Use Of Graphs Research Articles

Guidelines for setup‐cost reduction programs to achieve zero inventory

AbstractHistorically, academics and managers have approached inventory management by assuming setup cost is constant. However, recently, particularly through the experience of the Japanese, we have seen that setup time and setup cost are by no means fixed. For example, one approach to reduce setup, SMED (single minute exchange of die) suggests setups can be reduced from days to minutes. Furthermore, setup reduction is identified as one of the key facilitating factors for just‐in‐time manufacturing.In light of this development, there is an emerging stream of literature on setup reduction. This research stream generally follows the tradition of the lot‐sizing literature; the optimal amount of setup reduction is determined given a total cost model and a setup cost/reduction investment function. However, a limitation of these models is that they focus on a single item and typically include only setup and inventory costs. A key insight from the literature is the counter‐intuitive notion that setup reduction yields increasing marginal returns. Thus, we consider the issues faced by a manager trying to prioritize setup reductions for multiple items. As with the SMED philosophy, where the target is to reduce all setups to less than ten minutes, we do not seek to optimize the amount of setup reduction. Instead we are concerned with establishing an economical sequence for reductions. In general, we assume setup reductions are cost‐justified by direct or indirect benefits.This paper is organized into six sections. The first two sections introduce the problem and review the relevant literature. The third section determines for a single item operating under the EOQ assumptions, what fraction setup must be reduced to achieve a target order quantity. The target may be zero‐inventory, which is alternately defined as an EOQ of one or lot‐for‐lot production. A simple graph for use by managers is provided to show the relationship of target order quantity and fraction setup reduction required.In the fourth section, the implications of setup reduction are extended to multiple items. The principal management issue in this situation is that given two items, which item should be scheduled for setup reduction first. We provide the manager with a simple guideline in the form of the savings ratio (SR), which contrasts the potential savings of the two setups. We show that the decision between two items is dependent on the dollar volume of the items adjusted for how far each item is from a period order quantity of one.Section five develops a formula for determining the maximum allowable setup cost to achieve lot‐for‐lot (zero‐inventory) production for the case of time‐varying demand. Using a marginal cost approach, we determine that a manager need only target setup reduction to justify not batching the lowest expected single period demand over the planning horizon. We show that a setup should be reduced more when a longer planning horizon is considered because there is a greater chance for a low single period demand. In the special case where there are periods of zero demand we find that the maximum setup cost may be higher because the setup cost is compared against multiple periods of carrying charges.The final section considers the application of the savings ratio concept to multiple items with time‐varying demand. SR is defined only for the general case, because the unique interactions of item parameters and the calculation of total costs with the Wagner‐Whitin algorithm preclude a closed‐form solution. However, we did find items with greater variability and. therefore, lower expected single period demands will tend to have higher priority for setup reduction. Thus. a management objective parallel to setup reduction may be to manage the variability of demand.This research is unique in that it suggests guidelines for managers initiating setup‐reduction agendas with multiple items. Our research shows that the potential savings and preferred sequence of reductions is dependent on the interactions of several item parameters (i.e., current setup cost, unit costs, total demand, demand variability, and target lot‐size). To account for these interactions we introduce the savings ratio as a simple procedure to prioritize items for setup reduction.This paper concentrates on setup defined as setup time and assumes a “relevant range” of capacity in which the opportunity costs are constant per unit time. Thus. we assume that regardless of how much additional time is generated by setup‐time reduction, each time unit will yield the same benefit.

Graphs for use with the Lilliefors Test for Normal and Exponential Distributions

Abstract Graphs are presented on which the empirical distribution function can be plotted to test the assumption of normality by the Lilliefors test. A second set of graphs is presented for using the Lilliefors test on exponential distributions. The graphs allow for tests at the 10 percent, 5 percent, and 1 percent levels of significance. Use of these graphs makes it easy for students in a first course in statistics to test normal and exponential distributions without having to unravel the mystery associated with putting together a chi-squared goodness-of-fit test.

Graphs for Use with the Lilliefors Test for Normal and Exponential Distributions

Graphs for Use with the Lilliefors Test for Normal and Exponential Distributions

Construction and Utilization of Item Relational Structure Graphs for Use in Test Analysis

Construction and Utilization of Item Relational Structure Graphs for Use in Test Analysis

A two-dimensional graph for use in digital circuit design

An improved version of a two-dimensional graph is presented. Various aspects of the method, in addition to some new definitions are explained. Some practical digital systems are designed to illustrate the validity of a two-dimensional graph.

Graphs for Use in Testing Equality of Two Correlation Coefficients

Graphs are presented to provide quick and accurate 5% and 1% tests of the equality of two correlation coefficients based on equal-size samples. For unequal samples, the harmonic mean 2n1n2/(n1 + n2) provides a good compromise sample size for using the graphs.

Hydrology of Porous Pavement Parking Lots

Numerical solutions of the Boussinesq equation were used to examine the hydrologic behavior of porous pavement systems incorporating subdrains in open graded base courses placed on impermeable membranes. A series of numerical experiments showed that substantial control of the runoff hydrograph from parking lots could be obtained through the use of porous pavements. The numerical experiments conducted with synthetic design storms were used to develop equations and graphs for use by engineers designing porous pavement systems for runoff control.

