Inventory Routing Problem arises in a Vendor Managed Inventory setting where the supplier manages the inventory at the retailers. We study a finite horizon (multi-period) Inventory Routing Problem where a single supplier serves multiple retailers. The demands incurred at the retailers are deterministic and dynamic (time-varying). Back-orders are allowed at the retailers either to leverage on savings in transportation costs or because of capacity constraints. The supplier makes the decision on delivery schedules, delivery quantities, and delivery routes, with an objective of minimizing the total cost. The total cost comprises of inventory holding cost, back-ordering cost, and vehicle routing cost (fixed and variable transportation cost). The supplier benefits by coordinating orders from different retailers and the retailers benefit by not allocating resources for inventory management. We propose two Mixed Integer Linear Programming Models to solve two variants of the Inventory Routing Problem, with and without split deliveries. We compare the performance of the proposed models with an existing model using a set of randomly generated data instances. Both the proposed models perform better than the existing model in terms of CPU time. We also propose three math-model based methods to find lower bounds for the problem. These models are also tested on the same data instances. The models reported good lower bounds within a few minutes of CPU time. Furthermore, feasible solutions to the IRP can be derived from the lower bound solutions by using simple heuristics to solve the Travelling Salesman sub-problem. The models can be incorporated in decision-making tools to help supply chain managers make quick tactical level decisions in vendor managed supply chains. © 2018, Curran Associates Inc. All rights reserved.