Variability reduction and business-process synchronization are acknowledged as keys to achieving sharp and timely deliveries in supply-chain networks. In this paper, we introduce a new notion, which we call six sigma supply chains to describe and quantify supply chains with sharp and timely deliveries, and develop an innovative approach for designing such networks. The approach developed in this paper is founded on an intriguing connection between mechanical design tolerancing and supply-chain lead-time compression. We show that the design of six sigma supply chains can be formulated as a mathematical programming problem, opening up a rich new framework for studying supply-chain design optimization problems. To show the efficacy of the notion and the design methodology, we focus on a design optimization problem, which we call the inventory optimization (IOPT) problem. Given a multistage supply-chain network, the IOPT problem seeks to find optimal allocation of lead time variabilities and inventories to individual stages, so as to achieve required levels of delivery performance in a cost-effective way. We formulate and solve the IOPT problem for a four-stage make-to-order liquid petroleum gas supply chain. The solution of the problem offers rich insights into inventory-service level tradeoffs in supply-chain networks and proves the potential of the new approach presented in this paper.
Note to Practitioners-This paper builds a bridge between mechanical design tolerancing and supply-chain management. In particular, the paper explores the use of statistical tolerancing techniques in achieving outstanding delivery performance through variability reduction. Informally, a six sigma supply chain is that which delivers products within a customer specified delivery window, with at most 3.4 missed deliveries per million. The innovations in this paper are the following: 1) to define two performance metrics delivery probability and delivery sharpness to describe the precision and accuracy of deliveries, in terms of process capability indexes Cp,Cpk, and Cpm; 2) to formulate the supply-chain design optimization problem using the process capability indices; 3) to suggest an efficient solution procedure for the design optimization pr- oblem. The paper presents the case study of a two-echelon distribution network and using the framework developed in the paper shows the role of inventory in controlling lead time variability and achieving six sigma levels of delivery performance.