Optimal Production Planning in Stochastic Jobshops with Long-Run Average Cost

Optimization, Dynamics, and Economic Analysis, Essays in Honor of Gustav Feichtinger, E.J. Dockner, R.F. Hartl, M. Luptačik, and G. Sorger (Eds.), Physica-Verlag, Heidelberg, 2000, 259-274

16 Pages Posted: 6 May 2020

See all articles by Ernst Presman

Ernst Presman

Russian Academy of Sciences (RAS)

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Hanqin Zhang

Institute of Applied Mathematics Academia Sinica

Date Written: 2000

Abstract

We consider a production planning problem for a general jobshop producing a number of products and subject to breakdown and repair of machines. The machine capacities are modeled as Markov chains. The objective is to choose the rates of production of the final products and intermediate parts on the various machines over time in order to meet the demand for the system’s production at the minimum long-run average cost of production and surplus. The problem is formulated as a stochastic dynamic program. We prove a verification theorem and derive the optimal feedback control policy in terms of the directional derivatives of the so-called potential function. Finally, we construct a potential function in the special case of a jobshop producing only one final product.

Keywords: Optimal Production, Stochastic Jobshop

JEL Classification: C61, M11, M20

Suggested Citation

Presman, Ernst and Sethi, Suresh and Zhang, Hanqin, Optimal Production Planning in Stochastic Jobshops with Long-Run Average Cost (2000). Optimization, Dynamics, and Economic Analysis, Essays in Honor of Gustav Feichtinger, E.J. Dockner, R.F. Hartl, M. Luptačik, and G. Sorger (Eds.), Physica-Verlag, Heidelberg, 2000, 259-274, Available at SSRN: https://ssrn.com/abstract=3590555

Ernst Presman

Russian Academy of Sciences (RAS) ( email )

Leninsky Ave, 14
Moscow, 119991
Russia

Suresh Sethi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

Hanqin Zhang

Institute of Applied Mathematics Academia Sinica ( email )

Beijing, 100080
China

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