Macro E-Nets for Representation of Parallel Systems

An extension of Petri nets called evaluation nets (E-nets) has been developed for use in representation of computer systems. These lead to interpreted graphs for use in human communication and to machine-interpretable descriptions. They may be used as aids in development of simulations and planning of measurements for examining characteristics such as throughput, turnaround time, and utilization of resources. This paper reviews the five primitives used to form nets expressing logical interactions among tokens (or tasks) flowing through the net and system resources represented by the net. Inherent in the use of the primitives is the ability to express time delays associated with the flow of tokens through the network and the modification of attributes of these tokens. This paper extends previous work on evaluation nets through the use of macro nets that represent structures made up of the primitives, allowing compression of the net for easier understanding. The macro nets are ``open-ended'' in the sense that the user can develop new macros to suit the needs of a particular study. Evaluation nets can be used informally like flow charts or block diagrams, although they provide greater power of expression than either. They can also be used more formally to develop machine aids, e.g., for on-line editing of evaluation nets or for development of simulation programs. Some examples of evaluation nets are provided that model a CDC 6400 and the cooperation of n independent sequential processes.

Dosimetry of californium 252.

Abstract Methods to measure the dose rates of 252Cf sources are described and the results of the measurements are presented. A computer program, using empirical constants based on the measurements, calculated the dose rates for arrays of 252Cf sources and for 1.5, 2.0, and 3.0 cm linear sources. A Paterson-Parker type graph for use with 252Cf surface applicators is included.

A Suggestion for Compressible Flow Graphs for use in Subsonic Flow

The present re-look at compressible flow graphs arose during extensive testing of jet blowing models in low speed tunnels. In these tests, it is often necessary to calculate such quantities as jet thrusts, mass flow rates and velocities assuming isentropic expansion to the tunnel static pressure from the measured values of the stagnation pressure and temperature. These jet flows are usually compressible but subsonic and, in order to make these calculations, use has to be made either of Bernoulli's compressible flow equation or, alternatively, the extensive compressible flow graphs that are now available.

A GRAPH FOR USE IN DETERMINING OXYGEN SATURATION OF BLOOD BY MEANS OF SPECTROPHOTOMETRY.

A GRAPH FOR USE IN DETERMINING OXYGEN SATURATION OF BLOOD BY MEANS OF SPECTROPHOTOMETRY.

COFFERDAMS.

The functions of cofferdams are defined, and their types are divided into two main classifications: the first constructed of soil, concrete or timber, and the second depending primarily on steel sheet piling. These are further sub-divided and listed in two charts. The choice available to the designer is discussed in relation to the permanent structure to be built within the dam, the site conditions, the depth of the cofferdam and the nature of the ground. For design purposes cofferdamas re divided into two categories, namely singleskin and doubleskin, the latter including cellular cofferdams. The basic principles are discussed and attention is drawn to certain aspects of the design of cofferdams in both categories. Graphs for use in the preparation of preliminary designs and estimates for cofferdams of conventional construction are given. Finally, the mechanisms of failure of cofferdams are reviewed. Reference is made to the fact that they are generally derived from the inability of the ground inside the cofferdam to withstand the external forceasn d not fromth e structural failure of the materials used in the construction.

A variable structure-factor graph for use in crystal-structure determination

The instrument incorporates two tables, linked so that a rotation of one causes an identical rotation of the other. A drawing of proposed atomic positions is placed on one table and lies under a net of parallel wires which represent the contours of a structure-factor graph.(4) The spacings of these wires and the relative orientation of the drawing may be adjusted to correspond with any given point on a representation of the diffraction pattern placed on the second table. Suggestions may then be obtained, from the relative disposition of atomic positions and contour lines, for changes that would improve the agreement between the diffraction patterns of the proposed and actual structures. The instrument has already given useful assistance in a number of problems.

A Selection of Graphs for use in Calculations of Compressible Airflow. Prepared on behalf of the A.R.C, by the Compressible Flow Tables Panel (Chairman: Professor L. Rosenhead). Clarendon Press, 1954. 115 pp. 84s.

A Selection of Graphs for use in Calculations of Compressible Airflow. Prepared on behalf of the A.R.C, by the Compressible Flow Tables Panel (Chairman: Professor L. Rosenhead). Clarendon Press, 1954. 115 pp. 84s.

Oil-Spray Investigations of the N.A.C.A.: Oil-Engine Performance—Combustion Losses—Value of Research—Oil-Spray Investigations of the National Advisory Committee for Aeronautics—Photographic Records of Fuel Sprays and Graphs for Use in Studying Spray Characteristics and Fuel Injection in High-Speed Engines

Oil-Spray Investigations of the N.A.C.A.: Oil-Engine Performance—Combustion Losses—Value of Research—Oil-Spray Investigations of the National Advisory Committee for Aeronautics—Photographic Records of Fuel Sprays and Graphs for Use in Studying Spray Characteristics and Fuel Injection in High-Speed Engines