scholarly journals A Production-Inventory Control Model with a Mixture of Back-Orders and Lost-Sales

1978 ◽  
Vol 24 (10) ◽  
pp. 1078-1087 ◽  
Author(s):  
B. T. Doshi ◽  
F. A. van der Duyn Schouten ◽  
J. J. Talman
Keyword(s):  
Inventory Control ◽  
Control Model ◽  
Lost Sales ◽  
Production Inventory ◽  
Inventory Control Model

Asymptotic analysis for a production–inventory control model with renewal arrivals and exponential demands

1985 ◽  
Vol 22 (03) ◽  
pp. 653-667
Author(s):  
A. G. De kok
Keyword(s):  
Asymptotic Analysis ◽  
Inventory Control ◽  
Renewal Process ◽  
Control Model ◽  
Critical Number ◽  
Inventory Problem ◽  
Hitting Probabilities ◽  
Production Inventory ◽  
Inventory Control Model ◽  
Random Fluctuations

We consider a production–inventory problem in which the production rate can be dynamically adjusted to cope with random fluctuations in demand. Customers arrive according to a renewal process, and the customer's demand is assumed to be exponentially distributed. Excess demand is backlogged. The production is controlled by a two-critical-number rule that prescribes which one of the two possible production rates must be used. Tractable expressions are given for several services measures including the fraction of demand backlogged. The analysis is based on the results for hitting probabilities in random walks, where the jump distribution has an exponential right or left tail.

Use of “e” and “g” operators to a fuzzy production inventory control model for substitute items

2019 ◽  
Vol 53 (2) ◽  
pp. 473-486 ◽  
Author(s):  
Debnarayan Khatua ◽  
Anupam De ◽  
Kalipada Maity ◽  
Samarjit Kar
Keyword(s):  
Inventory Control ◽  
Differential System ◽  
Control Model ◽  
Graphical Form ◽  
Selling Price ◽  
Deterministic System ◽  
State Variables ◽  
Fuzzy Variables ◽  
Production Inventory ◽  
Inventory Control Model

In this paper, a fuzzy optimal control model for substitute items with stock and selling price dependent demand has been developed. Here the state variables (stocks) are assumed to be fuzzy variables. So the proposed dynamic control system can be represented as a fuzzy differential system which optimize the profit of the production inventory control model through Pontryagin’s maximum principle. The proposed fuzzy control problem has been transformed into an equivalent crisp differential system using “e” and “g” operators. The deterministic system is then solved by using Newton’s forward-backward method through MATLAB. Finally some numerical results are presented both in tabular and graphical form.

Asymptotic analysis for a production–inventory control model with renewal arrivals and exponential demands

1985 ◽  
Vol 22 (3) ◽  
pp. 653-667
Author(s):  
A. G. De kok
Keyword(s):  
Asymptotic Analysis ◽  
Inventory Control ◽  
Renewal Process ◽  
Control Model ◽  
Critical Number ◽  
Inventory Problem ◽  
Hitting Probabilities ◽  
Production Inventory ◽  
Inventory Control Model ◽  
Random Fluctuations

We consider a production–inventory problem in which the production rate can be dynamically adjusted to cope with random fluctuations in demand. Customers arrive according to a renewal process, and the customer's demand is assumed to be exponentially distributed. Excess demand is backlogged. The production is controlled by a two-critical-number rule that prescribes which one of the two possible production rates must be used. Tractable expressions are given for several services measures including the fraction of demand backlogged. The analysis is based on the results for hitting probabilities in random walks, where the jump distribution has an exponential right or left tail.

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