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.
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