Roger D.H. Warburton

The strategic integration of agile and lean supply

Lean supply is closely associated with enabling flow and the elimination of wasteful variation within the supply chain. However, lean operations depend on level scheduling and the growing need to accommodate variety and demand uncertainty has resulted in the emergence of the concept of agility. This paper explores the role of inventory and capacity in accommodating such variation and identifies how TRIZ separation principles and TOC tools may be combined in the integrated development of responsive and efficient supply chains. A detailed apparel industry case study is used to illustrate the application of these concepts and tools.

Questioning the relentless shift to offshore manufacturing

A device for providing a voltage indicating the angular velocity of rotation of the armature in a limited rotation, polarized, moving iron galvanometer. The device includes a means for providing a first voltage dependent upon the angular velocity of the armature, the self-inductance of the galvanometer drive coil, and the drive current in the drive coil. A compensation coil is magnetically coupled to the drive coil and magnetically isolated from the effects of the rotating armature to provide a second voltage which is dependent upon mutual inductance between the drive and compensation coils and upon the drive current, but is not dependent upon the effects of the rotating armature due to the magnetic isolation of the compensation coil from the armature. A combining means proportionally combines the first and second voltages to provide a voltage indicating the angular velocity of rotation of the armature. The means for providing the first voltage includes either the drive coil, with the first voltage appearing across the drive coil, or a pickoff coil wound coaxially with and adjacent to the drive coil so that the first voltage appears across the pickoff coil and is proportional to the voltage appearing across the drive coil. The velocity signal thus derived is introduced to the drive circuit to provide effective damping.

Technical Note: Further insights into 'the stability of supply chains'

Riddalls and Bennett (2002) presented a stability criterion for a supply chain model in continuous time. It is shown here their solution is in error and the correct stability criterion is provided. The results were substantiated by deriving the correct criterion by several independent theoretical analyses and validating the solution via numerical simulation. The weight of evidence suggests that the new derivations lead to correct predictions of the stability boundary for this important and widely used supply chain model.

Analysis of asymptotic projectile motion with air resistance using the Lambert W function

We calculate the range of a projectile experiencing air resistance in the asymptotic region of large velocities by introducing the Lambert W function. From the exact solution for the range in terms of the Lambert W function, we derive an approximation for the maximum range in the limit of large velocities. Analysis of the result confirms an independent numerical result observed in an introductory physics class that the angle at which the maximum range occurs, θmax, goes rapidly to zero for increasing initial firing speeds v0≫1. We show that θmax∼(ln v0)/v0.

Inventory management for stochastic lead times with order crossovers

We study the impact of stochastic lead times with order crossover on inventory costs and safety stocks in the order-up-to (OUT) policy. To motivate our research we present global logistics data which violates the traditional assumption that lead time demand is normally distributed. We also observe that order crossover is a common and important phenomenon in real supply chains. We present a new method for determining the distribution of the number of open orders. Using this method we identify the distribution of inventory levels when orders and the work-in-process are correlated. This correlation is present when demand is auto-correlated, demand forecasts are generated with non-optimal methods, or when certain ordering policies are present. Our method allows us to obtain exact safety stock requirements for the so-called proportional order-up-to (POUT) policy, a popular, implementable, linear generalization of the OUT policy. We highlight that the OUT replenishment policy is not cost optimal in global supply chains, as we are able to demonstrate the POUT policy always outperforms it under order cross-over. We show that unlike the constant lead-time case, minimum safety stocks and minimal inventory variance do not always lead to minimum costs under stochastic lead-times with order crossover. We also highlight an interesting side effect of minimizing inventory costs under stochastic lead times with order crossover with the POUT policy—an often significant reduction in the order variance.

Managing and Predicting the Costs of Real-Time Software

The Putnam model can be used to predict and manage software development projects. It is a management tool that takes, as input, easily obtained manpower data and produces cost and schedule estimates. This paper examines data from two real-time software projects and analyzes the applicability of the Putnam model. We propose a variation ation of the model which more reliably follows the staffing curve of real-time software applications. A critical analysis of the assumptions is presented and the parameters are reinterpreted so that they reflect the environment of embedded applications. Two projects are analyzed from actual data. It is shown how management decisions are reflected in the model. Even erratic and incomplete data can yield valuable conclusions. It is also shown that the model is appropriate to software developed with modern practices. We show how valuable management information can be obtained by laying out the data in a systematic manner.

EOQ extensions exploiting the Lambert W function

We analyse several extensions to the Economic Order Quantity (EOQ) model: when the inventory deteriorates over time; when the demand contains a stock dependent term; and when the present value, or discounted cost, is included. We derive exact analytical expressions for the order that minimises the total cost, and in each case the Lambert W function arises, adding to the growing list of useful applications for this recently rediscovered function. The analytical solutions have immediate practical and pedagogic applications. [Received 06 September 2007; Revised 13 January 2008; Accepted 01 April 2008]

The optimal quantity of quick response manufacturing for an onshore and offshore sourcing model

Consumer demand for innovative and fashion products is highly unpredictable, but could be fulfilled through quick response manufacturing (QRM). However, the extra cost is usually considered to be a barrier to such an approach. The newsvendor algorithm is applied to demonstrate that a strategic combination of onshore and offshore manufacturing can be more profitable than a 100% offshore approach, highlighting the growing importance of a cost versus response trade-off. The optimal split between onshore and offshore manufacturing is calculated. We discuss the successful application of the QRM model in two practical cases: quick response manufacturing for athletic wear; and onshore garment dyeing versus offshore yarn dyeing. In the right context, QRM is a viable and profitable option. Issues in the practical application of the model are discussed.

Inventory resonances in multi-echelon supply chains

We consider multi-echelon supply chains, typically consisting of retailer, manufacturer, supplier, etc., in which each actor chooses its own inventory replenishment strategy, and is subject to its own replenishment delay. We model the chain with a system of linear differential delay equations. In matrix form the system of equations is triangular and we derive an exact, algorithmic solution, which allows us to determine the inventory behaviour over time for each echelon. The solution is characterised by a set of Lambert modes, obtained from the solution to a set of transcendental equations. For a complete set of solutions the modes must be independent. When the modes are not independent, we find that additional solutions exist, and these exhibit a transient surge in inventory. In analogy with ordinary differential equations, we refer to this as a ‘resonance’ in the inventory. We discuss the practical import of this theoretical prediction.

An optimal replenishment policy for an inventory with decaying items and a ramp in demand

We present a model of an order-level inventory system that contains items that deteriorate over time while simultaneously reacting to a ramp in demand. An optimal analytical solution is found for the ordering policy that minimizes the inventory cost. The solution is in terms of the Lambert W function, adding to the list of applications for this recently rediscovered function. The exact solutions confirm numerical approximations derived previously. The analytical solutions allow a detailed sensitivity analysis to be performed, and we present some properties of the optimal solutions in which precision issues emerge.