scholarly journals Novel Solution Method for Inventory Models with Stochastic Demand and Defective Units

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Xu-Ren Luo ◽  
Chun-Hsiao Chu ◽  
Henry C. J. Chao
Keyword(s):  
Solution Method ◽  
Optimal Solution ◽  
Convergent Sequence ◽  
Threshold Value ◽  
The Other ◽  
Inventory Models ◽  
Previous Approach ◽  
Numerical Examples ◽  
Distinct Features ◽  
Ordering Quantity

This paper is a response to two papers. We improve the lengthy proof for the first paper by an elegant verification. For the second paper, we point out the three-sequence approach will result in different convergent rates such that when the other two sequences are converged, the ordering quantity sequence may still not converge to the optimal solution. We construct a novel iterative method to simplify the previous approach proposed by the three-sequence approach for the optimal solution. By the same numerical examples of three published papers, we demonstrate that we can control our findings to converge more accurately than previous results. Moreover, we show that there are three distinct features of our proposed approach. (i) It converges to the desired solution within the preassigned threshold value. (ii) We estimate the convergent ratio. (iii) We find the dominant factors for our proposed convergent sequence.

scholarly journals Inventory Models with Defective Units and Sub-Lot Inspection

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1038
Author(s):  
Han-Wen Tuan ◽  
Gino K. Yang ◽  
Kuo-Chen Hung
Keyword(s):  
Lower Bound ◽  
Optimal Solution ◽  
Upper Bounds ◽  
Interior Solution ◽  
Order Quantity ◽  
Inventory Models ◽  
Defective Items ◽  
Numerical Examples ◽  
Counter Example ◽  
Analytical Foundation

Inventory models must consider the probability of sub-optimal manufacturing and careless shipping to prevent the delivery of defective products to retailers. Retailers seeking to preserve a reputation of quality must also perform inspections of all items prior to sale. Inventory models that include sub-lot sampling inspections provide reasonable conditions by which to establish a lower bound and a pair of upper bounds in terms of order quantity. This should make it possible to determine the conditions of an optimal solution, which includes a unique interior solution to the problem of an order quantity satisfying the first partial derivative. The approach proposed in this paper can be used to solve the boundary. These study findings provide the analytical foundation for an inventory model that accounts for defective items and sub-lot sampling inspections. The numerical examples presented in a previous paper are used to demonstrate the derivation of an optimal solution. A counter-example is constructed to illustrate how existing iterative methods do not necessarily converge to the optimal solution.

scholarly journals The Convergence of Gallego’s Iterative Method for Distribution-Free Inventory Models

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 484 ◽  
Author(s):  
Ting-Chen Hu ◽  
Kuo-Chen Hung ◽  
Kuo-Lung Yang
Keyword(s):  
Iterative Method ◽  
Optimal Solution ◽  
Threshold Value ◽  
Optimal Order ◽  
Order Quantity ◽  
Inventory Models ◽  
Worst Case ◽  
Distribution Free ◽  
Second Moments ◽  
Optimal Order Quantity

For inventory models with unknown distribution demand, during shortages, researchers used the first and the second moments to derive an upper bound for the worst case, that is the min-max distribution-free procedure for inventory models. They applied an iterative method to generate a sequence to obtain the optimal order quantity. A researcher developed a three-sequence proof for the convergence of the order quantity sequence. We directly provide proof for the original order quantity sequence. Under our proof, we can construct an increasing sequence and a decreasing sequence that both converge to the optimal order quantity such that we can obtain the optimal solution within the predesigned threshold value.

scholarly journals Improvement for Amelioration Inventory Model with Weibull Distribution

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Han-Wen Tuan ◽  
Shu-Cheng Lin ◽  
Peterson Julian
Keyword(s):  
Weibull Distribution ◽  
Solution Method ◽  
Shape Parameter ◽  
Optimal Solution ◽  
Inventory Model ◽  
Inventory Systems ◽  
Inventory Models ◽  
Numerical Example ◽  
Analytical Work

Most inventory models dealt with deteriorated items. On the contrary, just a few papers considered inventory systems under amelioration environment. We study an amelioration inventory model with Weibull distribution. However, there are some questionable results in the amelioration paper. We will first point out those questionable results in the previous paper that did not derive the optimal solution and then provide some improvements. We will provide a rigorous analytical work for different cases dependent on the size of the shape parameter. We present a detailed numerical example for different ranges of the sharp parameter to illustrate that our solution method attains the optimal solution. We developed a new amelioration model and then provided a detailed analyzed procedure to find the optimal solution. Our findings will help researchers develop their new inventory models.

scholarly journals Ordering Cost Reduction in Inventory Model with Defective Items and Backorder Price Discount

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Karuppuchamy Annadurai ◽  
Ramasamy Uthayakumar
Keyword(s):  
Cost Reduction ◽  
Optimal Solution ◽  
Computer Code ◽  
Inventory Model ◽  
Inventory Models ◽  
Price Discount ◽  
Defective Items ◽  
Numerical Examples ◽  
Ordering Cost Reduction ◽  
Real Market

