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Optimize inventory for omni-channel retailers

Inventory optimization for an omni-channel retailer

The development of e-commerce worldwide leads to a drastic change in the way people are purchasing their goods. Nowadays consumers make use of a variety of channels to gather information about products, compare prices, buy and ultimately pick up their products. For example, a customer may discover a product online or in store, can search for information about the product on the web, in stores, via apps or social media. Finally, the customer may buy it online or from the store, and choose to have it delivered at home or a convenient pick up location (store, post office, or specially designed boxes).

In response to these new customer behavior and expectations, retailers around the world are starting to expand their services, enabling consumers to make their purchases via their preferred channel combination. Many retailers offer customers the possibility to shop online and have the items delivered from a nearby store or a distribution center. Similarly, traditional online retailers open new facilities where customers can view items or purchase them. recently opened Amazon Bookstores, a series of physical stores where customers can buy books, order them online or download, and place them on their wish lists. These developments gave rise to what is referred to as omni - channels.

In order to adapt to the new trends in commerce, both online and offline retailers need to redesign their networks and operations. In this project, we will study omni-channels with a focus on pricing and demand fulfillment strategies for a retailer who collects orders both via a store as via an online channel.

Problem description

In this project, we consider the inventory problem of one retailer with one shop and one central warehouse (two stage supply chain). There are two types of customers: those who buy online and customers who visit the shop (offline customers). The warehouse serves online customers directly and replenishes the shop, while the shop serves offline customers only. If the inventory level drops below a critical level, the retailer offers offline customers the possibility to have the items delivered later against a price discount (from the central warehouse). Customers who do not accept the discount are either served from the stock on hand if there is sufficient stock or supplied from the central warehouse. The price discount can also be offered in case of a stockout.

Costs we consider: transportation costs (warehouse-retailer, warehouse-online customer), inventory costs (warehouse + retailer, inventory costs smaller at the warehouse), lost sales costs at retailer, backorder costs at warehouse, (shelf space usage costs – related to maximum inventory on hand), ‘discount’ cost

Objective: Decide inventory levels at both central warehouse as at the shop, and the discounts to give such that the expected total costs are minimized. Compare this system with a system without discounts (shop serves only offline and warehouse only online + replenishments).

Extension: Multiple products


  1. K.L. Cheung, A continuous review inventory model with time discount, IIE Transactions 30, 1998
  2. Q. Ding, Kouvelis P. and Milner, J.M., Dynamic pricing through discounts for optimizing multiple-class demand fulfillment, Operations Research, Vol. 54 (1), pp. 169-183, 2006

Details of the project

This project is in collaboration with dr. Adriana Gabor and dr. Youssef Boulaksil from United Arab Emirates University, Al Ain, UAE

Duration of project: 6 months
Salary: 700 Euro/month
Benefits: At the end of the project, the student will be invited in Al Ain to present his/her results

Information: Jan-Kees van Ommeren