# CQM – Optimal Order Picking from a Large Retailer Warehouse #SWI2018

The situation is as follows: A conventional retail warehouse handles customer orders. A customer order is picked into different totes. The totes are picked by order pickers. For efficiency reasons, an order picker picks a set of totes. This set is called a batch. Products are stored in racks divided over multiple aisles. Ideally, a batch is created in such a way that all totes of a batch touch the same aisles as this has a positive effect on the walking distance of the order picker. A poor solution is a batch of totes all touching different aisles as this has a negative impact on the walking distance of the order picker.

An algorithm is available to generate the batches. We are looking for a mathematical model that would provide insight into the performance of this batching algorithm. How is the performance influenced by the number of aisles in the warehouse, the number of aisles an individual tote needs to visit, the number of totes in a batch?

The results of the batching algorithm may be translated into random variables describing the distribution of the aisles being visited by a single tote and the probability that totes need to visit common aisles. We are interested in whether it is possible to formulate such a mathematical model that captures the relevant parameters of the system and the batching algorithm solutions and gives insight into the performance given the uncertainties of the system. A relevant performance measure would be the total number of aisles in a batch divided by the actual number of aisles visited. Thus, the higher the measure the better the performance. Example: there are 5 totes each visiting 3 aisles (out of 10 aisles). The best situation is that only 3 aisles are visited giving a measure of 5. The worst situation is that all 10 aisles are touched giving a measure of 1.5.

All in all, for this problem we are aiming at the creation of a model, which provides inside into the quality, robustness, and sensitivity of the output of the batching algorithm, given the characteristics of the warehouse layout, and tote x aisle combinations.