In the real market, as unsatisfied demands occur, the longer the length of lead time is, the smaller the proportion of backorder would be. In order to make up for the inconvenience and even the losses of royal and patient customers, the supplier may offer a backorder price discount to secure orders during the shortage period. Also, ordering policies determined by conventional inventory models may be inappropriate for the situation in which an arrival lot contains some defective items. To compensate for the inconvenience of backordering and to secure orders, the supplier may offer a price discount on the stockout item. The purpose of this study is to explore a coordinated inventory model including defective arrivals by allowing the backorder price discount and ordering cost as decision variables. There are two inventory models proposed in this paper, one with normally distributed demand and another with distribution free demand. A computer code using the software Matlab 7.0 is developed to find the optimal solution and present numerical examples to illustrate the models. The results in the numerical examples indicate that the savings of the total cost are realized through ordering cost reduction and backorder price discount.

scholarly journals Inventory models with stock - and price-dependent demand for deteriotating items based on limited space

2022 ◽  
Vol 12 (1) ◽  
pp. 0-0
Keyword(s):  
Optimal Solution ◽  
Selling Price ◽  
Order Quantity ◽  
Inventory Models ◽  
Stock Level ◽  
Numerical Examples ◽  
Eoq Model ◽  
Eoq Models ◽  
Demand Rate ◽  
Dependent Demand

This paper deals with the problem of determining the optimal selling price and order quantity simultaneously under EOQ model for deteriorating items. It is assumed that the demand rate depends not only on the on-display stock level but also the selling price per unit, as well as the amount of shelf/display space is limited. We formulate two types of mathematical models to manifest the extended EOQ models for maximizing profits and derive the algorithms to find the optimal solution. Numerical examples are presented to illustrate the models developed and sensitivity analysis is reported.

scholarly journals An Inventory Model under Trapezoidal Type Demand, Weibull-Distributed Deterioration, and Partial Backlogging

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Lianxia Zhao
Keyword(s):  
Sensitivity Analysis ◽  
Waiting Time ◽  
Optimal Solution ◽  
Inventory Model ◽  
Partial Backlogging ◽  
Inventory Models ◽  
Numerical Examples ◽  
Replenishment Policy ◽  
Demand Rate ◽  
Theoretical Results

This paper studies an inventory model for Weibull-distributed deterioration items with trapezoidal type demand rate, in which shortages are allowed and partially backlogging depends on the waiting time for the next replenishment. The inventory models starting with no shortage is are to be discussed, and an optimal inventory replenishment policy of the model is proposed. Finally, numerical examples are provided to illustrate the theoretical results, and a sensitivity analysis of the major parameters with respect to the optimal solution is also carried out.

scholarly journals A demand independent inventory model

2013 ◽  
Vol 23 (1) ◽  
pp. 129-135 ◽  
Author(s):  
Jennifer Lin ◽  
Henry Chao ◽  
Peterson Julian
Keyword(s):  
Waiting Time ◽  
Operational Research ◽  
Optimal Solution ◽  
Decision Makers ◽  
Inventory Models ◽  
Negative Function ◽  
Replenishment Policy ◽  
Ramp Type Demand ◽  
Optimal Ordering ◽  
Ordering Quantity

This paper is an extension of Deng et al. (2007) that was published in the European Journal of Operational Research. We have generalized their model from ramp type demand to arbitrary positive demand while theoretically discovering an important phenomenon: the optimal solution is actually independent of the demand as pointed out by Wou (2010), Hung (2011) and Lin (2011). We extend their inventory models in which the deteriorated rate is any non-negative function and backlog rate is inversely linearly related to the waiting time. Our findings will provide a new inventory system to help decision makers decide the optimal ordering quantity and replenishment policy.

A new algorithm for finding CRM-model coefficients

2019 ◽  
Vol 5 (3) ◽  
pp. 164-185 ◽  
Author(s):  
Alexander D. Bekman ◽  
Sergey V. Stepanov ◽  
Alexander A. Ruchkin ◽  
Dmitry V. Zelenin
Keyword(s):  
Approximate Solution ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Complex Form ◽  
Approximate Solutions ◽  
The Other ◽  
Programming Algorithm ◽  
Stochastic Algorithms ◽  
Large Set ◽  
Flow Rates

The quantitative evaluation of producer and injector well interference based on well operation data (profiles of flow rates/injectivities and bottomhole/reservoir pressures) with the help of CRM (Capacitance-Resistive Models) is an optimization problem with large set of variables and constraints. The analytical solution cannot be found because of the complex form of the objective function for this problem. Attempts to find the solution with stochastic algorithms take unacceptable time and the result may be far from the optimal solution. Besides, the use of universal (commercial) optimizers hides the details of step by step solution from the user, for example&nbsp;— the ambiguity of the solution as the result of data inaccuracy.<br> The present article concerns two variants of CRM problem. The authors present a new algorithm of solving the problems with the help of “General Quadratic Programming Algorithm”. The main advantage of the new algorithm is the greater performance in comparison with the other known algorithms. Its other advantage is the possibility of an ambiguity analysis. This article studies the conditions which guarantee that the first variant of problem has a unique solution, which can be found with the presented algorithm. Another algorithm for finding the approximate solution for the second variant of the problem is also considered. The method of visualization of approximate solutions set is presented. The results of experiments comparing the new algorithm with some previously known are given.

