Computers and Chemical Engineering 80 (2015) 199–210 Contents lists available at ScienceDirect Computers and Chemical Engineering j ourna l ho me pa g e: www.elsevier.com/locate/compchemeng An incremental approach using local-search heuristic for inventory routing problem in industrial gases Tejinder Singh a,∗ , Jeffrey E. Arbogast a , Nicoleta Neagu b a Air Liquide, Delaware Research and Technology Center, Newark, DE 19702, United States b Air Liquide, Paris-Saclay Research Center, 78350 Jouy-en-Josas, France a r t i c l e i n f o Article history: Received 30 July 2014 Received in revised form 5 May 2015 Accepted 28 May 2015 Available online 7 June 2015 Keywords: Vendor managed inventory Liquefied gases Industrial gases distribution Inventory routing problem Bulk gas distribution Local-search heuristic a b s t r a c t In this paper we solve the inventory routing problem (IRP) occurring in industrial gas distribution where liquefied industrial gases are distributed to customers that have cryogenic tanks to store the gases on-site. We consider a multi-period inventory routing problem with multiple products assuming deterministic demand rates and the proposed model is formulated as a linear mixed-integer program. We propose an incremental approach based on decomposing the set of customers in the original problem into sub- problems. The smallest sub-problem consists of the customer that needs to be delivered most urgently along with a set of its neighbors. We solve each sub-problem with the number of customers growing suc- cessively by providing the solution of the previously solved sub-problem as an input. Each sub-problem is then solved with a randomized local-search heuristic method. We also propose an objective function that drives the local-search heuristics toward a long-term optimal solution. The main purpose of this paper is to develop a solution methodology appropriate for large-scale real-life problem instances particularly in industrial gas distribution. © 2015 Elsevier Ltd. All rights reserved. 1. Introduction The inventory routing problem (IRP) is a challenging problem that arises in various real-life distribution systems. It involves managing inventory and vehicle routing simultaneously where the vendor is responsible for the replenishment of a set of geographi- cally dispersed customers (Campbell et al., 1998). These customers have demands for different products spread over time, and are enti- tled to keep local inventory. Deliveries are usually made using a fleet of capacitated trucks. The usual vehicle routing problem (VRP) is a much less complex problem than the IRP problem (Bertazzi and Speranza, 2012). In the VRP, routing decisions are made to ful- fill, by the end of the day, fixed orders placed by the customers. In the IRP, the routing decisions are dictated by the anticipated inventory behavior of the customers, which is itself driven by their daily demand patterns. Given the customers’ inventory data and information on the customers’ demands, the logistics analyst must consequently make following important decisions over a given planning horizon: ∗ Corresponding author. Tel.: +1 713 896 2164. E-mail address: tejinder.singh@airliquide.com (T. Singh). • When to visit each customer during the planning horizon • How much to deliver to each customer on each visit • How to combine customer visits into vehicle routes In an industrial setting, the IRP can be applied to various distri- bution systems. Traditionally, researchers and practitioners have focused on applications to the maritime, automotive and super- market industries, for example (Campbell and Savelsbergh, 2004). In this paper, we focus on the IRP problem in industrial bulk gas dis- tribution for a finite-horizon scenario (e.g., 2 weeks). We assume that the customer’s demand is known (deterministic) and is also dynamic. In industrial gas distribution, liquefied gases [e.g., oxygen (O 2 ), nitrogen (N 2 ), argon (Ar), carbon dioxide (CO 2 ), and hydrogen (H 2 )] are transported from production plants to cryogenic stor- age tanks placed at customer sites using cryogenic trailers. This is primarily done through a VMI system (You et al., 2011). In a VMI system, it is the vendor’s responsibility to prevent customer stock- out of the product and avoid penalty consequences. However, there are generally a relatively small percentage of customers that call the vendor to place their orders (non-VMI/call-in customers). There are some features of IRP for bulk gas distribution which are unique compared to the classical IRP model. The IRP for bulk gas distri- bution includes inventory level constraints for both suppliers and customers. Unlike typical IRP systems, a cryogenic trailer cannot deliver different products in a single delivery. There can be other http://dx.doi.org/10.1016/j.compchemeng.2015.05.023 0098-1354/© 2015 Elsevier Ltd. All rights reserved.