Optimal Production Control in Stochastic Manufacturing Systems with Degenerate Demand

2011 ◽  
Vol 1 (1) ◽  
pp. 89-96 ◽  
Author(s):  
Azizul Baten ◽  
Anton Abdulbasah Kamil
Keyword(s):  
Control Problem ◽  
Manufacturing Systems ◽  
Production Control ◽  
Hjb Equation ◽  
Dynamic Programming Principle ◽  
Inventory Problem ◽  
Production Inventory ◽  
Production Cost Control ◽  
Inventory Control Problem ◽  
Ito's Lemma

AbstractThe paper studies the production inventory problem of minimizing the expected discounted present value of production cost control in manufacturing systems with degenerate stochastic demand. We have developed the optimal inventory production control problem by deriving the dynamics of the inventory-demand ratio that evolves according to a stochastic neoclassical differential equation through Ito's Lemma. We have also established the Riccati based solution of the reduced (one- dimensional) HJB equation corresponding to production inventory control problem through the technique of dynamic programming principle. Finally, the optimal control is shown to exist from the optimality conditions in the HJB equation.

scholarly journals Some Results on Bellman Equations of Optimal Production Control in a Stochastic Manufacturing System

2009 ◽  
Vol 2009 ◽  
pp. 1-23
Author(s):  
Azizul Baten ◽  
Anton Abdulbasah Kamil
Keyword(s):  
Production Cost ◽  
Manufacturing System ◽  
Production Control ◽  
Inventory Problem ◽  
Present Value ◽  
Hjb Equations ◽  
Bellman Equations ◽  
Production Inventory ◽  
Production Cost Control ◽  
Hamilton Jacobi Bellman

The paper studies the production inventory problem of minimizing the expected discounted present value of production cost control in a manufacturing system with degenerate stochastic demand. We establish the existence of a unique solution of the Hamilton-Jacobi-Bellman (HJB) equations associated with this problem. The optimal control is given by a solution to the corresponding HJB equation.

MINIMUM AVERAGE COST PRODUCTION PLANNING IN STOCHASTIC MANUFACTURING SYSTEMS

1998 ◽  
Vol 08 (07) ◽  
pp. 1251-1276 ◽  
Author(s):  
SURESH P. SETHI ◽  
HANQIN ZHANG ◽  
QING ZHANG
Keyword(s):  
Control Problem ◽  
Production Planning ◽  
Average Cost ◽  
Production Cost ◽  
Manufacturing Systems ◽  
Production Control ◽  
Production Capacity ◽  
Production Rates ◽  
Planning Problems

Recently, the production control problem in stochastic manufacturing systems has generated a great deal of interest. The goal is to obtain production rates to minimize total expected surplus and production cost. This paper reviews the research devoted to minimum average cost production planning problems in stochastic manufacturing systems. Manufacturing systems involve a single or parallel failure-prone machines producing a number of different products, random production capacity, and constant demands.

scholarly journals Queue Length Forecasting in Complex Manufacturing Job Shops

Forecasting ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 322-338
Author(s):  
Marvin Carl May ◽  
Alexander Albers ◽  
Marc David Fischer ◽  
Florian Mayerhofer ◽  
Louis Schäfer ◽  
...  
Keyword(s):  
Operations Management ◽  
Queue Length ◽  
Manufacturing Systems ◽  
Production Control ◽  
Data Sets ◽  
Job Shops ◽  
Static Data ◽  
Queue Lengths ◽  
Operational Excellence

Currently, manufacturing is characterized by increasing complexity both on the technical and organizational levels. Thus, more complex and intelligent production control methods are developed in order to remain competitive and achieve operational excellence. Operations management described early on the influence among target metrics, such as queuing times, queue length, and production speed. However, accurate predictions of queue lengths have long been overlooked as a means to better understanding manufacturing systems. In order to provide queue length forecasts, this paper introduced a methodology to identify queue lengths in retrospect based on transitional data, as well as a comparison of easy-to-deploy machine learning-based queue forecasting models. Forecasting, based on static data sets, as well as time series models can be shown to be successfully applied in an exemplary semiconductor case study. The main findings concluded that accurate queue length prediction, even with minimal available data, is feasible by applying a variety of techniques, which can enable further research and predictions.

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.

NUMERICAL APPROACH TO AN OPTIMAL MULTI-ITEM IMPERFECT PRODUCTION CONTROL PROBLEM IN UNCERTAIN ENVIRONMENT

2014 ◽  
Vol 22 (01) ◽  
pp. 125-144
Author(s):  
DIPAK KUMAR JANA ◽  
K. MAITY ◽  
M. MAITI
Keyword(s):  
General Model ◽  
Production Control ◽  
Measure Theory ◽  
Control Variable ◽  
Uncertain Variable ◽  
Production Costs ◽  
Uncertain Measure ◽  
Fuzzy Variables ◽  
Imperfect Production ◽  
Production Inventory

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.

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