Elsevier

Expert Systems with Applications

Volume 39, Issue 3, 15 February 2012, Pages 2296-2305
Expert Systems with Applications

Modified savings heuristics and genetic algorithm for bi-objective vehicle routing problem with forced backhauls

https://doi.org/10.1016/j.eswa.2011.08.009Get rights and content

Abstract

The cost of distribution and logistics accounts for a sizable part of the total operating cost of a company. However, the cost associated with operating vehicles and crews for delivery purposes form an important component of total distribution costs. Small percentage saving in these expenses could result in a large amount of savings over a number of years. Increase in the number of automated teller machines (ATMs) in the bank industry enforced the researchers to concentrate much on the optimization of distribution logistics problem. The process of replenishing money in the ATMs is considered as a scope with bi-objectives such as minimizing total routing cost and minimizing the span of travel tour. Some of the pick-up routes of the problem are forced and it is termed as forced backhauls. This problem is termed as bi-objective vehicle routing problems with forced backhauls (BVFB). We developed three heuristics to solve BVFB. Two heuristics are modified savings heuristics and the third heuristic is based on adapted genetic algorithm (GA). Standard data sets of VRPB of real life cases for BVFB and randomly generated datasets for BVFB are solved using all the three heuristics. The results are compared and found that all the three heuristics are competitive in solving BVFB. GA yields better solution compared to the other two heuristics.

Highlights

► Vehicle routing problem (VRP) incorporating forced backhauls, routing cost minimisation and minimisation of span of travel tour is considered. ► Extended variant termed as bi-objective vehicle routing problem with forced backhauls (BVFB). ► Three heuristics for BVFB are: modified savings heuristic with arc removal procedure, with node swap procedure and adapted genetic algorithms. ► Randomly generated data-sets of BVFB and nine real-life cases of BVFB are considered. ► It is evident from the results that GA promises to be a useful tool for solving BVFB.

Introduction

Commercial banks are trying to change customer behavior from doing banking transactions through branch channel to electronic channel. Consequently, there is an increasing number of automated teller machines (ATM). This paper is concerned with the vehicle routing problem (VRP) arisen for an ATM scheduling, a real-world routing-scheduling problem.

There are two types of ATMs in the banking sector. The first type is the ATM situated in the concerned bank premises itself. Second type are the ones provided in many other places such as department stores, markets, petrol bunks, etc. Those ATMs located in the buildings of the banks will take care of by the branches themselves. Where as ATMs at other locations will be taken care of by the cash centers. The number of ATMs is increasing at a higher rate because of many reasons. Planners need a decision support system to devise the routing for multiple vehicles/drivers to collect and distribute the cash in all the ATMs.

Generally, the main objective for the VRP is to minimize the total routing cost or traveling distance. This objective is sometimes insufficient to provide a good practical solution. In this research, we attempt to reformulate the problem with simultaneous consideration of two objectives: minimizing the total routing cost and minimizing the span of travel tour. The longest tour may lead delay in on-time delivery of cash and the security of cash will also be less. So, we consider the objective of minimizing the span of travel tour. The prime reason for the objective of minimizing the span of travel tour is to increase the security of cash and reduce the delivery delay. The vehicles should collect and distribute cash to all ATMs and the banks provide due importance for the security and on-time delivery of cash in order to improve the service. Banks would like to have the compromise between minimizing the routing cost and span of travel tour. Vehicles should deliver the required amount in all the ATMs and also should collect the cash from some of the ATMs with the forced route.

Cash pick-up with the forced route is called as forced backhauls. This problem is termed as bi-objective vehicle routing problem with forced backhauls (BVFB). We develop three heuristics to solve the variant BVFB. The remainder of the paper is organized as follows: Section 2 details the literature review. Problem definition is presented in Section 3. Two modified savings heuristic is detailed in Section 4. Results and Analysis have been discussed in Section 5. Section 6 deals with the applications and finally conclusions are in Section 7.

Section snippets

Vehicle routing with backhauls

Heuristics are commonly used because of the complexity to deal with the classical VRPB and it has been studied by several researchers for more than two decades. The first constructive method for classical VRPB was proposed by Deif and Bodin (1984) which is the extension of Clarke and Wright’s (1964) savings algorithm. Goetschalckx and Jacobs-Blecha (1989) formulated the first mathematical problem explicitly dealing with the vehicle routing problem with clustered backhauls (VRPCB). In their next

Problem definition

Let G = (T, A) be a graph with a set T = N U {0} and arc set A = {(i, j), i ∈ T, j ∈ T, i ≠ j}, where N = {1, 2, … , n} represents the node set and node 0 refers to the node of origin. Some of the nodes i ∈ T require delivery of di units and some others require pick-up of pi. For every arc (i, j) ∈ A, distance yij is known.

BVFB can be stated as follows: A set of N nodes with deterministic demands for delivery and pick-up services have to be visited by a fleet of homogeneous vehicles, all of which originate and terminate

Modified savings heuristics for BVFB

We developed two modified savings heuristics to solve BVFB. Clarke and Wright (1964) suggested a simple method for optimum routing of a fleet of trucks of varying capacities used for delivery from a central depot to a large number of delivery points. They have modified the original method by Dantzig and Ramser (1959). Here it is required to allocate loads to vehicles in such a manner that all the merchandise are assigned and the total mileage covered is at minimum. The procedure suggested by

Results and analysis

All the heuristics are coded in C and run on a PC Pentium IV 1.70 GHz processor. There is no bench-mark problem available in the literature for BVFB. VRP does not consider pick-up or delivery and pick-up nodes; VRPB considers delivery nodes which precede pick-up nodes. Hence, for the purpose of comparison, the proposed methodology is tested on standard VRPB data-sets, set of real-life cases of BVFB and randomly generated data-sets of BVFB. MSAR is named as Heuristic 1 (H1), MSNS is named as

Applications and Implications

The applications can be divided into two categories, in category (A), Natural backhauls and in category (B) Men made backhauls. In case of flood/fire/earth quacks/volcano, etc.; the ATMs are to be attended either for taking currency out of it or to pick up the customer stuck up in ATM. Due to this the vehicle may have to change its pre-defined routes. The men made back hauls can be some accidents on a particular route or traffic jam due to weather or due to some other reasons may lead to change

Conclusion

This study has addressed the VRP incorporating forced backhauls with two objectives namely cost minimization and minimization of span of travel tour. The problem is an extended variant of VRPB and it is termed as BVFB. Among various applications of BVFB, we have considered one application pertain to bank industry. The problem is to deliver the required cash to automated teller machines (ATMs) and collect the dropped cash back to the cash centers. For this NP-hard problem, we have developed

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