Mohd Kamarul Irwan Abdul Rahim

Modelling and solving the multiperiod inventory-routing problem with stochastic stationary demand rates

The inventory-routing problem (IRP) is a typical logistics optimisation problem that supply chains, implementing vendor managed inventory (VMI), are confronted with. It combines inventory control and vehicle routing. The main objective of the IRP is to jointly determine optimal quantities of the product to be delivered to the retailers, delivery periods and optimal vehicle routes for the shipment of these quantities. This paper considers a multiperiod inventory-routing problem with stochastic stationary demand rates (MP-SIRP). The problem is first formulated as a linear mixed-integer stochastic program for which we propose a deterministic equivalent approximation model (MP-DAIRP). This latter model can be decomposed into two well-know subproblems: an inventory allocation subproblem and a vehicle routing subproblem. The stochastic aspect of the demand is accounted for in the inventory allocation subproblem. The vehicle routing subproblem is solved as a deterministic mixed-integer problem. Lagrangian relaxation is used to determine close to optimal feasible solutions for the MP-DAIRP. Results of the proposed Lagrangian relaxation approach on some numerical examples are reported and thoroughly discussed.

Implementing a vendor managed inventory policy in a two-stage supply chain with stochastic demands

In a two-stage supply chain, implementing Vendor Managed Inventory policies (VMI), the supplier assumes, in addition to his own inbound inventory, the responsibility of maintaining inventory at its retailers and ensuring that they will not run out of stock at any moment. This paper discusses an optimization approach, considering the impact of demand uncertainty on the inbound as well as the outbound inventory, for a two-stage supply chain implementing VMI. In the proposed approach, retailers are first clustered to minimize the within-cluster travel costs and/or distances and are then replenished using an optimal direct shipping strategy satisfying some additional restrictions.

Analysing the effectiveness of vendor-managed inventory in a single-warehouse, multiple-retailer system

This paper considers a two-stage supply chain, consisting of a single warehouse and multiple retailers facing deterministic demands, under a vendor-managed inventory (VMI) policy. It presents a two-phase optimisation approach for coordinating the shipments in this VMI system. The first phase uses direct shipping from the supplier to all retailers to minimise the overall inventory costs. Then, in the second phase, the retailers are clustered using a construction heuristic in order to optimise the transportation costs while satisfying some additional restrictions. The improvement of the systems performance through coordinated VMI replenishments against the system with direct shipping only is shown and discussed in the comparative analysis section.

Effectiveness of vendor managed inventory approach in a two-stage supply chain when demand rates are static

Vendor Managed Inventory (VMI) is an effective policy of integration between the different stages in a supply chain system. In VMI, the supplier takes the responsibility of maintaining inventory at its retailers and ensuring that they will not run out of stock at any moment. The aim of this paper is to optimize the inventory holding costs and the transportation costs of the retailers within the same set partition and/or combining the retailers in the different set partitions, for a two-stage supply chain. The problem is to determine the delivery quantities as well as the times and routes to the retailers, while ensuring feasibility regardless of the realized demands, and minimizing the total cost composed of distribution and inventory holding costs. In the proposed approach, retailers are first clustered to determine the possible retailers set partitions and are then replenished using an optimal routing strategy satisfying some additional restrictions. The improvement of the system’s performance is shown and discussed in the comparative analysis section.