There have been two typical schools of thought on Warehouse Automation justification and they have become quite blurred in the last few years. I have no idea how you do things, so this is a classic abstract justification and might be a reasonable starting point. (There are many excellent books, courses, and sites which can be very useful and applied to your specific situation.)

Warehouse automation is typically the highest return application that one can implement. Often paying for itself in months and rarely over a year.

Prior to Y2K, almost all warehouse/inventory justification used financial justification, and then as early as 1996 or so we started to see the beginnings of on-demand/customer service justification. I would try to look at both to get a balanced perspective.

Traditionally, financial justification was fairly straight forward. It started with the existing inventory let's say $5,000,000. The key ratios of inventory turns would be calculated which is just the sales divided by the inventory value. Let's say 4X. Management would try to either reduce inventory without impacting sales or customer service levels, or try to grow with the same inventory levels. Let's say we could improve by 10% to 4.4X. In this example, inventory could be reduced by $454,545 or sales could increase $2,000,000 without increasing inventory levels. Additionally, the savings on inventory is usually tax free and can be used for other purposes. This is the one-time savings. This can be especially critical and change the analysis if the inventory growth is forcing a new or additional warehouse. This can often be a proxy for a control/level issue.

Also in Traditional analysis, there usually an on going savings calculated. This has to do with Inventory Carrying Costs. In a simplified state, management would decide on what their inventory carrying costs are. This would include things like inventory shrinkage (theft, lost, breakage, etc.), obsolesce, interest charges, if any, on borrowing for inventory purchases, warehouse space, insurance, etc. Over the years and between companies it has typically varied between 25% and 40%. So, in the prior example, the $454,545 reduction would also generate an on going savings of approximately $113,636 per year.

Management sets the objectives for the turns and the warehouse system is implemented to achieve a return on investment. Often a small reduction like even 3% in inventory could pay for the system given the reduced prices these days.

Often these traditional implementations would tie in Purchasing and implement some variation of a "Gordon Graham" planning algorithms which tried to balance service levels with the inventory carrying costs. Few do this formally today though conceptually most companies have a feel for this balance.

There have been many variations on these themes over the last 30 years but conceptually they have pretty much remained the same.

On Demand is driving many of the decisions today. We first encountered this in 1996 when we provided project management and testing for a large company when they went from 13 warehouses to 4 Distribution Centers. Though originally justified many times over by the closure of the warehouses and the improved inventory efficiencies what it really set up was the just in time link initially with a major innovative key customer. This customer started sending, several times a day, the sales data on our customer's products from their stores. This was loaded into our customer's forecasting system and the manufacturing plan was modified to meet the real demand at the store level. Additionally, it setup a cross dock situation from our customer's Warehouse to their customer's Warehouse right around the corner. The inventory did not have to be stocked and then re-picked. Customer service levels improved dramatically. This became the real justification, and the infrastructure allowed them to participate early and often in the "on demand" world. This is a component of many strategic partnerships. Much of these strategies are fairly common today.

The "on demand justification" is more on shipping metrics, it assumes error free shipping, real time customer status both order and shipping, cross docking, customization and other value added services are included in customer partnering. Many decisions today are driven by key customers demanding and getting better interfacing into their systems (EDI or B2B direct into their purchasing and warehouse systems) on an on demand basis. This is usually mutually beneficial and easily justified on sales/marketing and customer service basis. In this case, properly done the financial justification is also achieved because the just in time/ on demand scenario with high customer service also should reduced inventory levels for both partners and produce higher sales. This can be implemented a customer at a time and often is....

Your justification might come from financial impact due to better inventory control and levels, on demand customer service, visibility into warehouse production metrics for productivity improvements and early problem detection, and the implementation of an infrastructure which can allow closer partnering with your key customers.

Managing a warehouse is more than managing inventory. Software, systems, Radio Frequency devices have all significantly reduced in price. What has remained constant is the effort it takes to install them. Few system impact every area and policy in a business like the warehouse. It gets clinched that you need top management support for systems, don't try to implement a warehouse system without real support. 50 to 80% of warehouse \ system's cost is in the implementation side, and that could be generous because the implied cost of the implementing company's personnel is not really included. There are lots of decisions to be made, lot's of people to train, many levels of people to train, customer interfaces to worry about. The one forgiving aspect of warehouse systems is that they can be implemented a module at a time, a product line at a time, and sometimes even a customer at a time. This incremental aspect can be used in one's favor to adjust as you go....rather implement with a big bang theory (all at once). Either way.... it is usually very much worth the effort.