scholarly journals A JUMP-FLUID PRODUCTION–INVENTORY MODEL WITH A DOUBLE BAND CONTROL

2014 ◽  
Vol 28 (3) ◽  
pp. 313-333 ◽  
Author(s):  
Yonit Barron ◽  
David Perry ◽  
Wolfgang Stadje
Keyword(s):  
Phase Type Distribution ◽  
Time Intervals ◽  
Flow Models ◽  
Long Run ◽  
Average Criterion ◽  
Production Inventory ◽  
Fluid Production ◽  
Reflecting Boundaries ◽  
Inventory Control Model ◽  
Cost Functionals

We consider a production–inventory control model with two reflecting boundaries, representing the finite storage capacity and the finite maximum backlog. Demands arrive at the inventory according to a Poisson process, their i.i.d. sizes having a common phase-type distribution. The inventory is filled by a production process, which alternates between two prespecified production rates ρ1 and ρ2: as long as the content level is positive, ρ1 is applied while the production follows ρ2 during time intervals of backlog (i.e., negative content). We derive in closed form the various cost functionals of this model for the discounted case as well as under the long-run-average criterion. The analysis is based on a martingale of the Kella–Whitt type and results for fluid flow models due to Ahn and Ramaswami.

A Fluid EOQ Model with Markovian Environment

2015 ◽  
Vol 52 (02) ◽  
pp. 473-489
Author(s):  
Yonit Barron
Keyword(s):  
Continuous Time ◽  
Inventory Level ◽  
Continuous Time Markov Chain ◽  
Holding Costs ◽  
Eoq Model ◽  
Long Run ◽  
Average Criterion ◽  
Production Inventory ◽  
Finite State ◽  
Cost Functionals

We consider a production-inventory model operating in a stochastic environment that is modulated by a finite state continuous-time Markov chain. When the inventory level reaches zero, an order is placed from an external supplier. The costs (purchasing and holding costs) are modulated by the state at the order epoch time. Applying a matrix analytic approach, fluid flow techniques, and martingales, we develop methods to obtain explicit equations for these cost functionals in the discounted case and under the long-run average criterion. Finally, we extend the model to allow backlogging.

A Fluid EOQ Model with Markovian Environment

2015 ◽  
Vol 52 (02) ◽  
pp. 473-489 ◽  
Author(s):  
Yonit Barron
Keyword(s):  
Continuous Time ◽  
Inventory Level ◽  
Continuous Time Markov Chain ◽  
Holding Costs ◽  
Eoq Model ◽  
Long Run ◽  
Average Criterion ◽  
Production Inventory ◽  
Finite State ◽  
Cost Functionals

We consider a production-inventory model operating in a stochastic environment that is modulated by a finite state continuous-time Markov chain. When the inventory level reaches zero, an order is placed from an external supplier. The costs (purchasing and holding costs) are modulated by the state at the order epoch time. Applying a matrix analytic approach, fluid flow techniques, and martingales, we develop methods to obtain explicit equations for these cost functionals in the discounted case and under the long-run average criterion. Finally, we extend the model to allow backlogging.

scholarly journals A Fluid EOQ Model with Markovian Environment

2015 ◽  
Vol 52 (2) ◽  
pp. 473-489 ◽  
Author(s):  
Yonit Barron
Keyword(s):  
Continuous Time ◽  
Inventory Level ◽  
Continuous Time Markov Chain ◽  
Holding Costs ◽  
Eoq Model ◽  
Long Run ◽  
Average Criterion ◽  
Production Inventory ◽  
Finite State ◽  
Cost Functionals

We consider a production-inventory model operating in a stochastic environment that is modulated by a finite state continuous-time Markov chain. When the inventory level reaches zero, an order is placed from an external supplier. The costs (purchasing and holding costs) are modulated by the state at the order epoch time. Applying a matrix analytic approach, fluid flow techniques, and martingales, we develop methods to obtain explicit equations for these cost functionals in the discounted case and under the long-run average criterion. Finally, we extend the model to allow backlogging.

