mem·o·ry·less·ness

My original thesis project in graduate school related to optimal ambulance routing. It’s good to see people using operations research in that manner, and it’s not surprising how lucrative it can be.

“It’s about how you match the resources you have got available most effectively to the emergency calls that are coming in and it’s not just matching the ambulance to the call but also matching it from a geographic sense as well,” said Mackay. “It’s a very difficult thing for somebody to do in their head which is typically what happens in most dispatch centres.”

…

In the United States there are 15,000 individual ambulance providers and another 30,000 fire providers.

“North America alone for us is potentially a billion dollar market. Even if we can get 5 per cent of that we’ll be doing well.”

Here’s an interesting paper by Gurvich et al. that’s in the current issue of Management Science.

Full paper here.

via chlady:

The system is just one example of how Seattle Children’s Hospital says it has improved patient care, and its bottom line, by using practices made famous by Toyota and others. The main goals of the approach, known as kaizen, are to reduce waste and to increase value for customers through continuous small improvements.

…

Brian Lucas, a spokesman for Children’s Hospitals and Clinics of Minnesota, says the lean efforts have been used to reduce unnecessary tasks and have not resulted in lower nurse-to-patient ratios. “To the contrary,” he said, “they have allowed nurses to spend more time delivering care to patients.”

It’s good to see that OR/IE is alive in healthcare.  While I agree with the nurses who think time studies are inappropriate for hospitals, inventory management could greatly benefit healthcare providers from both a cost and a patient care perspective.

Now if someone would just implement this.  :-)

Prof. Laura McLay over at Punk Rock Operations Research (which is among the cooler names for a blog I’ve ever seen) included these awesome questions on a stochastic processes final exam this past semester:

The werewolf question: The werewolf population in the Richmond area can be modeled as a linear growth birth and death process.  Each werewolf independently reproduces at a rate of lambda = 0.15 werewolves/year and is killed by vampires at a rate of mu = 0.1/year.  If the population started with a pack of three werewolves in the year 1860, find the average size of the werewolf population today (150 years later).

The Star Wars question (pre-Episode IV): Suppose that every month, Darth Vader organizes a gathering on the Death Star to build morale and promote bonding among the Storm Troopers.  The Storm Troopers’ attendance at the gatherings is represented by a Markov chain.  Given that a Storm Trooper has attended the last gathering (state 0), they go to the next gathering with probability p₀.  In general, given that they last attended the kth prior gathering, they go to the next gathering with probability p_k, with0 < p_k < 1 , k = 0,1,2,3,4.   Storm Troopers are required to attend a gathering every six months, and hence, given that they last attended the 5th prior gathering, they go to the next gathering with probability 1 (p₅ = 1)_.

a. Define the Markov chain for this problem, specify the classes, and determine whether they are recurrent or transient.

b. What is the cumulative density function representing the number of months until a Storm Trooper first returns to the gathering (i.e., the first return to state 0)?  Assume that they have just attended a gathering (i.e., they start in state 0).

b.  In the long run, what is the proportion of Storm Troopers that have attended one of the last three gatherings?