Performance Modeling of Supply Chains using Queueing Networks

Supply chain networks are formed out of complex interactions amongst several companies whose aim is to produce and deliver goods to the customers at the time and place specified by them. Computing the total lead time for customer orders entering such a complex network of companies is an important exercise. In this paper, we present analytical models for evaluating the average lead times of make-to-order supply chains. In particular, we illustrate the use of fork-join queueing networks to compute the mean and variance of the lead time.The existing literature on approximate methods of analysis of fork-join queueing systems assume heavy traffic and require tedious computations.We present two applications of a tractable approximate analytical method for lead time computations in a class of fork-join queueing systems. For the case where the arrivals are deterministic and service times are normally distributed, we present an easy to use approximate method. Specifically, we illustrate the use of the above method in setting service levels in assemble-to-order type supply chains. 1 Supply Chain Networks Supply chain networks (SCNs) are formed out of complex interconnections amongst various manufacturing companies and service providers such as raw material vendors, original equipment manufacturers (OEMs), logistics operators, warehouse operators, distributors, retailers and customers (see Figure 1). One can succinctly define supply chain management(SCM) as the coordination or integration of the activities of all the companies involved in procuring, producing, delivering and maintaining products and services to customers located in geographically different places. Traditionally, each company performed marketing, distribution, planning, manufacturing and purchasing activities independently, optimizing their own functional objectives. SCM is a process-oriented approach to coordinating all organizations and all functions involved in the delivery process. The product moving through the SCN transits several organizations and each time a transition is made, logistics is involved. Also since each of the organizations is under independent control, there are interfaces between organizations and material and information flows depend on how these interfaces are managed. We define interfaces US T O M E R S Logistics OEM Distribution Centres Logistics Outbound Retailers Inbound Raw material Vendors Intermediate Inventory Inventory Finished Goods Figure 1: The supply chain network as the procedures and vehicles for transporting information and materials across functions or organizations such as negotiations, approvals (so called paper work), decision making, and finally inspection of components/assemblies, etc. For example, the interface between a supplier and manufacturer involves procurement decisions such as price, delivery frequencies and nature of information sharing at the strategic level and the actual order processing and delivery at the operational level. The coordination of the SCN plays a big role in the over all functioning of the SCP. In most cases, there is an integrator for the network, who could be an original equipment manufacturer, coordinating the flow of orders and materials through out the network. Modeling and analysis of such a complex system is crucial for performance evaluation and for comparing competing supply chains. In this paper, we view a supply chain as a probabilistic network and present a modeling approach to compute performance measures such as lead time and work in process inventory. In particular, we investigate the use of queueing network models for computing the lead time and other performance measures. In the rest of this section we review the types of supply chain networks and the different order-fulfilment policies. 1.1 Operational Models An important aspect of the supply chain operation is the supply chain planning and control methodology (SPC). A customer order for a product triggers a series of activities in the supply chain facilities, and these have to be synchronized so that the end customer order is satisfied. The SPC specifies the business model and hence determines the paths for the information and material flow in the supply chain. There are three broad models followed in practice: Maketo-stock (MTS), Make-to-order (MTO), Assemble-to-order 0-7803-6475-9/01/$10.00© 2001 IEEE Proceedings of the 2001 IEEE International Conference on Robotics & Automation Seoul, Korea • May 21-26, 2001