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.

A Variant of L♮-Convexity and its Application to Inventory Models with Batch Ordering

2014 ◽  
Vol 31 (06) ◽  
pp. 1450042 ◽  
Author(s):  
Zhiyuan Chen ◽  
Yanchu Liu ◽  
Yi Yang ◽  
Yun Zhou
Keyword(s):  
Operations Research ◽  
General Concept ◽  
Inventory Model ◽  
Inventory Systems ◽  
Lost Sales ◽  
Pricing Model ◽  
Inventory Models ◽  
Optimal Decisions ◽  
Batch Ordering ◽  
System States

Previous studies show that the concept of L♮-convexity is helpful in characterizing the optimal policy for some inventory models with positive leadtimes. Such examples include the lost-sales inventory model by Zipkin (2008). On the structure of lost-sales inventory models. Operations Research, 56(4) 937–944. and the inventory-pricing model by Pang et al. (2012). A note on the structure of joint inventory-pricing control with leadtimes. Operations Research, 60(3), 581–587. However, when taking batch ordering into account, L♮-convexity does not work anymore. In this paper, we extend L♮-convexity to a more general concept termed as Q-jump-L♮-convexity and apply it to batch ordering inventory models including a lost-sales inventory model and an inventory-pricing model with batch ordering and positive leadtimes. By utilizing this new concept, we can partially characterize the structure of the optimal policies for both the models. Moreover, we are able to evaluate the sensitivity of the optimal decisions with respect to system states. Our results can also be applied to the serial and the assembly inventory systems with lost-sales and batch ordering.

scholarly journals An Inventory Model for Imperfect Quality Products with Rework, Distinct Holding Costs, and Nonlinear Demand Dependent on Price

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1362
Author(s):  
Leopoldo Eduardo Cárdenas-Barrón ◽  
María José Lea Plaza-Makowsky ◽  
María Alejandra Sevilla-Roca ◽  
José María Núñez-Baumert ◽  
Buddhadev Mandal
Keyword(s):  
Optimal Solution ◽  
Inventory Model ◽  
Inventory System ◽  
Inventory Level ◽  
Selling Price ◽  
Lot Size ◽  
Inventory Models ◽  
Holding Costs ◽  
Imperfect Items ◽  
The Moment

Traditionally, the inventory models available in the literature assume that all articles in the purchased lot are perfect and the demand is constant. However, there are many causes that provoke the presence of defective goods and the demand is dependent on some factors. In this direction, this paper develops an economic order quantity (EOQ) inventory model for imperfect and perfect quality items, taking into account that the imperfect ones are sent as a single lot to a repair shop for reworking. After reparation, the items return to the inventory system and are inspected again. Depending on the moment at which the reworked lot arrives to the inventory system, two scenarios can occur: Case 1: The reworked lot enters when there still exists inventory; and Case 2: The reworked lot comes into when the inventory level is zero. Furthermore, it is considered that the holding costs of perfect and imperfect items are distinct. The demand of the products is nonlinear and dependent on price, which follows a polynomial function. The main goal is to optimize jointly the lot size and the selling price such that the expected total profit per unit of time is maximized. Some theoretic results are derived and algorithms are developed for determining the optimal solution for each modeled case. It is worth mentioning that the proposed inventory model is a general model due to the fact that this contains some published inventory models as particular cases. With the aim to illustrate the use of the proposed inventory model, some numerical examples are solved.

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 Planning Horizon for Production Inventory Models with Production Rate Dependent on Demand and Inventory Level

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Jennifer Lin ◽  
Henry C. J. Chao ◽  
Peterson Julian
Keyword(s):  
Production Rate ◽  
Optimal Solution ◽  
Planning Horizon ◽  
Inventory Model ◽  
Inventory Level ◽  
Inventory Models ◽  
New Production ◽  
Production Inventory ◽  
Infinite Planning Horizon ◽  
Finite Planning Horizon

This paper discusses why the selection of a finite planning horizon is preferable to an infinite one for a replenishment policy of production inventory models. In a production inventory model, the production rate is dependent on both the demand rate and the inventory level. When there is an exponentially decreasing demand, the application of an infinite planning horizon model is not suitable. The emphasis of this paper is threefold. First, while pointing out questionable results from a previous study, we propose a corrected infinite planning horizon inventory model for the first replenishment cycle. Second, while investigating the optimal solution for the minimization problem, we found that the infinite planning horizon should not be applied when dealing with an exponentially decreasing demand. Third, we developed a new production inventory model under a finite planning horizon for practitioners. Numerical examples are provided to support our findings.

