Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration

Pervin, Magfura
Roy, Sankar Kumar
Weber, Gerhard Wilhelm
In this paper, a deterministic inventory control model with deterioration is developed. Here, the deterioration rate follows stochastic deterioration, especially Weibull distribution deterioration. A time-dependent demand approach is introduced to show the applicability of our proposed model and to be up-to-date with respect to time. The main purpose of the paper is to investigate the optimal retailer's replenishment decisions for deteriorating items including time-dependent demand for demonstrating more practical circumstances within economic-order quantity frameworks. Keeping in mind the criterion of modern era, we consider that the holding cost is totally dependent on time, and shortages are allowed for this model. Subject to the formulated model, we minimize the total inventory cost. The mathematical model is explored by numerical examples to validate the proposed model. A sensitivity analysis of the optimal solution with regard to important parameters is also carried out to elaborate the quality, e.g., stability, of our result and to possibly modify our model. The paper ends with a conclusion and an outlook to future studies.


Assessment Of Artificial Neural Network To Improve Hidden Markov Model For Financial Data
Aydoğan Kılıç, Dilek; Kestel, Sevtap Ayşe; Department of Financial Mathematics (2022-7-27)
The aim of this thesis is to eliminate the possible weaknesses of HMMs, which is a successful statistical model that is frequently used in time series modeling. Depending on the selection of the initial parameters of the HMMs, RNN is used as a solution to the failure to reach the global maximum, and it is aimed to benefit from the classification power of this method. The hybrid model, which is developed with this motivation, is built in a way that is suitable for use in non-categorical data, contrary to the...
Stochastic inventory modelling t
Özkan, Erhun; Serin, Yaşar Yasemin; Department of Industrial Engineering (2010)
In this master thesis study, new inventory control mechanisms are developed for the repairables in Nedtrain. There is a multi-item, multi echelon system with a continuous review and one for one replenishment policy and there are different demand supply options in each control mechanism. There is an aggregate mean waiting time constraint in each local warehouse and the objective is to minimize the total system cost. The base stock levels in each warehouse are determined with an approximation method. Then dif...
Optimal control of stochastic hybrid system with jumps: A numerical approximation
Temoçin, Büşra Zeynep; Weber, Gerhard Wilhelm (2014-03-15)
The generalized class of stochastic hybrid systems consists of models with regime changes including the occurrence of impulsive behavior. In this paper, the stochastic hybrid processes with jumps are approximated by locally consistent Markov decision processes that preserve local mean and covariance. We further apply a randomized switching policy for approximating the dynamics on the switching boundaries. To investigate the validity of the approximation, we study a stochastic optimal control problem. On the...
Uncertainty quantification of parameters in local volatility model via frequentist, bayesian and stochastic galerkin methods
Animoku, Abdulwahab; Uğur, Ömür; Department of Financial Mathematics (2018)
In this thesis, we investigate and implement advanced methods to quantify uncertain parameter(s) in Dupire local volatility equation. The advanced methods investigated are Bayesian and stochastic Galerkin methods. These advanced techniques implore different ideas in estimating the unknown parameters in PDEs. The Bayesian approach assumes the parameter is a random variable to be sampled from its posterior distribution. The posterior distribution of the parameter is constructed via “Bayes theorem of inverse p...
A two-echelon inventory model with stock-dependent demand and variable holding cost for deteriorating items
Pervin, Magfura; null, null; Kumar Roy, Sankar; Wilhelm Weber, Gerhard (American Institute of Mathematical Sciences (AIMS), 2017)
In this study, we develop an inventory model for deteriorating items with stock dependent demand rate. Shortages are allowed to this model and when stock on hand is zero, then the retailer offers a price discount to customers who are willing to back-order their demands. Here, the supplier as well as the retailer adopt the trade credit policy for their customers in order to promote the market competition. The retailer can earn revenue and interest after the customer pays for the amount of purchasing cost to ...
Citation Formats
M. Pervin, S. K. Roy, and G. W. Weber, “Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration,” ANNALS OF OPERATIONS RESEARCH, pp. 437–460, 2018, Accessed: 00, 2020. [Online]. Available: