Inefficiency at the Shift Level

Our first approach to identifying local inefficiencies is to look at an individual shift s in the current schedule, and study the relation between the amount of driving time (dts) and non-driving time (ndts). Intuitively, the efficiency of a shift s will increase

when dts increases or ndts decreases. Standard ways of expressing this would be to

• dts/ndts

• dts/(dts+ ndts), or dts/spreadovers

• dts− ndts

It may also make sense to limit the considerations to maximizing dts or minimizing

ndts: these still indirectly look at the relation between dts and ndts because shifts are constrained in total length, i.e. dts+ ndts = spreadovers < max spreadover. We find that it is usually more intuitive to identify excessive non-driving time as an inefficiency, hence implicitly looking at minimizing ndts. In any case, it is possible to consider more than one of these criteria simultaneously, for example by checking them against pre-determined bounds and triggering specific actions if one of these bounds is exceeded.

In the following paragraphs, we decompose a shift into atomic components of driving and non-driving time and categorize the types of non-driving time, with the aim of finding ways to reduce those times. We start our analysis by considering a typical 3-spell shift s, with the following breakdown:

a: sign on at depot 3 b: travel to location 5

c: drive vehicle 7 for 2h15m, ending at location 8 d: travel to canteen

e: have a 30-minute mealbreak/PNB f: travel to location 6

g: drive vehicle 2 for 1h42m, ending at location 2 h: wait for 20 minutes

i: drive vehicle 9 for 1h35m, ending at location 4 j: travel to depot 3

In this example, only stages c, g and i are strictly driving time; all other stages (traveling, waiting, mealbreaks, and signing on and off) are non-driving time. We look at these types of non-driving time in more detail, and briefly illustrate how inefficiency may arise in them; we present them in what we believe is their order of importance in terms of the role they play in determining the overall efficiency of a schedule.

1. travel time: drivers frequently need to travel from one location to another in the network; for example, to start the next spell of driving work (on a different vehicle). This may also happen between sign-on and the first spell of work, or before sign-off. Inefficient distribution of work among shifts in relation to the resulting required travel time is one of the major causes for inefficient schedules. In shift s, travel time is incurred in stages b, d, f and j.

2. idle (slack) time: it occurs when the shift includes some time on which the driver is neither driving, nor traveling, nor having a mealbreak. For example, it may happen that the travel time required to connect two consecutive spells of work in a shift is shorter that the time that is physically available, and it can’t be used as a PNB. In this case, the driver will simply have nothing to do during that time, but will still be paid for it. It can also happen that some breaks between vehicles are longer than what is actually required by the labour agreements, which from the point of view of the operator is unnecessary paid non-working time. In shift s, this happens in stage h. It is likely that not all 20 minutes are ‘wasted’, since there may be a minimum joinup time (the time allowed to a driver between two consecutive spells) mandated by the labour agreement; however, even in this case it may be argued that a shift with fewer spells would incur less total absolute joinup time, since the total minimum joinup time is proportional to the number of spells in a shift.

A second (and less intuitive) example arises when a shift cannot start less than a certain length of time t from the beginning of the first mealbreak. When a shift is breaking this rule, it is not uncommon to solve this by padding it with some minutes of non-driving time at the beginning of the shift, so that the mealbreak will start t minutes from the start of the shift.

3. mealbreak/PNB time: although PNBs are usually mandatory, the labour agreement frequently offers some options regarding the distribution of PNB time over the length of a shift; for example, a 3-spell shift may have one or two mealbreaks. It may be possible that the different options result in a different total amount of PNB time (say, one 30-minute PNB against two 20-minute PNB, with 30 vs 40 total PNB minutes). In these cases, it can be argued that a shift whose PNBs are distributed in a way that is not optimal regarding total PNB time is inefficient.

4. sign-on/off time: while the sign-on/off times are usually viewed as fixed, it may happen that the allowances for sign-on/off vary according to the depot where the procedure is carried out; in these cases, choosing the right depot for a shift may result in decreased sign-on/off times.