Noname manuscript No. (will be inserted by the editor) Analysis of the effects of Lead-Time variation and Lateral Transshipment insertion in a Supply Chain Network Mohamed Salim Amri Sakhri Mounira Tlili Ouajdi Korbaa Received: date / Accepted: date Abstract In a supply chain, inventory is the single largest source of costs for a company. This is due to the various physical and informational activities that ac- company inventory management, primarily the holding and transportation of inventory. Companies are looking to streamline these activities and minimize the associ- ated costs. One of the most coveted models to jointly solve these two problems is the Inventory Routing Prob- lem (IRP), which will be the focus of this study. This paper addresses the case of a deterministic replenish- ment demand in a distribution network consisting of a supplier and a number of customers to be served by a single vehicle over a finite planning horizon. We will first study the impact of increasing supplier lead times on network costs. Then, we will study the effects of the Lateral Transshipment (LT) technique on the overall network cost. A mathematical model is developed and solved by an exact method. The results obtained will show that LT is an effective tool capable of improving the total network cost and balancing the customers’ in- ventory level. Keywords Inventory Routing Problem · Replenish- ment Lead-Time · Lateral Transshipment · Supply chain network · Exact methods · Optimization Universite de Tunis, Institut Superieur de Gestion, SMART Research Laboratory, LR11ES03, 2000, Bardo, Tunisia; E-mail: Mohamedsalim.Amrisakhri@ISG.rnu.tn Universite de Sousse, Institut Superieur de Transport et de la Logistique, 4023, Sousse, Tunisia; E-mail: Mounira.Tlili@gmail.com Universite de Sousse, ISITCom, MARS Research Labo- ratory, LR17ES05, 4011, Hammam Sousse, Tunisia; E-mail: Ouajdi.Korbaa@MARS.rnu.tn 1 Introduction Logistics is a constantly evolving concept because of its direct impact on business growth. It is based on logis- tical practices that allow to control the different costs of the supply chain, namely the costs of ordering, dis- tribution, storage and return of stock. Indeed, logistics allows better cost management by analyzing, planning and anticipating any event that may occur during the supply process. One of the most well-known logistics problems is the Inventory Routing Problem (IRP). This problem has been the subject of much research over the past decade. It combines two important supply chain activities, namely inventory management and product transportation. The first definition of IRP is given by [1]. They con- sidered IRP as a process of periodic distribution of a single product from a supplier to a set of customers with deterministic demand, using an infinite and ho- mogeneous fleet of vehicles. The vehicles start and end their tours at the supplier location. Next, the IRP was defined by [2] as an extension of the classical Vehicle Routing Problem (VRP) while controlling the inven- tory level at the different customers and suppliers. This problem consists of making simultaneous vehicle rout- ing and inventory management decisions. Many variants of IRP have emerged since its incep- tion and the original definition has been reconstructed. The variant of IRP considered in this article looks at the possibility of having stocks not only with the sup- plier but also from an exchange between customers us- ing the technique of lateral transshipment (LT) as an additional means of replenishment. In other words, LT means that in case of need or to improve its perfor- mance, the customer can cover its necessary demand from other customers [3]. LT is very often used when the