Scheduling spatially distributed jobs with degradation: Application to pothole repair

Abstract

This paper considers scheduling spatially distributed jobs with degradation. A mixed integer programming (MIP) model is developed for the linear degradation case in which no new jobs arrive. Properties of the model are analyzed, following which three heuristics are developed, enhanced greedy, chronological decomposition and simulated annealing. Numerical tests are conducted to: (i) establish limits of the exact MIP solution, (ii) identify the best heuristic based on an analysis of performance on small problem instances for which exact solutions are known, (iii) solve large problem instances and obtain lower bounds to establish solution quality, and (iv) study the effect of three key model parameters. Findings from our computational experiments indicate that: (i) exact solutions are limited to instances with less than 14 jobs; (ii) the enhanced greedy heuristic followed by the application of the simulated annealing heuristic yields high quality solutions for large problem instances in reasonable computation time; and (iii) the factors “degradation rate” and “work hours” have a significant effect on the objective function. To demonstrate applicability of the model, a case study is presented based on a pothole repair scenario from Buffalo, New York, USA. Findings from the case study indicate that scheduling spatially dispersed jobs with degradation such as potholes requires: (i) careful consideration of the number of servers assigned, degradation rate and depot location; (ii) appropriate modeling of continuously arriving jobs; and (iii) appropriate incorporation of equity consideration.