Wen-Chuan Lee

Computational algorithm for inventory model with a service level constraint, lead time demand with the mixture of distributions and controllable negative exponential backorder rate

Abstract In this paper, let the backorder rate be a control variable to widen applications of Wu and Tsai’s model [J.W. Wu, H.Y. Tsai, Mixture inventory model with back orders and lost sales for variable lead time demand with the mixtures of normal distribution, International Journal of Systems Science 32 (2001) 259–268.]. And, we also assume that the backorder rate is dependent on the length of lead time through the amount of shortages. In addition, we assume that the lead time demand follows a mixture of normal distributions, and then we relax the assumption about the form of the mixture of distributions for the lead time demand and apply the minimax distribution free procedure to solve the problem. Further, instead of having a stock-out term in the objective function, a service level constraint is added to the models. Finally, we develop two computational algorithms to find the optimal order quantity and the optimal lead time. Furthermore, two numerical examples are also given to illustrate the results.

Inventory model involving controllable backorder rate and variable lead time demand with the mixtures of distribution

In the model of Ouyang and Chuang [Comput. Ind. Eng. 40 (2001) 339], they assume that the backorder rate is dependent on the length of lead time through the amount of shortages and let the backorder rate is a control variable. But, since they only assumed a single distribution for the lead time demand, when the demand of the different customers are not identical in the lead time, then we cannot use a single distribution (such as [Comput. Ind. Eng. 40 (2001) 339]) to describe the demand of the lead time. Hence, in our studies, we first assume that the lead time demand follows a mixtures of normal distribution, and then we relax the assumption about the form of the mixtures of distribution functions of the lead time demand and apply the minimax distribution free procedure to solve the problem. We develop an algorithm procedure, respectively, to find the optimal order quantity and the optimal lead time. Furthermore, two numerical examples are also given to illustrate the results.

Computational algorithmic procedure for optimal inventory policy involving ordering cost reduction and back-order discounts when lead time demand is controllable

Abstract In many practical situations, the ordering cost can be reduced by capital investment and the back-order rate is dependent on the amount of shortages and back-order price discounts. Hence, in this paper, we consider an inventory model with random yield in which the ordering cost can be reduced through capital investment, lead time can be shortened at an extra crashing cost and allow the back-order rate as a control variable to widen applications of Wu and Tsai’s [J.W. Wu, H.Y. Tsai, Mixture inventory model with back-orders and lost sales for variable lead time demand with the mixtures of normal distribution, International Journal of Systems Science 32 (2001) 259–268] model. Moreover, we also consider the back-order rate that proposed by combining Ouyang and Chuang [L.Y. Ouyang, B.R. Chuang, Mixture inventory model involving variable lead time and controllable backorder rate, Computers & Industrial Engineering 40 (2001) 339–348] (or Lee [W.C. Lee, Inventory model involving controllable backorder rate and variable lead time demand with the mixtures of distribution, Applied Mathematics and Computation 160 (2005) 701–717]) with Pan and Hsiao [J.C.-H. Pan, Y.C. Hsiao, Inventory models with back-order discounts and variable lead time, International Journal of Systems Science 32 (2001) 925–929; J.C.-H. Pan, Y.C. Hsiao, Integrated inventory models with controllable lead time and backorder discount considerations, International Journal of Production Economics 93–94 (2005) 387–397] (also see Pan et al. [J.C.-H. Pan, M.C. Lo, Y.C. Hsiao, Optimal reorder point inventory models with variable lead time and backorder discount considerations, European Journal of Operational Research 158 (2004) 488–505]) to present a new general form. The objective is to simultaneously optimize the order quantity, ordering cost, back-order discount and lead time. In addition, we also develop an algorithmic procedure and use the computer software Compaq Visual Fortran V6.0 (inclusive of IMSL) to find the optimal inventory policy. Finally, a numerical example is also given to illustrate the results.

