John E. Tyworth

Robustness of the normal approximation of lead-time demand in a distribution setting

Abstract: Previous studies criticize the general use of the normal approximation of lead-time demand on the grounds that it can lead to serious errors in safety stock. We reexaminethis issue for the distribution of fast-moving finished goods. We first determine the optimalreorder points and quantities by using the classical normal-approximation method and atheoretically correct procedure. We then evaluate the misspecification error of the normalapproximation solution with respect to safety stock, logistics-system costs, total costs (logis-tics costs, including acquisition costs), and fill rates. The results provide evidence that thenormal approximation is robust with respect to both cost and service for seven major industrygroups. q 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 165–186, 1997 INTRODUCTIONThe (s, Q) continuous-review inventory model has been widely used and extensivelystudied in the literature. In the stochastic version of this model, where demand (D) andlead time (L) are independent random variables, the analyst must know the distributionlead-time demands (X ) to assess stockout risks or expected shortages. The simplest wayto model lead-time demand is to determine the first two moments ofX and then assumethat X has a normal distribution. This classic approach, found in virtually every textbookon production-inventory, operations, and logistics management, rests on two premises:1. The underlying distribution of X is not important.2. The first two moments are the only relevant parameters.Many scholars, however, have criticized the use of this normal theory approach on twogrounds. First, the distribution of X is likely to have a nonnormal shape, which means thatthe normal approximation will produce errors in the estimates of replenishment levels andthus the amount of safety stock needed to support customer-service targets or to counterbal-ance stockout costs. Second, if the coefficient of variation ofX is large—say, greater than

ESTIMATING THE EFFECTS OF CARRIER TRANSIT-TIME PERFORMANCE ON LOGISTICS COST AND SERVICE

Joint determination of an appropriate transportation mode and an optimal inventory control policy is important in supply chain management. We present a method of estimating the effects of carrier transit-time performance on logistics cost and service. Unlike current approaches, this method enables users to develop accurate estimates when non-normal shapes characterize the probability distributions of both demand and lead time. Additionally, the methodology includes two important refinements to the standard transportation-inventory model. First, we relaxed the assumption that the shipping cost is a linear function of the order quantity. Second, we treated transit time as a segment of lead time. We used the gamma distribution to illustrate the flexibility of the method and developed an enhanced sensitivity-analysis tool for examining the effects of carrier transit time on both cost and service. The methodology is appropriate for the transportation of service-sensitive, independent-demand inventory items controlled by a continuous review inventory system.

AIRLINE MARKET SHARE AND CUSTOMER SERVICE QUALITY: A REFERENCE-DEPENDENT MODEL

Traditional models that explain the nature of the relationship between customer service quality and airline demand assume that the relationship can be approximated by using smooth or differentiable curves. Suzuki and Tyworth, however, recently argued that this assumption may not be valid, and that, if it is invalid, the model performance can be improved by using non-smooth functions to represent the relationship (Suzuki, Y., Tyworth, J.E., 1998. A theoretical framework for modeling sales-service relationships in the transportation industry. Transportation Research E 34 (2), 87-100). We use their framework to develop a model that represents the relationship between service quality and market share in the airline industry and then empirically compare its performance with conventional airline demand models. The results indicate that the relationship is characterized by a non-smooth curve and that our model provides a significantly better goodness of fit than other conventional demand models.

DUAL SOURCED SUPPLY CHAINS: THE DISCOUNT SUPPLIER OPTION

In this paper, we examine the dynamics of a supply chain that has the option of using two suppliers - one reliable, and the other unreliable. We characterize the unreliable supplier with long lead-time mean and variance. Although the use of the unreliable supplier might potentially warrant higher inventory and transportation costs, it is attractive because of the willingness of the supplier to provide a discount on the purchase price. We analyze the cost economics of two suppliers in a broader inventory-logistics framework, one that includes in-transit inventories and transportation costs. In this broader perspective, we provide a simple heuristic and sample exchange curves to determine: (i) if the order should be split between the suppliers; and (ii) if the order is split, the amount of discount and the fraction ordered to the secondary supplier to make order-splitting a worth-while policy. ©

Transportation’s role in the sole‐ versus dual‐sourcing decision

Current studies indicate that buyers can improve lead‐time performance and reduce total inventory‐system costs by splitting orders between two suppliers. These studies, however, treat transportation only implicitly as an element of the cost of placing an order. This is an important limitation, because shipping costs increase disproportionately as the size of shipment decreases and typically comprise a sizeable portion of total logistics cost. Investigates the role of transportation in the decision to procure from either one or two suppliers. A state‐of‐the art model was first modified to treat transportation costs explicitly and then used to conduct 54 experiments to measure the gains or losses in total logistics costs under a variety of representative conditions.

A note on solutions to the inventory model for gamma lead‐time demand

Namit and Chen recently created two algorithms to solve the inventory model for gamma lead‐time demand without using tabulated values. However, other less complicated solutions that do not require the use of tabulated values are currently available. This note demonstrated the relative simplicity of those solutions and discussed some practical considerations.

A theoretical framework for modeling sales–service relationships in the transportation industry

This paper presents a theoretical framework for estimating the functional form of the relationship between sales and service performance for transportation providers. We introduce a method of improving model performance by utilizing a concept of human behavior that has never been incorporated into the models of sales-service relationships. This concept, called the loss aversion property, claims that customers (shippers) react more strongly when they experience service performance below their reference point (expectation) than when they experience service performance above their reference point. Using this concept, we posit that a one unit decrease in service quality from the customers reference point would decrease a carriers sales more than an equivalent-sized increase in service quality would increase sales. To incorporate an asymmetric pattern of the sales-service relationship, we develop a model that makes a key distinction between sales response to service increase and to service decrease. The model is demonstrated using hypothetical data. The discussion addresses multiple service quality measures as well as data implementation issues.

Simulation based approach to study the interaction of scheduling and routing on a logistic network

This research investigates the interaction of production scheduling and routing/transportation on a logistic network. Basic scheduling rules and existing rou ting/transportation alternatives were studied using a simulation model, with cost and customer service le vels as measures of performance. The simulation model, including network configuration, orders, service times, etc., was based on a “real world” electronic manufa cturer, where the production process requires comp onents to flow through three facilities. The two existing routing/transportation alternatives are ocean and air freight. The analysis of the results indicated that ce rtain combinations of scheduling and routing rules r esult in low manufacturing-logistic costs while maintain high levels of customer service.

Transport Selection: Computer Modelling in a Spreadsheet Environment

Trade‐offs among logistics cost and service elements often make transport selection analysis difficult, especially when demand is uncertain and carriers offer different rates and services. The spreadsheet environment offers a powerful, manager‐friendly medium for analysing these trade‐offs. This microcomputer application exploits some of the recent advances in spreadsheet technology to provide transport buyers with a tool for evaluating such complex logistical trade‐offs. This tool demonstrates how the emerging spreadsheet technology makes it relatively easy to develop a computer‐based model that can capture a rich level of detail that is beyond the scope of the current transport selection models using analytical approaches.