scholarly journals Technical Note on(Q,r,L)Inventory Model with Defective Items

2010 ◽  
Vol 2010 ◽  
pp. 1-8 ◽  
Author(s):  
Cheng-Tan Tung ◽  
Yu-Wen Wou ◽  
Shih-Wei Lin ◽  
Peter Deng
Keyword(s):  
Analytical Approach ◽  
Optimal Solution ◽  
Technical Note ◽  
Inventory Model ◽  
Reasonable Assumption ◽  
Robust Method ◽  
Inventory Models ◽  
Defective Items ◽  
Stochastic Inventory ◽  
Stochastic Inventory Models

Under a reasonable assumption, we derive an analytical approach that verifies uniqueness of the optimal solution for stochastic inventory models with defective items. Our approach implies a robust method to find the optimal solution.

Inventory Control Strategy Analysis for Repairable Units

2013 ◽  
Vol 347-350 ◽  
pp. 220-223
Author(s):  
Qing Tian Han
Keyword(s):  
Inventory Control ◽  
Control Strategy ◽  
Optimal Solution ◽  
Inventory Model ◽  
Equipment Management ◽  
Random Demand ◽  
Strategy Analysis ◽  
Numerical Example ◽  
Eoq Model

Firstly, considering the actual status and the characteristics of equipment management, the typical EOQ model was studied. Secondly, taking the ordering model with random demand as the research object, the inventory model under the condition with definite demand was established, and the optimal solution was given out. Finally, the simulation and calculation were carried out for a numerical example. The result shows the reasonable and applicable of the model.

A Gentle Introduction to the Bayesian Paradigm for Some Inventory Models

2016 ◽  
pp. 340-359
Author(s):  
Vinti Dhaka ◽  
Chandra K. Jaggi ◽  
Sarla Pareek ◽  
Piyush Kant Rai
Keyword(s):  
Probability Distributions ◽  
Probability Model ◽  
Inventory Model ◽  
Inventory Systems ◽  
Deteriorating Items ◽  
Bayesian Probability ◽  
Inventory Models ◽  
Bayes Theory ◽  
Q Model ◽  
Basic Probability

The recent era describes the demand of inventory systems which are governed through random cause effect phenomenon prevailing the strongest use of random models in the concerned area. Bayesian probability model serve the demands of present need in such inventory systems. The present study deals the use of basic Bayesian theory in the development of some of the inventory models, for e.g.: The inventory model for deteriorating items; Designing of the classical (s, Q) models, etc. Here the motivation of use of Bayes theory is to test the efficacy of optimal design of above said models when demand is supposed to be random having some basic probability distributions. In this regard we discuss the inventory model for deteriorating items and the (s, Q) model and their mathematical solution under Bayesian approach.

scholarly journals Production inventory models for deteiorative items with three levels of production and shortages

2017 ◽  
Vol 27 (4) ◽  
pp. 499-519
Author(s):  
Chickian Krishnamoorthi ◽  
C.K. Sivashankari
Keyword(s):  
Production Rate ◽  
Consumer Satisfaction ◽  
Optimal Solution ◽  
Inventory Model ◽  
Lot Size ◽  
Inventory Models ◽  
Total Cost ◽  
Initial Stage ◽  
Production Inventory ◽  
Holding Cost

In this paper, three level production inventory models for deteriorative items are considered under the variation in production rate. Namely, it is possible that production started at one rate, after some time, switches to another rate. Such a situation is desirable in the sense that by starting at a low rate of production, a large quantum stock of manufacturing items at the initial stage are avoided, leading to reduction in the holding cost. The variation in production rate results in consumer satisfaction and potential profit. Two levels of production inventory models are developed, and the optimum lot size quantity and total cost are derived when the production inventory model without shortages is studied first and a production inventory model with shortages next. An optimal production lot size, which minimizes the total cost, is developed. The optimal solution is derived and a numerical example is provided. The validation of the results in this model was coded in Microsoft Visual Basic 6.0.

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 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.

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