Estimation of expected stockout delays in divergent multi-echelon inventory systems using simulation

Abstract

Stockout delay is an important component of lead time calculations in inventory control literature. This thesis presents a deep dive into the topic through a literature review, which is accompanied by a numerical study. This numerical study provides a comparison of available models along with a simulation model that looks
at two different order fulfillment types: complete and partial. Based on the findings, we present an analysis of the results that focus on the accuracy of the models and how different variables/parameters interact. We present future areas of research that were identified as gaps from the thesis along with examining ongoing
research.

Popular Abstract

This project has investigated how well methods for estimating shipping delays perform.

As a customer you can nearly always expect to find the item that you want in the store at a competitive price. In part, that experience can be attributed to companies’ efforts to model inventory dynamics. The problem they face is the uncertainty of the system. From the retailer’s perspective they don’t know how many customers will demand a specific product in the coming week, and they also don’t know with certainty how long it will take until an order is sent from the warehouse. These delays are due to stockouts at the warehouse and the frequency of their occurrence is influenced by how much stock is at hold. Previous research has shown that a rather low service level at the warehouse is optimal. While forecasting demand has typically been the focus, in this thesis we evaluate how well methods for estimating stockout delays actually perform.

To begin, evaluating these methods requires something to compare them against. Ideally, we would go out into the real world and make predictions from the setup of an actual inventory system, but this was not feasible. Instead, we make use of a simulation program that follows all the rules and standard behaviour a computerized inventory system would follow. The setup has eight retailers that place orders with a central warehouse, which in turn orders from an outside supplier. To properly test the performance of the methods, they are evaluated under different conditions to ensure the results are valid.

The four methods are implemented in Python and can then output estimates for each setup. These estimates are then compared to the simulation results. What we found is that the method proposed by Berling and Farvid (2014) performs the best of the 4 methods tested. One thing worth noting is that the worst performing method does not differentiate the delay between the retailers and considers only the average delay.

Of the different setup factors, the warehouse fill rate contributed the most to delay. More specifically, a higher fill rate leads to lower delay. Higher mean time between arrivals and larger batch sizes both lead to increases in delay but their effect was not as large.

For future research, methods that cover a partial delivery policy could be explored. Under this policy the warehouse always delivers what it has on hand even if that is not enough for a full order. In our thesis we include one possible method in this area that can be researched.

• author: Svanholm, David and Boissonnault, Jacob
• supervisor: Peter Berling
• organization: Department of Industrial and Mechanical Sciences; Production Management
• course: MIOM05 20261
• year: 2026
• type: H2 - Master's Degree (Two Years)
• subject: Technology and Engineering
• keywords: stockout delay, delay, multi-echelon, complete delivery, partial delivery, order fulfilment, simulation, lead time
• other publication id: 26/5351
• language: English
• id: 9234931
• date added to LUP: 2026-06-10 13:50:09
• date last changed: 2026-06-10 13:50:09