A max-min ant system for the finance-based scheduling problem

•Overview of the Finance Based Scheduling Problem (FBSP) variants.•A theoretical discussion of the different solution techniques.•A modified integer programming model of the FBSP.•A comparison between four Min-Max Ant System to solve the problem.•A set of 60 instances to be used for benchmarking.

Construction contractors depend on bank overdrafts to finance their expenses; however, these overdrafts cannot exceed an imposed Credit Line (CL). The Finance-Based Scheduling Problem (FBSP) is about scheduling activities without exceeding the CL. In this paper, we provide a more eloquent formulation of the FBSP and list its different variants. Three Max-Min Ant System (MMAS) algorithms, which use different heuristic information when generating solutions, are then developed to solve the FBSP. To test the MMAS algorithms, we generate 60 instances that are used to tune the MMAS algorithms and then use these algorithms to solve the generated instances. The found solutions are compared with the best bounds found using a Branch and Bound (B&B) algorithm. A 0.6% improvement is achieved by the B&B algorithm when compared to the best results found by the MMAS algorithms; moreover, the comparison shows that using the number of successors as heuristic outperformed other heuristics. Furthermore, the MMAS algorithm outperformed other meta-heuristics that use repair operators or penalize infeasible solutions in terms of computation time while having comparable solution values.