EEG and Behavioral Changes following Neurofeedback Treatment in Learning Disabled Children

2003 ◽  
Vol 34 (3) ◽  
pp. 145-152 ◽  
Author(s):  
T. Fernández ◽  
W. Herrera ◽  
T. Harmony ◽  
L Díaz-Comas ◽  
E. Santiago ◽  
...  
Keyword(s):  
Threshold Value ◽  
Learning Disabled ◽  
The Other ◽  
Control Group ◽  
Relative Power ◽  
Normal Children ◽  
Absolute Power ◽  
And Gender ◽  
Socioeconomical Status ◽  
Experimental Group

Neurofeedback (NFB) is an operant conditioning procedure, by which the subject learns to control his/her EEG activity. On one hand, Learning Disabled (LD) children have higher values of theta EEG absolute and relative power than normal children, and on the other hand, it has been shown that minimum alpha absolute power is necessary for adequate performance. Ten LD children were selected with higher than normal ratios of theta to alpha absolute power (theta/alpha). The Test Of Variables of Attention (TOVA) was applied. Children were divided into two groups in order to maintain similar IQ values, TOVA values, socioeconomical status, and gender for each group. In the experimental group, NFB was applied in the region with highest ratio, triggering a sound each time the ratio fell below a threshold value. Noncontingent reinforcement was given to the other group. Twenty half-hour sessions were applied, at a rate of 2 per week. At the end of the 20 sessions, TOVA, WISC and EEG were obtained. There was significant improvement in WISC performance in the experimental group that was not observed in the control group. EEG absolute power decreased in delta, theta, alpha and beta bands in the experimental group. Control children only showed a decrease in relative power in the delta band. All changes observed in the experimental group and not observed in the control group indicate better cognitive performance and the presence of greater EEG maturation in the experimental group, which suggests that changes were due not only to development but also to NFB treatment.

scholarly journals ON THE MECHANISM OF TONIC IMMOBILITY IN VERTEBRATES

1928 ◽  
Vol 11 (6) ◽  
pp. 715-741 ◽  
Author(s):  
Hudson Hoagland
Keyword(s):  
Tonic Immobility ◽  
Threshold Value ◽  
Temperature Characteristic ◽  
The State ◽  
Rate Of Change ◽  
The Other ◽  
Negative Slope ◽  
Selective Inhibitors ◽  
Initial Stimulus ◽  
Temperature Range

1. The durations of successive periods of induced tonic immobility in the lizard Anolis carolinensis was examined as a function of temperature. An automatic recording method was employed and observations were made of 12,000 to 15,000 immobilizations with six animals over a temperature range of 5° to 35°C. during 5 months. 2. The durations of the immobile periods were found to vary rhythmically in most cases. The reciprocal of the duration of the rhythm, i.e., the rate of change of the process underlying the rhythms, when plotted as a function of temperature according to the Arrhenius equation show distributions of points in two straight line groups. One of these groups or bands of points extends throughout the entire temperature range with a temperature characteristic of approximately µ = 31,000 calories, and the other covers the range of 20° to 35°C. with µ equal to approximately 9,000 calories. 3. The initial stimulus in a series of inductions of immobility appears to set off a mechanism which determines the duration of the state of quiescence. Succeeding forced recoveries seem to have no effect on the normal duration of the rhythm. 4. These results are interpreted by assuming the release, through reflex stimulation, of hormonal substances, one effective between 5° and 35°C. and the other effective between 20° and 35°C. These substances are assumed to act as selective inhibitors of impulses from so called "higher centers," allowing impulses from tonic centers to pass to the muscles. 5. In some experiments a progressive lengthening in successively induced periods of immobility was observed. The logarithm of the frequency of recovery when plotted against time in most of these cases (i.e., except for a few in which irregularities occurred) gave a linear function of negative slope which was substantially unaffected by temperature. In these cases it is assumed that a diffusion process is controlling the amount of available A substance. 6. The results are similar to those obtained by Crozier with Cylisticus convexus. The duration of tonic immobility seems to be maintained in both arthropod and vertebrate by the chemical activity of "hormonal" selective inhibitors. The details of the mechanisms differ, but there is basic similarity. 7. Injections of small amounts of adrenalin above a threshold value are found to prolong the durations of tonic immobility of Anolis, by an amount which is a logarithmic function of the "dose." It is possible that internally secreted adrenalin, above a threshold amount, may be involved in the maintenance of tonic immobility. 8. The production of tonic immobility reflexly is a problem distinct from that of the duration of immobility. It is suggested that the onset may be induced by "shock" to the centers of reflex tonus causing promiscuous discharge of these centers with accompanying inhibition of the higher centers. Such a condition may result when an animal is suddenly lifted from the substratum and overturned, or when, as in the case of Anolis, it struggles with dorsum down. This reaction of the "tonic centers" may at the same time lead to discharge of the adrenal glands by way of their spinal connections thus prolonging the state.

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