Performance modeling and analysis of integrated logistic chains: An analytic framework

Abstract

This paper is geared toward developing a network of inventory-queue models for the performance modeling and analysis of an integrated logistic network. An inventory-queue is a queueing model that incorporates an inventory replenishment policy for a store, which is a basic modeling element for an integrated logistic network. To achieve this objective, first, this paper presents an analytical modeling framework for integrated logistic chains, in which the interdependencies between model components are captured. Second, a network of inventory-queue models for performance analysis of an integrated logistic network with inventory control at all sites is developed. Then this paper extends the previous work done on the supply network model with base-stock control and service requirements. Instead of one-for-one base stock policy, batch-ordering policy and lot-sizing problems are considered. In practice, the assumption of uncapacitated production is often not true, therefore, GI^x/G/1 queueing analysis is used to replace the M^x/G/∞ queue based method. To include lot-sizing issue in the analysis of stores, a fixed-batch target-level production authorization mechanism is employed to explicitly obtain performance measures of the logistic chain queueing model. The validity of the proposed model is illustrated by comparing the results from the analytical performance evaluation model and those obtained from the simulation study.

Introduction

An integrated logistic chain can be viewed as a network of suppliers, fabrication sites, assembly sites, distribution centers, and customer locations through which components and products flow. The inventory in each site is controlled by some inventory control policy. An important issue in integrated logistic network design is to control the inventory at different sites or stores while meeting end-customer service level requirements, therefore quantifying the trade-off between inventory investment and end-customer service levels. The dynamic nature of complex logistic chains causes that this trade-off changes over time. In turn, the performance of logistic chains must be reevaluated continuously. Therefore, an analytic framework to be used for both performance modeling and analysis is in need. Furthermore, to answer “what–if” questions quickly, such an analytic model has to be computed efficiently.

The arborescent structure of the networks treated by multi-echelon inventory networks and related models are appropriate for distribution networks. However, in a general logistic chain network, the model involves not only distribution but also assembly, in which multiple components are required for the production of one part. Integrating manufacturing and logistic functions together is the key determinant for an organization to obtain the competing advantages in business. Extending multi-echelon inventory networks into integrated manufacturing logistic chains is not straightforward. See Ernst and Pyke (1993) and Cohen and Lee (1988) for research in this direction.

Lee and Billington (1993) present an analytical model for a decentralized supply chain. Their model assumes each site operates under a periodic-review, base-stock inventory policy and the demands for end-products are normally distributed. A key assumption in the model is that the replenishment lead time for a product at a node comprises the material lead time, the production lead time, and the delay time. The network performance is obtained by aggregating the solutions of multiple single-product, single-site inventory problems. One of the advantages of this framework is the ability to analyze the first two moments of all the performance metrics.

Garg (1999) develops a decentralized supply chain modeling and analysis tool (SCMAT) on designing products and processes for supply chain management. SCMAT contains two sub-models: queueing network sub-model which is used to attain the production lead time for a site and inventory network sub-model which is used to calculate the base-stock level for each stock keeping unit (SKU) flowing through every site. The output (production lead time) of the queueing network sub-model is one input of the inventory network sub-model. Given the base-stock level and the values of its three drivers (demand, replenishment lead time, and the service-level), one can compute various performance measures useful for obtaining managerial insight. These performance measures include the mean and variance of on-hand inventory, backorder level and response time, and the capacity utilization at each node in the network. SCMAT explicitly incorporates the congestion effects due to capacity limitations at each node, and the interference effect because of multi-product flows through each node.

Ettl et al. (2000) develop a supply chain model that takes as input the bill-of-materials, the nominal lead times, the demand and cost data, and the required customer service levels. In return, the model generates the base-stock level at each store––the stocking location for a component or an end-product. They assume a distributed inventory control mechanism whereby each site in the network operates according to a base-stock control policy. This base-stock policy makes authors avoid the consideration on determining the lot sizes at each store. They further assume that, given there are no stock-outs at upstream stores, the replenishment lead time of any store is independent of the number of outstanding orders. In this sense, stores are uncapacitated.

The paper by Srinivasa Raghavan (2001) present an analytical method for evaluating the performance of make-to-order supply chains using general queueing networks (GQNs). Through some examples, they illustrate the use of multi-class open generalized queueing networks to compute the mean and variance of the lead time. They also investigate the effect of variance reduction on the average lead time and average WIP inventory. For supply chain configurations with both assembly function (convergent structure) and distribution function (divergent structure), the authors provide a decomposition–aggregation approach for the performance analysis with a fork-join queueing network (FJQN). The network is decomposed into GI/G/1 queues and these queues can be analyzed independently of each other and for each queue the performance measures can be calculated. After composing the network again it is possible to determine the performance measures for the entire network. In order to use a general open fork-join queueing network, this paper considers a supply chain where all the members work on a make-to-order basis and assumes that demand arrivals are deterministic, while processing times at the facilities are normally distributed. In practice, the demand information flows backward (from customers to manufacturers to suppliers) and the demand interdependence between different stages complicates the analysis of the supply chain. To use the open fork-join queueing network, this paper assumes an independent demand relationship between different stages and the demand information flows forward in their models. This limits the application of their approach. Inventory control in multi-echelon systems is the core of integrated supply chain analysis, however, this paper does not consider this issue.

This paper is geared toward developing effective modeling framework and analyzing methods for performance evaluation of integrated logistic chains. In view of the above, the following objectives are pursed: (1) to provide an integrated modeling framework for logistic chains, in which the interdependencies between model components are captured; (2) to develop a network of inventory-queue models for performance analysis of an integrated logistic network with inventory control at all sites; and (3) to extend the previous work developed for supply network model with base-stock control and service requirements. Instead of one-for-one base stock policy, batch-ordering policy and lot-sizing problems are considered. The assumption of uncapacitated production is often not true in practice, therefore, GI^x/G/1 queueing analysis is used to replace the M^x/G/∞ queue based method.

The remainder of this paper is organized as follows. Section 2 provides an analytical modeling framework for integrated logistic chains. In Section 3, performance analysis with GI^x/G/1 queue is developed. Through the performance analysis, different performance measures of a store such as order fill-rate and stock-out probability in the network are obtained. Section 4 introduces the performance analysis for the entire logistic chain. The performance measures of other stores at different stages can be derived by making use demand dependence and lead time dependence. Several numerical examples are used to illustrate the validity of the proposed methodology in Section 5. Section 6 summarizes this research.