Uncertain Variable

Author(s):  
Baoding Liu
Keyword(s):  
Author(s):  
DIPAK KUMAR JANA ◽  
K. MAITY ◽  
M. MAITI

In this paper, some multi-item imperfect production-inventory models without shortages for defective and deteriorating items with uncertain/imprecise holding and production costs and resource constraint have been formulated and solved for optimal production. Here, the rate of production is assumed to be a function of time and considered as a control variable. Also the demand is time dependent and known. Uncertain or imprecise space constraint is also considered. The uncertain and imprecise holding and production costs are represented by uncertain and fuzzy variables respectively. These are converted to crisp constraint/numbers using uncertain measure theory for uncertain variable and possibility/necessity measure for fuzzy variable. The multi-item production inventory model is formulated as a constrained single objective cost minimization problem with the help of global criteria method. The reduced problem is then solved using Kuhn-Tucker conditions and generalized reduced gradient(GRG-LINGO 10.0) technique. Form the general model, models for particular cases with different production and demand functions are derived. Models for a single item are also presented. The optimum results for different models are presented in both tabular and graphical forms. Sensitivity analysis of average cost for the general model with respect to the changes in holding and production costs are presented.


Author(s):  
Tang Zhangchun ◽  
Lu Zhenzhou ◽  
Pan Wang ◽  
Zhang Feng

Based on the entropy of the uncertain variable, a novel importance measure is proposed to identify the effect of the uncertain variables on the system, which is subjected to the combination of random variables and fuzzy variables. For the system with the mixture of random variables and fuzzy variables, the membership function of the failure probability can be obtained by the uncertainty propagation theory first. And then the effect of each input variable on the output response of the system can be evaluated by measuring the shift between entropies of two membership functions of the failure probability, obtained before and after the uncertainty elimination of the input variable. The intersecting effect of the multiple input variables can be calculated by the similar measure. The mathematical properties of the proposed global sensitivity indicators are investigated and proved in detail. A simple example is first employed to demonstrate the procedure of solving the proposed global sensitivity indicators and then the influential variables of four practical applications are identified by the proposed global sensitivity indicators.


2016 ◽  
Vol 8 (1) ◽  
pp. 62
Author(s):  
Atikah Aghdhi Pratiwi ◽  
Rosa Rilantiana

AbstractBasically, the purpose of a company is make a profit and enrich the owners of the company. This is manifested by development and achievement of good performance, both in financial and operational perspective. But in reality, not all of companies can achieve good performance. One of them is because exposure of risk. This could threaten achievement of the objectives and existence of the company. Therefore, companies need to have an idea related to possible condition and financial projection in future periods that are affected by risk. One of the possible method is Monte Carlo Simulation. Research will be conducted at PT. Phase Delta Control with historical data related to production/sales volume, cost of production and selling price. Historical data will be used as Monte Carlo Simulation with random numbers that describe probability of each risk variables describing reality. The main result is estimated profitability of PT. Phase Delta Control in given period. Profit estimation will be uncertain variable due to some uncertainty


2011 ◽  
Vol 50-51 ◽  
pp. 140-144
Author(s):  
Jian Jun Liu ◽  
Yu Fu Ning

Based on uncertainty theory, this paper proposes a method that constructs and analyzes fault tree. In this paper, it would be characterized as crisp number if fault rate of bottom event is obtained from reliable handbook, empirical data and so on; it would be characterized as uncertain variable if fault rate of bottom event has no statistical data but is obtained from expert's subjective judgment. The optimistic value of overall system’s top event is calculated by using uncertain simulation technology. Finally feasibility and validity of this method is confirmed by taking fault tree of internal combustion engine as example.


Kybernetes ◽  
2019 ◽  
Vol 49 (2) ◽  
pp. 601-626
Author(s):  
Chi Zhou ◽  
Geni Xu ◽  
Zhibing Liu

Purpose Internet referral services are a common form of online marketing operating activities. To incentivize infomediaries and improve referral performance, brand retailers typically apply the cost-per-click (CPC) or the cost-per-sale (CPS) payments. The purpose of this paper is to investigate the effect of referral services on the optimal contract with CPC or CPS payments. Design/methodology/approach This paper studies a mechanism design problem for internet referral services. To maximize the expected utility of the brand retailer, an uncertain contract model is established in which the brand retailer's assessment of the infomediary's referral service capability is characterized as an uncertain variable. Then equivalent models under CPC and CPS payments are presented to obtain the optimal solutions. Findings The results demonstrate that under CPC payments, as the referral service capability increases, the optimal sales volume is increasing, and the optimal transfer payment first shows a declining and then a rising trend. The brand retailer is less likely to raise the optimal transfer payment for the infomediary given a higher CPC revenue-sharing fee percentage, which is counterintuitive. Under CPS payments, the optimal sales volume and transfer payment are also increasing in the referral service capability. In addition, an increase in the click-through rate leads to the infomediary's incremental marginal utility. Originality/value The value of this research is its application of incentive contracts to the internet referral services considering CPC or CPS payments. The results of this research can serve as a guide for retailers and infomediaries in their decision-making around online retailing.


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