Intertemporal Choice with Continuity Constraints

2021 ◽  
Author(s):  
Marcus Pivato
Keyword(s):  
Linear Functional ◽  
Intertemporal Choice ◽  
Continuous Functions ◽  
Stieltjes Integral ◽  
Affine Transformations ◽  
Time Intervals ◽  
Long Run ◽  
Discounted Utility ◽  
Intertemporal Preferences ◽  
Open Time

We consider a model of intertemporal choice where time is a continuum, the set of instantaneous outcomes (e.g., consumption bundles) is a topological space, and intertemporal plans (e.g., consumption streams) must be continuous functions of time. We assume that the agent can form preferences over plans defined on open time intervals. We axiomatically characterize the intertemporal preferences that admit a representation via discounted utility integrals. In this representation, the utility function is continuous and unique up to positive affine transformations, and the discount structure is represented by a unique Riemann–Stieltjes integral plus a unique linear functional measuring the long-run asymptotic utility.

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.

Investigating rainfall trend over India using the wavelet technique

2015 ◽  
Vol 7 (2) ◽  
pp. 353-364 ◽  
Author(s):  
Ranjit Kumar Paul ◽  
P. S. Birthal
Keyword(s):  
Arid Zone ◽  
National Level ◽  
Rainfall Pattern ◽  
Rainfall Trend ◽  
Time Intervals ◽  
Climatic Zones ◽  
Long Run ◽  
Short Run ◽  
Semi Arid ◽  
Wavelet Technique

In this paper, using the wavelet technique we analysed rainfall behaviour in the country across different agro-climatic zones over a century. Findings indicate that at the national level there is no significant trend in rainfall in the long run, but there are pockets of change in the rainfall pattern. There was a significant increase in the rainfall in the arid zone, whereas in the humid, semi-arid tropics and semi-arid temperate zones the trend was downward but insignificant. The behaviour of rainfall was different during this period. Except in the arid zone, we find a similar trend in other zones – increasing initially, tapering off in the middle and then declining but with some difference in time intervals. In the arid zone, the behaviour of rainfall had been erratic. In the short run, the direction of change in trend remains the same as in the long run but the change is statistically significant.

scholarly journals Optimal Maintenance of a Production-inventory System With Continuous Repair Times and Idle Periods

2020 ◽  
Vol Volume 14 ◽  
Keyword(s):  
Preventive Maintenance ◽  
Average Cost ◽  
Inventory System ◽  
Control Limit ◽  
Raw Material ◽  
Production Unit ◽  
Numerical Examples ◽  
Long Run ◽  
Production Inventory ◽  
Production Inventory System

In this paper two similar models for the maintenance of a production-inventory system are considered. In both models, an input generating installation supplies a buffer with a raw material and a production unit pulls the raw material from the buffer. The installation in the first model and the production unit in the second model deteriorate stochastically over time and the problem of their optimal preventive maintenance is considered. In the first model, it is assumed that the installation, after the completion of its maintenance, remains idle until the buffer is evacuated, while in the second model, it is assumed that the production unit, after the completion of its maintenance, remains idle until the buffer is filled up. The preventive and corrective repair times of the installation in the first model and the preventive and corrective repair times of the production unit in the second model are continuous random variables with known probability density functions. Under a suitable cost structure, semi-Markov decision processes are considered for both models in order to find a policy that minimizes the long-run expected average cost per unit time. A great number of numerical examples provide strong evidence that, for each fixed buffer content, the average-cost optimal policy is of control-limit type in both models, i.e. it prescribes a preventive maintenance of the installation in the first model and a preventive maintenance of the production unit in the second model if and only if their degree of deterioration is greater than or equal to a critical level. Using the usual regenerative argument, the average cost of the optimal control-limit policy is computed exactly in both models. Four numerical examples are also presented in which the preventive and corrective repair times follow the Exponential, the Weibull, the Gamma and the Log-Normal distribution, respectively.

A martingale approach to the slow server problem

1991 ◽  
Vol 28 (2) ◽  
pp. 480-486 ◽  
Author(s):  
Richard H. Stockbridge
Keyword(s):  
Linear Programming ◽  
Queueing System ◽  
Direct Proof ◽  
Problem Analysis ◽  
Heterogeneous Servers ◽  
Martingale Approach ◽  
Long Run ◽  
Average Criterion ◽  
Server Problem ◽  
Markov Policy

A Markov queueing system having heterogeneous servers under a long-run average criterion is analyzed. A direct proof of the optimality of a stationary, Markov policy is given using martingale methods. Simultaneously, the problem is reduced to a linear programming problem. Analysis of the LP for a system having finite queueing length shows the optimal policy is not always of threshold type.

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