Ant Colony Optimization For Split Delivery Inventory Routing Problem

Abstract

A one-to-many inventory routing problem (IRP) network comprising of a warehouse and geographically dispersed customers is studied in this paper. A fleet of a homogeneous vehicle located at the warehouse transports multi products from the warehouse to meet customer's demand on time in a finite planning horizon. We allow the customers to be visited more than once in a given period (split delivery) and the demand for each product is deterministic and time varying. Backordering is not allowed. The problem is formulated as a mixed integer programming problem and is solved using CPLEX 12.4 to get the lower and upper bound (the best integer solution) for each problem considered. We propose a modified ant colony optimization (ACO) which takes into account not only the distance but also the inventory that is vital in the IRP. We also carried the sensitivity analysis on important parameters that influence decision policy in ACO in order to choose the appropriate parameter settings. The computational results show that ACO performs better on large instances compared to the upper bound and performs equally well for small and medium instances. The modified ACO requires relatively short computational time.Keywords: Ant Colony Optimization, Inventory, Routing INTRODUCTIONSupply chain management is the control of supply chain to manage the flow of commodity both within and among the companies. Inventory routing problem (IRP) is a challenging NP hard problem in supply chain management which combines the vehicle routing problem where the route to visit the customers is decided and inventory management which concerns on the amount to be delivered to the customers. The main objective of IRP is to minimize both the total transportation and inventory cost over the planning horizon.Generally, IRP can be divided by different criteria such as the type of demand, single or multi period, planning horizon, and inventory policy (order-up-to level or maximum level Coelho and Laporte [1] recently proposed a branch-and-cut algorithm to solve the multi-product multi-vehicle IRP with deterministic demand and stock out cost is not allowed. In their paper, Coelho and Laporte [1] implemented a solution improvement algorithm after branch-and-cut identifies a new best solution. The purpose of solution improvement algorithm is to approximate the cost of a new solution resulting from the vertex removal and reinsertions. In this paper, the authors also considered additional two features: the driver partial consistency and the visiting space consistency. The results show that the visiting space helps in reducing the search space while providing a meaningful solution. This is the first paper that solves the problem with heterogeneous vehicles.The planning horizon of the problem also can be categorized into finite or infinite horizon. We can observe that most of the earlier works concentrate on an infinite planning horizon (see for example Aghezzaf et al. IRP with finite planning horizon can be categorized as a single or multi-period scenario. Feder...

Trimmer sequencing time minimization during dynamically collimated proton therapy using a colony of cooperating agents

“…ACO is a heuristic, swarm-intelligence method that can solve optimization problems stochastically via a colony of cooperating agents (Dorigo et al 1996). It has been employed to solve a variety of optimization problems in CT reconstruction (Papenhausen et al 2013), split inventory routing (Wong and HasnahMoin 2017), and much more such as air traffic control (Haldenbilen et al 2013). The approach can be described with an anecdotal example of ants from an ant colony trying to locate the most food nearest to their ant hill.…”

The inventory routing problem with split deliveries

“…On the contrary, very little has been done on the IRPs with split deliveries. The literature so far has been mainly focused on the different algorithms to solve them, as done by Yu et al [34] and Wong and HasnahMoin [33]. Yu et al [34] developed a stochastic IRP with split deliveries, and proposed an approximate method to solve this problem.…”

“…Yu et al [34] developed a stochastic IRP with split deliveries, and proposed an approximate method to solve this problem. Meanwhile, Wong and HasnahMoin [33] proposed a three‐steps ant colony optimization algorithm for a split IRP. Both of these approaches provide good results in a reasonable amount of solving time.…”

Accelerating supply chains with Ant Colony Optimization across a range of hardware solutions

“…It was concluded that the proposed algorithm covered 94% of optimal solutions on small problems and 88% for large-size problems while consuming significantly less computation time. Similarly, [7] compared ACO and Cplex performance on multi-product and multi-period Inventory Routing Problem. On small instances ACO reached 95% of optimal solution while on large instances performed better than timeconstrained Cplex solver.…”