the inventory remaining at end of the period(28 days). Each item would perish after a fixed number of days and we can order items only on certain weekdays(M,T,S,S). Demand is ...
1 vote
262 views

### MILP modeling Code with pyomo or gurobi or cplex or GAMS. Any link?

I am looking for MILP modeling code with stochastic/deterministic demand for Inventory ordering policy (e.g. (q,r) or (s,S) policy) with pyomo or gurobi or cplex or GAMS. Any link?
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### Marginal Cost of Storage vs. sum of storage cost

I'm working on a model for inventory management. I'm trying to decide for each unit if it is worth holding, or if it should be liquidated at a cost $x$. I'm wondering about the argument that marginal ...
• 83
1 vote
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### Literature on fixed-charge network flow problems with inventory levels

I'm looking for optimization problem classes with inventory control constraints. Given a directed graph $G(V,A)$ where vertex set $V$ consists of production nodes and demand nodes. The arc set $A$ ...
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### Stochastic optimization for inventory management

The deterministic problem is to minimize operational cost subject to constraints in demand, supply and capacity. The ordering policy is periodic review, order-up-to. The stochastic version of the ...
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1 vote
71 views

### Improving Customer First Fulfillment Rate

Data Available: Historical Weekly Demand Total SKU's = ~ 2500 Historical Lead times (Most Suppliers' Shipping from Asia to the US) Problem to solve: Improve First Fulfillment Rate to the Customer ...
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1 vote
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### Simple inventory control with stochastic demand

There is a factory that produces one unit of stock uniformly so that $q$ units of stock are produced during a day. The warehouse near a factory has the maximal capacity of $q$ items, i.e. a daily ...
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### Expected onhand inventory in (s,S) policy

When we are doing inventory optimization, say implementing a base-stock policy, one of the KPIs we monitor is the average on-hand inventory, which we use to calculate the average inventory holding ...
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### Derivation of safety stock formula of an inventory model with probabilistic demand

I am applying the "Probabilistic inventory model with safety stock". There are some assumptions in this model: normally distributed demand, fixed lead time (time between placing the order of ...
1 vote
81 views

### Convex Optimization with Variable Dependency / no unmet demand carry forward

I'm running into an issue with a Linear Optimization Problem. The ultimate goal is to come back with an optimal production quantity (prod_qty) across several items ...
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### One-time price discount Inventory Model

I'm learning operations research and this is a question that I came across: The monthly demand for your family is 10kg, which is bought monthly. The maximum retail price (MRP) is INR400, on which ...
975 views

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### 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 ...
657 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 ...
1k 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, ...
74 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 ...
122 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 ...
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### 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-...
196 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 ...
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### 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 ...
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### 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 ...
297 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 ...
139 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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