Tuesday, 31 July 2007

Complicating Simplifications

Recently the court of The Hague gave a judgement on the remuneration of resident on call working of the firemen in the Netherlands. Direct cause of the judgement is that the firemen will work less hours a week with no reduction in salary, a loss of productivity of about 11%. The judgement was caused by an attempt of the Dutch government to simplify the rules in the working time directive. These adjustments were necessary because the rules were becoming to complex, also the Dutch working time directive did not follow the agreed working time directive on the European level and the Jaeger as well as the SiMAP judgement. Both judgements state that the hours spend during a resident on call duty should be valued as normal working hours.

From April 1st of 2007 on the simplified working time directive (s-WTD) came into force in the Netherlands. In this new law many rules were simplified or skipped, also some additions were made. The s-WTD sets rules to protect the safety, health and wellbeing of any employee. It contains, for example, rules on the maximum number of hours that employee can work during a shift, a week or consecutive number of weeks. Also it sets rules on the length of a rest period after a shift and after a number of consecutive shifts. The simplifications lead to an increase of possible deployments of employees of about 20%. The question is however if the employers understand the rules well enough to take advantage of the increase in deployment possibilities.

There is one rule in particular that has drawn my attention. I my opinion it is impossible to take that rule into account when construction a roster, without consulting an Operations research specialist or using an advanced planning system, since it requires you to solve the well know multiple knapsack problem. In normal English the rule states that when an employee performs one or more resident on call duties, each period of 7 times 24 hours must contain at least 90 hours of compensatory rest. So far this is simple, we can easily add up all the rest periods an see if it matches the requested 90 hours. There are additional restrictions however on how the compensatory rest period is divided up over the 168 hours period. These restrictions state that there should be at least one period of 24 hours compensatory rest, four of at least 11 hours, one of at least 10 hours and finally one of at least 8 hours. 7 rest periods in total. This still is simple to verify, however these periods of compensatory rest can be joined together. Because of this last condition we have a multiple knapsack problem to solve, which is NP-Hard. (see http://en.wikipedia.org/wiki/Knapsack_problem) I wonder if this crossed the minds of the clerks when writing the new laws. To see the analogy let each period of rest be equal to a knapsack, the capacity of the knapsack is equal to the length of the rest period. Now we have to find out how the 7 rest periods of various sizes can be fitted into the knapsacks. If we succeed, the roster is valid; if not then we need to change it.

To experience what kind of puzzle a planner has to solve, I will give you an example. Assume that an employee has 3 rest periods. The lengths of the periods are 32 hours, 31 hours and 28 hours. I invite you to react and tell me of it is possible to solve this puzzle.

Wednesday, 25 July 2007

Blood sample logistics

The diagnostic centre of a hospital asked me to analyze their blood sample collection process from a logistic point of view. They had a feeling that the performance of the collection process could be improved. They asked to verify this and also to provide a set of possibilities to improve the collection process.

The main activity of the diagnostic centre is to take blood samples from patients, analyze them and report the results back to the physician or patient. Sometimes they advise the patient with respect to the medicine they take, for example in the case of diabetes. Some of the patients come to the hospital to have a blood sample taken. Many of the blood samples however are taken at service locations of the diagnostic centre in the area around the location of the hospital. In this case there are about 30 different service locations where a patient can go, to have their blood sample taken.

The employees of the diagnostic center work at the service locations and take the blood samples from the service location to a laboratory to have them analyzed. As an extra service the employees also visits patients at home to take a blood sample. Currently the employees visit the patient at home before and after they work at the service location. This takes careful planning because patients at the service location must not be kept waiting. As you may guess an important condition in the collection process is to have the blood at the laboratory in time. Blood can not be kept indefinitely; it must be delivered on time to the laboratory, otherwise no analyses can be performed.

As you can see this is a rather complex logistic process. Many questions arise, such as
  • Are there enough locations available for the patients to go to, or should the number be changed?
  • What should be the opening times and the geographic position of each of these locations?
  • Should all the blood samples be taken directly to the laboratory, or should they be collected first at specific places in the network. In other words should hubs be used?
  • Should from an employees point of view the samples taken at the patient’s home be combined with the blood samples taken on the service locations of the diagnostic centre?

This is where Operations Research comes in. We analyzed the blood sample logistics with a model that we developed to analyze and optimize supply chains. With this model we can answer questions like where facilities should be situated, how large they should be and which customers should they serve. With this model we found that introducing a few hubs where blood samples are collected from the service locations before taking them to the laboratory saves about 25% of travel time of the employees. This saves time but also the distance traveled, which reduces the costs for the diagnostic center. This time saved can be used to take more blood samples boosting the workforce effectiveness as well.

Friday, 13 July 2007

OR in the OR

De Franz Edelman Award wordt elk jaar toegekend aan ‘outstanding examples of Operations Research (OR) – based projects’, die grote veranderingen bewerkstelligen in de samenleving, industrieën en het bedrijfsleven. Deze prestigieuze prijs voor het best wereldwijd toegepaste Operations Research project kan worden gezien als de ‘Superbowl’ in toegepaste O.R. Dit jaar waren onder andere Hewlett Packard, Daimler Chrysler, The Memorial Sloan-Kettering Cancer Centre en Coca Cola genomineerd.

ORTEC, het bedrijf waar ik voor werk, was dit jaar bij een van de genomineerde projecten betrokken. Coca-Cola Enterprises is genomineerd, omdat het bedrijf haar distributienetwerk wist te optimaliseren met rit- en routeplanningsoplossing Shortrec van ORTEC. Het systeem dat in 2004 werd geïmplementeerd heeft Coca-Cola Enterprises een besparing van 45 miljoen dollar per jaar opgeleverd.

De award werd uiteindelijke gewonnen door een zeer innovatief project van OR in het Memorial Sloan-Kettering Cancer Centre. De kern van de toepassing is het vinden van de beste positie voor het inbrengen van radioactieve "zaadjes" in de prostaat. Een soort locatie vraagstuk dus. Veelal wordt dit vraagstuk in het platte vlak opgelost, het feit dat het nu in 3 dimensies plaatsvindt en dat het real time (met de patient op tafel) wordt opgelost maakt het uniek. Kijk voor meer informate over dit project op http://www.lionhrtpub.com/orms/orms-6-07/fredelman.html. De toepassing heeft er toe geleid dat een kostenbesparing van 450 miljoen dollar per jaar kan worden bereikt, maar belangrijker is dat de levensverwachting van de behandelde patiënten vergroot wordt en dat de succeskans van de behandeling enorm is gestegen. Kortom "OR in the OR"