Genetic Algorithm for a Pickup and Delivery Problem with Time Windows

Abstract

A mathematical model for a multivehicle pickup and delivery problem with time windows is presented, and a genetic algorithm (GA) for solving it is proposed. The mathematical model is formulated as a mixedinteger linear programming problem. The objective of the proposed model is to minimize the total cost, which consists of the fixed cost for the vehicles, the routing cost, and the customer inconvenience cost, which is modeled as a penalty cost for violation of the time windows of each customer. Like other combinatorial problems, solving this pickup and delivery problem is time-consuming, and sometimes it is impossible to find an exact solution. The problem is solved exactly for up to six demands (12 nodes), and GA is used for larger problems with more than six demands. The proposed GA can solve a pickup and delivery problem in an extremely short time compared with the exact solution procedure. It also produces excellent results for small problems. A GA used to solve a 30-demands problem (60 nodes) with 10 vehicles is illustrated.

Artificial intelligence in supply chain management: theory and applications

“…Nevertheless, GAs have been applied successfully to a variety of challenging SC network design problems. These problems include: vehicle routing and scheduling (Malmborg 1996, Potvin et al 1996, Chen et al 1998, Park 2001; minimum spanning tree Gen 1998, 1999); delivery and pickup (Jung and Haghani 2000); bus network optimisation (Bielli et al 2002); and locationallocation problems (Hosage and Goodchild 1986, Jaramillo et al 2002, Min et al 2005. In addition, a GA was employed to solve well-known logistics and purchasing problems involving facility layout (Tam andChan 1998, Balamurugan et al 2006); pallet loading (Fontanili et al 2000); inventory control (Disney et al 2000, Haq andKannan 2006); container loading Bortfeldt 1997, Bortfeldt andGehring 2001); material handling (Wu and Appleton 2002), delivery reliability assurance (Antony et al 2006); freight consolidation (Min et al 2006a, b); supplier selection (Rao 2007); and express courier services (Ko et al 2007).…”

A branch-and-cut algorithm for a realistic dial-a-ride problem

“…the maximum riding constraints, are absent in the PDPTW. Heuristics that have been successfully applied to solve the PDPTW include tabu search (Nanry and Wesley Barnes, 2000), genetic algorithms (Jung and Haghani, 2000;Pankratz, 2005), simulated annealing (Li and Lim, 2003), adaptive large neighborhood search (Ropke and Pisinger, 2006), and a hybrid algorithm combining simulated annealing and large neighborhood search (Bent and Hentenryck, 2006). Exact algorithms for the PDPTW include branch-and-price algorithms (Dumas et al, 1991;Savelsbergh and Sol, 1998;Ropke and Cordeau, 2009), branch-and-cut algorithms (Ropke et al, 2007), and a hybrid exact algorithm with two dual ascent heuristics and a cut-and-column generation procedure (Baldacci et al, 2011).…”

A non-dominated sorting genetic algorithm for a bi-objective pick-up and delivery problem

“…In this article, the objective considered is the minimization of the total travelling time and the waiting time of the vehicle. Jung and Haghani (2000) also developed a genetic algorithm to solve a PDP with time windows and several vehicles. The problem studied considers soft time windows (a penalty is assigned when the vehicle arrival time is not in the time window).…”