To many drivers, it seems that the road from here to there is always under construction. And they may have a point. According to one study, motorists encounter an active work zone for one out of every hundred miles they travel on the National Highway System. About half of those encounters involve a lane closure. In another study, a third of the public expressed dissatisfaction with all the work zones they encountered. Slower speeds in work zones lengthen travel times, and today’s high fuel costs exacerbate drivers’ frustration levels.
Whether it is a function of those frustrations or just the product of increased congestion (or both), accident rates in work zones are 20 to 30% higher than in the same location before construction activity began. More than 40,000 injuries and 1,000 fatalities occur in roadway work zones each year. The fact that the number of annual work-zone fatalities has increased 45% over the past decade underscores the seriousness of this issue.
Transportation agencies are facing increasing pressures to reduce construction times and schedule work activities in a way that will minimize the impacts on local businesses and the traveling public. However, there are costs associated with schedule modifications. For example, accelerating the work to compress the schedule requires additional equipment and labor. Restricting work to off-peak periods or weekends may lengthen overall project duration, and it can increase costs by requiring multiple setups and removals of work zones. Frequent work stoppages also may inhibit productivity and degrade construction quality. Nighttime operations may decrease safety and productivity, while raising costs.
The gene tool
Scheduling roadway resurfacing or rehabilitation activities to address all of these concerns—and without triggering excessive costs—is a complex task. A new computer-based procedure can optimize the work-zone schedule so as to minimize total costs. Included in the total costs are the material, equipment and labor costs associated with the work zone, the idle-time costs associated with work breaks and road-user costs (including the lost value occasioned by time delays, the increased vehicle operating costs and the accident costs associated with traveling through a work zone). This computerized procedure, which simulates natural biological reproduction at the gene and chromosome levels, is called a genetic algorithm.
The following example shows how the procedure can be applied, and the kind of benefits it can produce. The sample project entails resurfacing a 3.1-mile-long segment with a 2-in.-thick overlay of asphalt pavement. The roadway, a principal arterial in New Jersey, has two travel lanes in each direction; the project will require closing one travel lane at a time.
Since the objective is to optimize the work-zone schedule and minimize the total project cost, a mathematical expression must be written that reflects all of the cost components affecting agencies and road users alike. Then appropriate baseline or typical values must be associated with each of the terms. For example, the user’s time was assigned a value of $15 per hour; work-zone setup was assumed to cost $1,000 per zone; and the total time for setting up and removing a work zone was estimated at two hours. Hourly traffic volumes were derived based on the traffic distribution indicated in the New Jersey Department of Transportation’s Road User Cost Manual and the average annual daily traffic (AADT) of the project location.
The genetic algorithm was run 30 times, with three pools of randomly produced “parent schedules” being used in 10 runs each. Each run lasted for 200 “generations.” This procedure took about 31/2 minutes on a personal computer. The entire procedure was done three times—once for each of the two selected AADTs of 40,000 and 45,000 with a maximum project duration of 64 hours and once again for the AADT of 45,000, but employing an accelerated crew so that the maximum project duration could be reduced to 44 hours.
For an AADT of 45,000 and a maximum project duration of 64 hours, the computer-generated optimal solution was to start the work at 6:45 p.m. and continue until 7:15 a.m., then stop for 21/2 hours. Work would resume at 9:45 a.m. and continue until 1:15 p.m. The final work period would be from 6:30 p.m. to 6 a.m. The morning and afternoon work breaks have the effect of preventing excessive travel delays and the associated user costs. The total work time is 27.5 hours, and the total elapsed project time is 35.25 hours. The project cost (including work time, equipment, materials, costs associated with idle times and road-user costs) was calculated to be $143,699 per lane.
Choosing the lower AADT of 40,000 along with the maximum project duration of 64 hours represents a normal level of work activity, but assumes the traffic will decrease. This could occur naturally (as some drivers individually elect to avoid the construction area), or it might be actively encouraged through some kind of diversion effort (e.g., variable message signs and highway advisory radio broadcasts). This option produced a better solution. The project would begin at 6 p.m. and activity would continue until 7:15 a.m. Work would resume at 9:30 a.m. and continue until 3:15 p.m. After a break for the afternoon peak traffic, work would begin again at 6 p.m., and the project would be finished at 6:45 a.m. In this case, the total work time increases to 31.75 hours and the total elapsed time increases slightly to 36.75 hours, but the total cost drops to $137,233 per lane, saving $6,466 over the first option.
The third option uses an accelerated work schedule to reduce the maximum project duration to 44 hours, and does not rely on traffic diversion. Reducing the allowable duration of the project may require larger crews and more equipment, but it has the potential to reduce the impact on motorists. In this case, the optimum solution found by the genetic algorithm was for work to begin at midnight and last until 7:15 a.m., resume from 9:45 a.m. until 2:45 p.m., and then finish in the period lasting from 6 p.m. to 7:15 a.m. The total work time is only 25.50 hours and the total elapsed time is 31.25 hours, but the total project cost rises to $149,688 per lane. Compared with the first solution, the time saving of four hours in total elapsed time reduces crew/equipment idle-time costs by $1,600 but raises the work costs by $2,461; it also actually increases road-user costs by $5,128. In particular, the analysis predicted substantially higher traffic queuing delay costs during the daytime and second evening work periods.
Showing some sensitivity
In all three of these cases the work schedule envisions two rounds of nighttime operations, with another period of work occurring in the intervening off-peak daytime period. However, the results show that slight alterations in scheduling can create notable cost savings—as well as potentially improving public perception. Without the benefit of computer simulation, these differences probably would not have been identified.
The final step in this example involved conducting a sensitivity analysis. This mathematical process illustrates the relationships among variables and identifies their relative importance in affecting results. In this example, the analysis used an AADT ranging from 37,500 to 50,000 and a range of maximum project durations from 40 to 90 hours. Not surprisingly, the analysis showed that the minimum total cost increases as AADT increases—in other words, higher traffic volumes result in higher project costs.
The minimum total cost generally declines when the maximum project duration increases. Longer project durations provide more flexibility in scheduling work zones to reduce labor and equipment costs as well as road-user costs. Interestingly, for each AADT, the graph of minimum total cost versus maximum project duration showed a noticeable drop between two threshold values but remained quite stable before and after that range. In other words, between those two threshold values is the range of maximum project durations whose selection can really make a difference in minimizing the total cost. Identifying the two threshold values for a particular job would help transportation agencies determine the appropriate project duration. Knowing the thresholds also is valuable for developing innovative contracting methods that take advantage of incentive and disincentive clauses.
This example shows the practical value of applying a genetic algorithm to the task of scheduling roadway maintenance activities. With the development of genetic algorithms, a few minutes of computer time can save thousands of dollars for transportation agencies and road users.
