Integrated Inventory Routing Problem with Quality Time Windows and Loading Cost for Deteriorating Items under Discrete Time

Tao Jia,Xiaofan Li,Ran Li,Nengmin Wang

doi:10.1155/2014/537409

Abstract

We investigate an integrated inventory routing problem (IRP) in which one supplier with limited production capacity distributes a single item to a set of retailers using homogeneous vehicles. In the objective function we consider a loading cost which is often neglected in previous research. Considering the deterioration in the products, we set a soft time window during the transportation stage and a hard time window during the sales stage, and to prevent jams and waiting cost, the time interval of two successive vehicles returning to the supplier’s facilities is required not to be overly short. Combining all of these factors, a two-echelon supply chain mixed integer programming model under discrete time is proposed, and a two-phase algorithm is developed. The first phase uses tabu search to obtain the retailers’ ordering matrix. The second phase is to generate production scheduling and distribution routing, adopting a saving algorithm and a neighbourhood search, respectively. Computational experiments are conducted to illustrate the effectiveness of the proposed model and algorithm.

Highlights

Perishable items exist widely in our daily life, such as fresh products, fruits, vegetables, and seafood, which decrease in quantity during their delivery and storage stages
We investigate an integrated inventory routing problem (IRP) in which one supplier with limited production capacity distributes a single item to a set of retailers using homogeneous vehicles
Considering the randomness of the perishable food delivery speed and the time-varying temperatures, Hsu et al [3] divided the corruption into transportation corruption and customer-site corruption that results from handling under normal temperatures

Summary

Introduction

Perishable items exist widely in our daily life, such as fresh products, fruits, vegetables, and seafood, which decrease in quantity (or utility) during their delivery and storage stages. Kleywegt et al [7] established an IRP model in which customers’ demands on different days were independent random vectors with a joint probability distribution F that did not change with time They formulated the inventory routing problem as a Markov decision process and proposed approximation methods to find good solutions that had reasonable computational effort. In most studies of inventory routing models with discrete time, the deliveries were assumed to be finished within one single period, but Savelsbergh and Song [11] investigated an inventory routing problem with designed delivery tours that spanned several days, covering enormous geographical areas and involving product pickups at different facilities They developed an integer programming-based optimisation algorithm that was embedded in a local search procedure to improve solutions that were produced by a randomised greedy heuristic.

Problem Description and Notation

Model Formulation

Solution Algorithm

Computational Experiments and Analysis

Findings

Conclusions