Solving a multi-period inventory routing problem with stochastic unstationary demand rates

The inventory routing problem (IRP) is one of the most challenging problems in logistics and supply chain management (SCM). It aims to optimise the integration between inventory management and vehicle routing operations in a supply network. IRP arise involving the inventory and distribution process consisting of a set of vehicle
routes, delivery quantities, and delivery times that minimise the total inventory and transportation costs with the implementation of vendor-managed inventory (VMI) policies. VMI is a policy in which a supplier assumes the responsibility of maintaining the inventory for the customer while ensuring that they will not run out of stock. Thus,
this research aims to develop a mathematical model known as a mixed-integer programming model to solve a multi-period stochastic unstationary inventory routing problem (MP-SUIRP) in which the demand is considered non-consistent over time. The problem focuses on the one-to-many network, where a single warehouse needs to serve several customers over the planning horizon. The inventories are transported from a warehouse to a set of customers using a fleet of homogeneous vehicles to meet the customer's requirements. As a condition, a customer is allowed to be visited once over a given period. A customer’s demand rates in each period are stochastic unstationary and the warehouse is implementing a VMI. This problem is solved using a simulation software called a mathematical programming language (AMPL) to achieve the optimization result. The mathematical model is modified by the addition of a forecasting technique to determine the customer demand rates to supply the inventories and develop the best vehicle routes for the delivery process. A sensitivity analysis is performed on the critical parameters that influence the optimization results. The computational results show that the algorithms that implement this modified formulation can achieve a better optimization result. Thus, this study helps the
organisation optimise the total inventory and transportation costs for the benefit of financial performance.