Continuous production/inventory model with analogy to certain queueing and dam models

1989 ◽  
Vol 21 (01) ◽  
pp. 123-141 ◽  
Author(s):  
David Perry ◽  
Benny Levikson
Keyword(s):  
Production Systems ◽  
Optimization Problems ◽  
Storage Systems ◽  
Continuous Production ◽  
Queueing Systems ◽  
Inventory Level ◽  
Model Optimization ◽  
Fixed Rate ◽  
Production Inventory ◽  
Finite Dam

We consider two storage/production systems in which items are produced continuously over time with fixed rate. In the first system items have infinite lifetime, while in the second system the lifetime of the items are finite and fixed. The inventory level distributions and other important functionals associated with these storage systems are derived. This derivation is accomplished by an analogy existing between the storage systems and certain queueing systems and a finite dam model. Optimization problems connected with these systems are also considered.

Continuous production/inventory model with analogy to certain queueing and dam models

1989 ◽  
Vol 21 (1) ◽  
pp. 123-141 ◽  
Author(s):  
David Perry ◽  
Benny Levikson
Keyword(s):  
Production Systems ◽  
Optimization Problems ◽  
Storage Systems ◽  
Continuous Production ◽  
Queueing Systems ◽  
Inventory Level ◽  
Model Optimization ◽  
Fixed Rate ◽  
Production Inventory ◽  
Finite Dam

We consider two storage/production systems in which items are produced continuously over time with fixed rate. In the first system items have infinite lifetime, while in the second system the lifetime of the items are finite and fixed. The inventory level distributions and other important functionals associated with these storage systems are derived. This derivation is accomplished by an analogy existing between the storage systems and certain queueing systems and a finite dam model. Optimization problems connected with these systems are also considered.

scholarly journals Production inventory policy under a discounted cash flow

2005 ◽  
Vol 15 (2) ◽  
pp. 289-300
Author(s):  
Chao-Ton Su ◽  
Cheng-Wang Lin
Keyword(s):  
Cash Flow ◽  
Production Scheduling ◽  
Production Systems ◽  
Simple Algorithm ◽  
Inventory Level ◽  
Discounted Cash Flow ◽  
Proposed Model ◽  
Production Inventory ◽  
Demand Rate ◽  
Holding Cost

This paper presents an extended production inventory model in which the production rate at any instant depends on the demand and the inventory level. The effects of the time value of money are incorporated into the model. The demand rate is a linear function of time for the scheduling period. The proposed model can assist managers in economically controlling production systems under the condition of considering a discounted cash flow. A simple algorithm computing the optimal production-scheduling period is developed. Several particular cases of the model are briefly discussed. Through numerical example, sensitive analyses are carried out to examine the effect of the parameters. Results show that the discount rate parameter and the inventory holding cost have a significant impact on the proposed model.

Approximations for the single-product production-inventory problem with compound Poisson demand and service-level constraints

1984 ◽  
Vol 16 (2) ◽  
pp. 378-401 ◽  
Author(s):  
A. G. De kok ◽  
H. C. Tijms ◽  
F. A. Van der Duyn Schouten
Keyword(s):  
Poisson Process ◽  
Compound Poisson Process ◽  
Service Level ◽  
Inventory Level ◽  
Inventory Problem ◽  
Single Product ◽  
Compound Poisson ◽  
Poisson Demand ◽  
Production Inventory ◽  
Random Fluctuations

We consider a production-inventory problem in which the production rate can be continuously controlled in order to cope with random fluctuations in the demand. The demand process for a single product is a compound Poisson process. Excess demand is backlogged. Two production rates are available and the inventory level is continuously controlled by a switch-over rule characterized by two critical numbers. In accordance with common practice, we consider service measures such as the average number of stockouts per unit time and the fraction of demand to be met directly from stock on hand. The purpose of the paper is to derive practically useful approximations for the switch-over levels of the control rule such that a pre-specified value of the service level is achieved.

Multi-objective particle swarm optimisation approach for production-inventory control systems

2018 ◽  
Vol 13 (4) ◽  
pp. 1037-1056 ◽  
Author(s):  
Huthaifa AL-Khazraji ◽  
Colin Cole ◽  
William Guo
Keyword(s):  
Control System ◽  
Control Systems ◽  
Inventory Control ◽  
Dynamic Performance ◽  
Particle Swarm ◽  
Particle Swarm Optimisation ◽  
Inventory Level ◽  
Content Type ◽  
Multi Objective ◽  
Production Inventory

Purpose This paper aims to optimise the dynamic performance of production–inventory control systems in terms of minimisation variance ratio between the order rate and the consumption, and minimisation the integral of absolute error between the actual and the target level of inventory by incorporating the Pareto optimality into particle swarm optimisation (PSO). Design/method/approach The production–inventory control system is modelled and optimised via control theory and simulations. The dynamics of a production–inventory control system are modelled through continuous time differential equations and Laplace transformations. The simulation design is conducted by using the state–space model of the system. The results of multi-objective particle swarm optimisation (MOPSO) are compared with published results obtained from weighted genetic algorithm (WGA) optimisation. Findings The results obtained from the MOPSO optimisation process ensure that the performance is systematically better than the WGA in terms of reducing the order variability (bullwhip effect) and improving the inventory responsiveness (customer service level) under the same operational conditions. Research limitations/implications This research is limited to optimising the dynamics of a single product, single-retailer single-manufacturer process with zero desired inventory level. Originality/value PSO is widely used and popular in many industrial applications. This research shows a unique application of PSO in optimising the dynamic performance of production–inventory control systems.

Fluctuations of random walk in R d and storage systems

1977 ◽  
Vol 9 (03) ◽  
pp. 566-587 ◽  
Author(s):  
Priscilla Greenwood ◽  
Moshe Shaked
Keyword(s):  
Random Walk ◽  
Unique Solution ◽  
Convex Cone ◽  
Storage Systems ◽  
Queueing Systems ◽  
Convolution Equation ◽  
Stopping Times ◽  
Multivariate Distributions ◽  
Explicit Formulas ◽  
And Storage

Two Wiener-Hopf type factorization identities for multivariate distributions are introduced. Properties of associated stopping times are derived. The structure that produces one factorization also provides the unique solution of the Wiener-Hopf convolution equation on a convex cone in R d . Some applications for multivariate storage and queueing systems are indicated. For a few cases explicit formulas are obtained for the transforms of the associated stopping times. A result of Kemperman is extended.

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.

Fluctuations of random walk in Rd and storage systems

1977 ◽  
Vol 9 (3) ◽  
pp. 566-587 ◽  
Author(s):  
Priscilla Greenwood ◽  
Moshe Shaked
Keyword(s):  
Random Walk ◽  
Unique Solution ◽  
Convex Cone ◽  
Storage Systems ◽  
Queueing Systems ◽  
Convolution Equation ◽  
Stopping Times ◽  
Multivariate Distributions ◽  
Explicit Formulas ◽  
And Storage

Two Wiener-Hopf type factorization identities for multivariate distributions are introduced. Properties of associated stopping times are derived. The structure that produces one factorization also provides the unique solution of the Wiener-Hopf convolution equation on a convex cone in Rd. Some applications for multivariate storage and queueing systems are indicated. For a few cases explicit formulas are obtained for the transforms of the associated stopping times. A result of Kemperman is extended.

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.

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