This is yet another post about the intersection of operations research and my frugality.
I occasionally stop by Jimmy John’s to pick up some day-old bread for $0.50 per loaf. I purchase a loaf for each one of my kids and then let them do whatever they want with it for dinner. They love it. Whenever I am in a Jimmy John’s, there is a huge stack of day-old bread. When I try to pick up some day-old bread at the grocery store, there are limited loaves and they disappear quickly. I often have to pay full price.
Is there an optimal strategy for how much bread to sell/bake each day?
The answer must be yes. The costs and revenues seem to be different for the grocery store and Jimmy John’s. At the grocery store, selling too much bread one day will eventually lead to a glut of day-old bread sold at a discount, since it’s unlikely that all of the bread will be sold for full price. Bread is usually discounted to 1/3 – 1/6 of the original price. Those who buy the bread at a discount may have purchased bread at full price if no discounted bread was available, thus leading to lost revenue. Over time, the regular availability of discount bread may make frugal shoppers like me unwilling to pay full price. I suppose a variation of the newsvender problem can be used here.
I don’t think the grocery store is analogous to Jimmy John’s (JJ). There is no “full price” bread available at JJ, since the fresh bread is used in sandwiches. The day-old bread also doesn’t seem to discourage people from buying sandwiches. This is interesting, since the bread is about 1/10 of the price if a sandwich – why not make my own sandwich with JJ bread and pocket the savings? I’m not sure that most sandwich consumers think the way I do. If the extra bread costs < $0.50 per loaf (cost = production + storage costs + labor cost to sell it), then JJ makes a profit for everyone who comes in to buy a sandwich and leaves with an extra loaf. Perhaps this is the dynamic that JJ aims for. Interestingly, the day-old bread I purchased yesterday clearly had just been taken out of the freezer, so Jimmy John’s preserves the day-old bread for future sales, rather than selling leftover bread that has been sitting out at a discount and possibly donating whatever is left.
Do you enjoy day-old bread? Do you see it priced in a way that would lead to lost revenue from the seller’s point of view?
Day old bread at Jimmy John’s.
Punk Rock Operations Research 
May 14th, 2013 at 2:17 pm
I knew a math professor who was a silent partner in a bakery. Something happened and he had to take over the operations temporarily. He was going over the books and realized they were baking way too much bread each day for what they were selling. Every day there were tons of loaves left over. He came in really early one morning and spoke to the bakers and found out the problem. The bakers had a recipe for say 50 loaves of bread, but were only instructed to bake 75, but were simply doubling the 50 loaf recipe. He went through a few lessons on fractions and got the problem sorted out.
May 14th, 2013 at 2:20 pm
Also a big fan of JJ’s day old bread (when there’s a JJ’s around at least), although I’m not a huge fan of their sandwiches. In that sense I suppose I am a complementary customer (or however that would be termed), and if they didn’t sell day old bread I wouldn’t buy anything from JJ’s — from that point-of-view maybe it should be priced higher! Sounds like a fun homework question for a decision analysis course.
On the same note I also enjoy day-old bagels — however, in that case I would fit the more ideal demographic you describe where I buy a “fresh” product and then also add on day-old bagels to my order to bring home.
May 14th, 2013 at 3:41 pm
Well, I had never heard of Jimmy Johns before. The franchise has not crossed the Atlantic yet, and I haven’t noticed any of their stores when I have been in the US. I looked at the JJ website, and there is a comment there that each store has a weekly delivery from JJ HQ apart from vegetables, sourced locally and delivered daily.
It strikes me that the model for a sandwich retailer (Doing one thing and doing it well was an expression on the site) is rather like the Newsvendor problem. There are several perishable items in parallel; bread, meat, cheese, vegetables. However, to a certain extent, the last three of these are different from the bread. Customers know when bread in a sandwich is day-old. Presumably, it is baked on the premises from frozen? And presumably, it is only baked at specific times each day? (Exercise for students to look at?) But cheese and meat have a longer shelf life, and so do most vegetables, so the canny manager will have sufficient stock (fresh or defrosted) for between one and two days of these, and will use items in rotation. But the bread can’t be used like that – the bread that was prepared yesterday can’t be used in sandwiches. Hence the Newsvendor problem applies.
So, one does the classic calculations about the cost of raw materials, the selling price of the sandwich, and a price to sell day-old stock – together with the distribution of the number of pieces of bread bought per day (with any seasonality included!) Perhaps the price of day-old stock is low that the outlet can be sure to get rid of all their surplus?
But there’s probably a marketing ploy here as well. Your local outlet is creating a secondary customer base. Come the day when you are 100 miles from home, hungry, and want food in a hurry – then you will be a loyal customer, pay the price of a sandwich because you have learnt to trust the brand.
And in the grocery store – a different model applies – in the UK, different chains of store have different policies on the discount for items which are labelled “display until today”. It may be 16%, 25%, or more, and the grocery store can increase it dynamically.
May 14th, 2013 at 4:48 pm
Why to buy a sandwich rather than making your own with day-old bread: (a) less labor, (b) saves having to buy/stock other ingredients, (c) the sandwich comes on fresh bread.
As David points out, this looks like a variant of the newsvendor problem. I once knew a family that owned several franchises of a chain of sub shops near where I live and worked. They shared one baker and oven among the multiple stores – it would not be cost-effective to do otherwise, so the stores got one bread delivery per day. You don’t want to end up sitting on a lot of unused bread, but you REALLY don’t want to tell customers you can’t make their orders because you used up the day’s allotment (and, for stores that consider their bread a feature, you don’t want to run over to a supermarket and buy some genetic substitute).
May 20th, 2013 at 2:56 pm
Several local grocery stores donate all their day old bread to food pantries – there’s one charity that sends a truck around to the grocery stores to pick up bread and produce. So it may just be that the stores have chosen to write off the loss as a charitable donation instead of picking up a revenue stream that may downgrade the perceived value of their products. We try to optimize the times visiting the store to find the marked-down meats, though.