Research News

A New Algorithm to Optimize Inventory and Fulfillment in Omnichannel Retail

February 7, 2023

Order fulfillment in an omnichannel environment is very complex but a Khalifa University researcher has developed an algorithm to minimize costs and optimize fulfillment for orders online and in-store.


Fueled by the Covid-19 pandemic, global e-commerce retail encompassed 19.6 percent of retail sales in 2021. And this is expected to grow, with experts predicting that online shopping will make a 24.5 percent share of all sales by 2025. Increasingly, however, brick-and-mortar stores are making a comeback as retailers choose an omnichannel strategy.


Dr. Adriana Gabor, Associate Professor in the Department of Mathematics, with researchers from Technical University Eindhoven, the Netherlands, studied an inventory-optimization problem for a retailer that faces stochastic online and in-store demand. They proposed a two-stage stochastic optimization method and designed an algorithm for dynamic fulfillment to minimize the retailer’s costs. They published their results in Computers and Industrial Engineering.


“Traditional retailers such as Wal-Mart and Target, who used to sell only through brick-and-mortar stores, expanded online to be able to offer their customers a larger assortment of products and the possibility to shop from the comfort of their own homes,” Dr. Gabor said. “Large e-commerce companies such as Amazon and Google, however, have purchased brick-and-mortar stores recently to offer their customers the opportunity to try their products before purchasing them. These retailers are using a variety of channels to fulfill customers’ orders, including dedicated fulfillment centers and existing stores where items can be collected by or sent directly to consumers.”


Order fulfillment in an omnichannel environment is very complex. “Integrating inventory for both types of customers (online and in-store), as well as designing cost-effective fulfillment decisions, is very complex and coupled with many practical difficulties,” Dr. Gabor said.


The research team chose to tackle a joint fulfillment and inventory optimization problem originally proposed in 2021. In the problem, an omnichannel retailer has a set of facilities that fulfill both online and in-store orders. The goal is to decide the initial inventory at each location for a number of time periods and to design a fulfilment strategy that minimizes the total expected costs of the retailers, including holding, transportation, and penalty costs.


“This problem is mathematically very difficult,” Dr. Gabor said. “Although combining dynamic fulfillment with inventory can reduce costs considerably, it makes the joint optimization problem very complex due to the uncertainty in demand and the fact that orders can be fulfilled from different locations.”


Due to the uncertainty in the demand process, the research team approached the problem with a two-stage stochastic optimization strategy, in which they decide the initial inventory in the first stage and find an order fulfillment policy in the second.


To reduce the computational burden of working with a large number of scenarios in the optimization problem, the team proposed a novel method for scenario reduction, based on clustering scenarios according to a predefined measure of similarity using Linear Programming and the Turing-Good estimator.


“The main advantage of our method is that it does not require us to specify in advance the number of scenarios needed,” Dr. Gabor said. “Our algorithm can lead to average cost reduction of 11.81 percent compared with existing methods, and for longer time horizons, the optimal solutions obtained by our algorithm are 3.93 percent lower.”


Their algorithm showed from a managerial point of view that for short time horizons, fulfillment costs are the major component of the total costs, so retailers should focus on having sufficient inventory since this decreases the probability of fulfilling items from distant locations. For longer time horizons, both inventory holding and fulfillment costs are important, so retailers need to find the balance between the two costs.


When the proportion of online customers increases, holding costs can be reduced by pooling inventory among different stores. However, pooling inventory results in higher fulfillment costs, so the relationship between online and in-store demand should be carefully considered when making inventory decisions in an omnichannel environment.


Finally, in situations with high demand variability, the researchers found it is better to focus on having sufficient inventory, as this can reduce both lost-sales costs and fulfillment costs.


“For future research, we want to look at improving the scalability of the algorithm to a large number of locations, long time horizons, and a low proportion of in-store customers,” Dr. Gabor said. “Another interesting venue for research is studying how to adapt our proposed scenario reduction method to other stochastic optimization problems.”


Jade Sterling
Science Writer
7 February 2023