Saravanan Venkatachalam

Formulations and algorithms for the multiple depot, fuel-constrained, multiple vehicle routing problem

We consider a multiple depot, multiple vehicle routing problem with fuel constraints. We are given a set of targets, a set of depots and a set of homogeneous vehicles, one for each depot. The depots are also allowed to act as refueling stations. The vehicles are allowed to refuel at any depot, and our objective is to determine a route for each vehicle with a minimum total cost such that each target is visited at least once by some vehicle, and the vehicles never run out fuel as it traverses its route. We refer to this problem as the Multiple Depot, Fuel-Constrained, Multiple Vehicle Routing Problem (FCMVRP). This paper presents four new mixed integer linear programming formulations to compute an optimal solution for the problem. Extensive computational results for a large set of instances are also presented.

Nodal decomposition–coordination for stochastic programs with private information restrictions

ABSTRACT We present a nodal decomposition–coordination method for stochastic programs with private data (information) restrictions. We consider coordinated systems where a single optimal or close-to-optimal solution is desired. However, because of competitive issues, confidentiality requirements, incompatible database issues, or other complicating factors, no global view of the system is possible. In our iterative methodology, each entity in the cooperation forms its own nodal deterministic or stochastic program. We use Lagrangian relaxation and subgradient optimization techniques to facilitate negotiation between the nodal decisions in the system without any one entity gaining access to the private information from other nodes. We perform a computational study on supply chain inventory coordination problem instances. The results demonstrate that the new methodology can obtain solution values that are close to the optimal within a stipulated time without violating private information restrictions. The results also show that the stochastic solutions outperform the corresponding expected value solutions.

Analysis of Mixed-Integer Linear Programming Formulations for a Fuel-Constrained Multiple Vehicle Routing Problem

This paper addresses a fuel-constrained, multiple vehicle routing problem (FCMVRP) in the presence of multiple refueling stations. We are given a set of targets, a set of refueling stations, and a depot where m vehicles are stationed. The vehicles are allowed to refuel at any refueling station, and the objective of the problem is to determine a route for each vehicle starting and terminating at the depot, such that each target is visited by at least one vehicle, the vehicles never run out of fuel while traversing their routes, and the total travel cost of all the routes is a minimum. We present four new mixed-integer linear programming (MILP) formulations for the problem. These formulations are compared both analytically and empirically, and a branch-and-cut algorithm is developed to compute an optimal solution. Extensive computational results on a large class of test instances that corroborate the effectiveness of the algorithm are also presented.This paper addresses a fuel-constrained, autonomous vehicle path planning problem in the presence of multiple refueling stations. We are given a set of targets, a set of refueling stations, and a depot where m vehicles are stationed. The vehicles are allowed to refuel at any refueling station, and the objective of the problem is to determine a route for each vehicle starting and terminating at the depot, such that each target is visited by at least one vehicle, the vehicles never run out of fuel while traversing their routes, and the total travel cost of all the routes is a minimum. We present four new mixed-integer linear programming formulations for the problem. These formulations are compared both analytically and empirically, and a branch-and-cut algorithm is developed to compute an optimal solution. Extensive computational results on a large class of test instances that corroborate the effectiveness of the algorithm are also presented.

Efficient formulation and heuristics for multi-item single source ordering problem with transportation cost

Integrated inventory and transportation decisions are critical in the supply chain, providing significant gains for all parties. In this paper, we present a mathematical formulation for the dynamic demand multi-item single source replenishment problem with a piecewise linear transportation cost. Through an extensive experimental study, we find that the new formulation provides a tighter LP relaxation of the problem, while requiring fewer computational resources to optimally solve the problem when compared with existing model in the literature. We also present a new metaheuristic for this general class of coordinated capacitated replenishment problems. On average, the solutions from heuristics are within 1.23% of the optimal solution for the comprehensive set of test problems.

Path planning for multiple heterogeneous Unmanned Vehicles with uncertain service times

This article presents a framework and develops a formulation to solve a path planning problem for multiple heterogeneous Unmanned Vehicles (UVs) with uncertain service times for each vehicle-target pair. The vehicles incur a penalty proportional to the duration of their total service time in excess of a preset constant. The vehicles differ in their motion constraints and are located at distinct depots at the start of the mission. The vehicles may also be equipped with disparate sensors. The objective is to find a tour for each vehicle that starts and ends at its respective depot such that every target is visited and serviced by some vehicle while minimizing the sum of the total travel distance and the expected penalty incurred by all the vehicles. We formulate the problem as a two-stage stochastic program with recourse, present the theoretical properties of the formulation and advantages of using such a formulation, as opposed to a deterministic expected value formulation, to solve the problem. Extensive numerical simulations also corroborate the effectiveness of the proposed approach.