A Branch-and-Cut Procedure for the Multimode Resource-Constrained Project-Scheduling Problem

Abstract

This paper considers the multimode resource-constrained project-scheduling problem (MRCPSP) with a minimum-makespan objective. An exact branch and cut algorithm is presented based on the integer linear programming (ILP) formulation of the problem. In the preprocessing stage, lower bounds on the distance between each pair of precedence-constrained activities are derived. These bounds are used to reduce the number of variables in the model and to generate cuts that tighten the linear programming relaxation. The solution process is accelerated by an adaptive branching scheme in conjunction with a bound-tightening scheme that is called iteratively after branching. To find good feasible solutions in the early stages of the computations, a high-level neighborhood search strategy known as local branching is included. Here, a neighborhood of a feasible solution is defined by the linear inequalities in the ILP model and is searched first. As implemented, the full algorithm is exact rather than heuristic in nature. Numerical results are reported for 20- and 30-activity benchmark problems. These are the largest instances available and are generally viewed to be notoriously difficult. Up until now, there were no confirmed optimal solutions for any of the 552 30-activity instances. We were able to find several better solutions and to show that at least 506 are optimal.

A survey of variants and extensions of the resource-constrained project scheduling problem

“…Multi-mode problems with generalized precedence constraints have been considered by Barrios et al [14], Brucker and Knust [30], Calhoun et al [34], de Reyck and Herroelen [47], Drexl et al [64], Heilmann [82,83], Nonobe and Ibaraki [141], and Sabzehparvar and Seyed-Hosseini [156] (see also Section 3). Zhu et al [198] employ a multi-mode problem with generalized resource constraints (see also Section 4).…”

The multi-mode, resource-constrained project scheduling problem in construction: state of art review and research challenges

“…Speranza, Vercellis, Hartmann, Sprecher, and Drexl [8,34,35,37] among others used the branch and bound method for classic MRCPSPs; Demeulemeester & Herroelen used the same method for solving a discrete time/resource trade-off problem [5]. In the year 2006, Zhu et al proposed the use of the branch-and-cut (B&C) algorithm [44]. Unfortunately, none of these methods can currently be used for solving complicated construction project scheduling problems since they are unable to find optimal solutions in reasonable computational times [40].…”

A Practical and Robust Execution Time-Frame Procedure for the Multi-Mode Resource-Constrained Project Scheduling Problem with Minimal and Maximal Time Lags

“…A situation in which some activities require personnel with certain skill levels was modeled and solved in [5]. Additionally, among others, Zu et al examined a variation of MRCPSP with generalized resource constraints in [6], while Heilmann, Nonobe and Ibaraki examined precedence constraints in [7][8][9], respectively.…”

“…The onlooker bees phase makes improvements to solutions based on the probability function described in Equation (6). With higher solution fitness, the probability for it being selected for improvement is increased.…”