OR in Restaurants

The topic for this month's INFORMS blog challenge is "OR and Food". I suspect that a number of my fellow bloggers will jump on the diet problem example, also known as the Stigler diet. That also happens to be the name of Tim Hopper's blog, so I'm inclined to leave it to him. Also, while LP diet models may be suitable for selecting animal feed, I think the Geneva Conventions prohibit their use on humans.

My expanding circumference and history at restaurants (*, **) makes it reasonable for me to write, instead, about applications of OR to food service. There are, in fact, a surprising (at least to me) number and variety of these.

• Here at Michigan State University we have The School of Hospitality Business (SHB), the second-ranked hospitality business school in the country (behind Cornell's). Years ago, one of my colleagues from SHB, Dr. Michael Kasavana, told me that restaurant chains (and perhaps individual restaurants) use linear programming as part of menu engineering.  (***) That's Mike getting credit in the first footnote of the Wikipedia entry, putting him one up on me in the Internet fame competition.  See, for instance, "How Do Restaurants Use Linear Programming for Menu Planning?" for a (very) non-technical introduction. Unfortunately, I couldn't find a more suitable link for an OR-savvy audience.
• Researching this entry, I tripped over a few papers using Data Envelopment Analysis to determine whether restaurants in general, and specifically their use of IT in at least one case, are operating "efficiently".
• I found a doctoral dissertation entitled "Managing Restaurant Tables Using Constraint Programming", whose connection to OR should be self-explanatory. The problem encompasses the assignment of tables to diners, both via reservations and walk-in traffic, the possible combination of tables for larger parties, negotiation of reservation start times, and possible on-the-fly reallocation of tables.
• Linear programming has been applied to staffing problems, including the staffing of restaurants (where service personnel, including cooks, are assigned to shifts).
• The "Caterer Problem" is a classic LP/IP application, in which a hypothetical caterer using linen napkins has to plan how to cover demand at minimum cost by acquiring new napkins and laundering soiled napkins (typically via either of two methods with differing lead times and costs). I don't know how often LP models are actually used by caterers or restaurants, but "it's the thought that counts".
• It is well-known that simulation is used to help design both facilities and production systems. Simulation modeling at Burger King was documented in an Interfaces article, and they apparently went so far as to distribute a simulation model to restaurant operators as part of a "Productivity for Planning for Profit Kit". Although I can't find the articles documenting it, BK famously redesigned their restaurants (quite a while back) using a simulation model.  At that time I was a fairly regular BK customer.  Originally, when I walked up to the counter inside, there would be multiple production lines oriented orthogonal to the counter, so that beef patties started at the back of the store and, in the process of moving toward me, magically transformed into ready-to-eat hamburgers.  One day I entered a BK and discovered that there was now a single, U-shaped production line, with the long sides parallel to the counter. A patty started at one end of the line and morphed into a burger by the time it reached the other end of the line. Apparently this redesign was the result of a simulation study.

So OR has its fingerprints all over the food service industry ... and is therefore to blame for the steepest ascent trajectory of my waistline. (This being an election year, I will join the candidates in abdicating all personal responsibility.)

(*) True story #1: In graduate school, friends would invite me to dine with them at a local all-you-can-eat buffet restaurant just to watch the carnage. 

(**) True story #2: A local sub shop once experimented with pizza sales. Someone posted a handwritten sign on the wall: "Pizza by the slice, Sunday noon to 4:00, all you can eat".  So I stopped by on Sunday. The following week, the sign was amended: "Pizza by the slice, Sunday noon to 4:00, all you can eat except Paul".

(***) True story #3: Early in my career, I was teaching linear programming to MBA students.  This being before the advent of free or affordable optimization software, I was in fact teaching them the simplex algorithm, by hand.  (I have since realized the error of my ways.)  At the end of one term, a young lady in the class came up to me, identified herself as a hospitality business major, and proceeded to "chew me a new one", pointing out to me in graphic detail just how useless all this simplex stuff was for her, particularly given her concentration.  I later learned that, the very next term, she had a course in her major from the aforementioned Prof. Kasavana ... in which she had to solve linear programs ... by hand.  The universe does, in fact, have a sense of humor.