Optimal Grocery Shopping Formula

by Sean on April 14, 2006

This falls into the “Just in Case You Doubted that I’m a Financial Nerd” category:

I had one of those “Aha!” moments earlier today while on my way to an Advanced Cost Accounting class at the university. We’re currently studying the cost accounting method for so-called “Just In Time” manufacturing systems, and I suddenly saw a real-world (okay, a “my world”) application for this formerly boring concept.
In Just-In-Time (JIT) manufacturing systems, raw materials are delivered “just in time” to the manufacturer, arriving exactly when they need to be inserted into the manufacturing process. Obviously, there are significant scheduling considerations and numerous calculations required in order to make sure that the right amount is delivered at the right time.

Order too much, or have it arrive too early, and you’ve got raw materials sitting in inventory. It doesn’t sound bad until you consider the costs associated with storing the raw materials, which includes the possibility of spoilage.

Order too little, or have it arrive too late, and you’ve got to hold up the entire manufacturing process until you’ve got the required quantity of raw materials. Either way, you’ve got to be as precise as possible when it comes to ordering raw materials. There’s even a formula for determining the quantity you should order each time. Here’s the basic version of the formula:

Economic Order Quantity = Square root (2 x Demand x ordering cost / carrying cost per unit)

This states that the best quantity to order (least overall associated costs) is the square root of 2 times the monthly demand in units, times the relevant ordering costs per purchase, divided by the carrying cost of keeping one unit in stock for a month.

Now here’s where it applies to you and me:

Let’s say that you go shopping once every two weeks. Each time you go, you spend about $5 in gas and wasted time. You buy the full range of groceries, including canned goods and fresh fruits and vegetables, with a total cost of $200. The canned stuff keeps pretty well, but the fresh food spoils at the end of the first week, costing you about $20 in lost food.

Based on the formula, and using $1 to represent one “unit” of food, here’s how much you should order every time you go shopping:

square root of (2 x 200 x $5 / $.10 per unit of food) = $141.42 of food.

Admittedly, I’ve used very sloppy math above, but it illustrates a common-sense concept. If you’re a bachelor and you lose 1/3 of your fresh food to spoilage after one week, you should shop that much more often and buy that much less each time. If you’re buying mostly boxed or canned foods that never spoil, you can shop much less often and buy more each time. If it costs you $10 in gas each time you go shopping, you should shop less.

I think I’ll actually run the numbers on my own grocery buying habits. I seem to lose a lot of fresh spinach and salad greens to spoilage…

{ 4 comments… read them below or add one }

Jocular Jarhead April 15, 2006 at 4:27 am

Wow! I knew spending $36,000 for an MBA would be worth the cost. Thanks for showing me the light! :)


Sean April 15, 2006 at 11:25 am

I know, I know. My wife said something like, “Well, if you knew it was a nerdy post, then why did you post it?” It’s a fiendish, nerdy compulsion, I tell you. I think that if I were ever homeless I’d carry a sign that said, “Will [bore you with personal finance minutiae] for food.” :)


Pat Sneath April 16, 2006 at 9:47 am

Duh, why are your spinach, and salad greens going bad? You could always add it to soups, or freeze it ( or eat it sooner!). Math challenged old lady, here, but still eating and wasting less.


Sean April 16, 2006 at 8:45 pm

It’s part of the curse of being a math nerd – even if you’re not doing everything right, you still try to find a mathematically optimal solution. Sure, I could have said, “I’ll just buy less food,” but where would be the fun in that? :)

Seriously, though we don’t waste a whole lot of food. It’s just the fresh stuff that goes bad, and that’s because I don’t have enough fruit-vegetable smoothies to use it all.


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