Computational algorithmic procedure of optimal inventory policy involving a negative exponential crashing cost and variable lead time demand

Abstract When the demand of the different customers are not identical in the lead time, we cannot use only a single distribution (such as Ouyang et al. (1996) [L.Y. Ouyang, N.C. Yeh, K.S. Wu, Mixture inventory model with backorders and lost sales for variable lead time, Journal of the Operational Research Society 47 (1996) 829–832] using normal distribution) to describe the demand of the lead time. Hence, in this paper, we extend the models of Ouyang et al. (1996) and Ouyang and Wu (1998) [L.Y. Ouyang, K.S. Wu, A minimax distribution free procedure for mixed inventory model with variable lead time, International Journal of Production Economics 56–57 (1998) 511–516] by considering the mixture of normal distributions and the mixture of free distributions (see Everitt and Hand (1981) [B.S. Everitt, D.J. Hand, Finite Mixture Distribution, Chapman and Hall, London, NY, 1981]), respectively. Moreover, we quote the continuous model which the total crashing cost is related to the lead time by a negative exponential function (such as Ben-Daya and Raouf (1994) [M. Ben-Daya, A. Raouf, Inventory models involving lead time as decision variable, Journal of the Operational Research Society 45 (1994) 579–582]). Finally, we give two algorithmic procedures to find the optimal inventory policy and two numerical examples to illustrate the results.

Original article: Computational procedure of assessing lifetime performance index of Weibull lifetime products with the upper record values

Process capability indices (PCIs) are used to measure process potential and performance. This study constructs an uniformly minimum variance unbiased estimator (UMVUE) of the lifetime performance index based on the upper record values for Weibull lifetime model. Then the UMVUE of the lifetime performance index is utilized to develop the new hypothesis testing procedure in the condition of known lower specification limit. Finally, two examples are presented to assess the behavior of this test statistic for testing null hypothesis under given significance level. Moreover, the product managers can then employ the new testing procedure to determine whether the process adheres to the required level.

Computational comparison for weighted moments estimators and BLUE of the scale parameter of a Pareto distribution with known shape parameter under type II multiply censored sample

In this paper, we propose the weighted moments estimators (WMEs) of the scale parameter of a Pareto distribution with known shape parameter under the type II multiply censored sample. Moreover, we give a computational comparison for these proposed WMEs and best linear unbiased estimator (BLUE) of the scale parameter on the basis of the exact mean squared error (MSE) for given sample sizes and different censoring schemes. Further, we also obtain the best estimator among the WMEs and BLUE.

Computational procedure of optimal inventory model involving controllable backorder rate and variable lead time with defective units

This article considers that the number of defective units in an arrival order is a binominal random variable. We derive a modified mixture inventory model with backorders and lost sales, in which the order quantity and lead time are decision variables. In our studies, we also assume that the backorder rate is dependent on the length of lead time through the amount of shortages and let the backorder rate be a control variable. In addition, we assume that the lead time demand follows a mixture of normal distributions, and then relax the assumption about the form of the mixture of distribution functions of the lead time demand and apply the minimax distribution free procedure to solve the problem. Furthermore, we develop an algorithm procedure to obtain the optimal ordering strategy for each case. Finally, three numerical examples are also given to illustrate the results.

Computational comparison of prediction future lifetime of electronic components with Pareto distribution based on multiply type II censored samples

Abstract We propose the weighted moments estimators (WMEs) of scale parameter σ of Pareto distribution with known shape parameter based on multiply type II censored sample of electronic components Y(r+1)

Computational procedure of lifetime performance index of products for the Burr XII distribution with upper record values

Process capability analysis has been widely applied in the field of quality control to monitor the performance of industrial processes. In practice, lifetime performance index (or the larger-the-better process capability indices (PCIs)) C L is a popular means to assess the performance and potential of their processes, where L is the lower specification limit. Moreover, record values often arise in industrial stress testing, meteorological analysis, hydrology, seismology, athletic events, and other similar situations. In this study, a two-stage maximum likelihood estimation applied to estimate lifetime performance index C L of non-normal processes. Further, this study will apply data transformation technology to construct a maximum likelihood estimator (MLE) of C L under the Burr XII distribution with the upper record values. The MLE of C L is then utilized to develop a hypothesis testing procedure in the condition of known L. Finally, we give simulation study and two examples to illustrate the use of the testing procedure under given significance level α .

Computational comparison of the prediction intervals of future observation for three-parameter Pareto distribution with known shape parameter

Abstract We propose the weighted moments estimators (WMEs) of the location and scale parameters of Pareto distribution with known shape parameter under the multiply type II censored sample Y ( r + 1 ) ⋯ Y ( r + k ) Y ( r + k + l + 1 ) ⋯ Y ( n - s ) . Hence, we use these WMEs and best linear unbiased estimator (BLUE) of scale parameter to find pivotal quantities and obtain the prediction intervals of the jth future observation ( Y ( j ) , n - s j ⩽ n ) based on the above censored sample. Finally, we give the Monte Carlo simulation to assess the computational comparison of these pivotal quantities for establishing prediction intervals of the jth future observation ( Y ( j ) , n - s j ⩽ n ) .