What's cheaper & faster for my lab, keep a stock of electronics components or order?
I'm going to disagree with others. No, don't bother keeping track of inventory. You are doing this for engineering, not production, so knowing the exact number of parts on hand is a lot less valuable than the time wasted keeping the system up to date, and the inevitable busywork when someone doesn't. Engineers need to be able to grab a resistor without having to fill out a form, even after the fact.
However, you do need to keep parts on hand. See my answer here for how we do it. That picture is quite old, and our parts stock is probably 30% bigger now, but the system is the same.
Instead of tracking inventory, keep a clipboard or a list in a computer somewhere of items that you are running low on, or wish you had. Whenever new parts are ordered, include the items on the wish list.
When you do order parts, get a few more than you need and put them in your lab stock. Usually buy to the next higher price break. For example, it makes no sense to buy less than 100 0805 resistors at a time. If you need three of one IC, buy 10 or 20. This is how items get added to lab stock. Sometimes when you buy one item, you realize you may have a use for a similar item and get a few of those too.
It also helps to standardize of certain parts. For example, there are many many small signal bipolar transistors that can handle a few 10s of volts, 100s of mA, and are reasonably fast with decent gain. In the absence of special requirements, I use MMTB4401 and MMTB4403 for these. We buy those a few 100 at at time, depending on where the price breaks are. Many other transistors would do, but sticking to a small number of jellybean parts when it doesn't matter simplifies your lab stock and ultimately production inventory.
One thing to keep in mind when ordering parts to keep on stock is the work time of the engineers.
If your engineers have to spend an hour writing an order list that includes common parts, then over time that will cost you more than just keeping a bunch of those common parts on hand all the time.
For example, a reel of 5000 100K resistors costs around $12. If you spend that $12 one time, then your engineers won't have to spend time rooting them out of the catalog and putting them on an order list everytime you need one.
For common parts, we used to have a rack with reels, and an organizer with trays.
We'd cut a few hundred off the reel, and put them in the organizer. When you needed some parts, you took then out of the organizer. When it ran out, you refilled from the reel. When the reel ran out, you'd reorder while you use up the parts in the organizer.
What would generally happen was that the reel would land on somebody's desk until we had to order something else anyway, and the new reel would just be part of that order.
If somebody had a project that needed more than few of some (cheap) part, we'd just order a reel and be done with it. Working that way, we built up a collection of common parts for the things we worked on.
Simple, cheap, no inventory software needed.
More expensive parts we kept in a storage area with an inventory and management program. We had stuff in there that ran from low price but too bulky for the organizer (audio connectors and the like) to expensive ($1000 per piece, low numbers in stock, mostly because our work consisted of customizing those expensive items.)
Step 1, take inventory now. Right now.
Step 2, keep inventory accurate and organized from now on.
Step 3, Reassess needs at some time in future after you have your inventory issue resolved.
You should have commonly used parts on hand. And if you don't keep track of what you have, then you shouldn't be running a lab/business. If the engineers won't bother to check for what you have on hand, and needlessly order, get new engineers that will.