Abstract
We propose a nonsmooth dynamic system integrating production and inventory where the items may deteriorate and the demand is stock-dependent. We aim to derive the optimal production rate. In our first model, backorders are not allowed, while in the second model they are. Using optimal control, necessary optimality conditions are obtained for general forms of the cost, demand, and deterioration rates and closed form solutions are derived for specific forms of these rates. Numerical simulations are presented and sensitivity of the solutions are examined.
Highlights
To take in consideration the nature of the dynamic behavior of inventory–production systems, many authors have successfully used control theory techniques
Zhang et al [4] studied the scheduling problem of a marketing production system where the demand depended on the status of the market
The deterioration rate depends, in a general way, on time and inventory level. We extend this first one to a more general model where backorders are allowed and the shortage is given in terms of on-hand stock
Summary
To take in consideration the nature of the dynamic behavior of inventory–production systems, many authors have successfully used control theory techniques. Khmelnitsky and Gerchak, in [5], were interested in the solution, using optimal control theory of a production system with state-dependent demand. Production cost) taken to be nonlinear functionals of the inventory level The policy minimizes the total cost of the inventory and production for the first model. The mathematical complexity observed in [5] is due to the state variable which can be either positive or negative When it is positive, a holding cost is incurred and when it is negative, a shortage cost is incurred, rendering the objective function nonsmooth (nondifferentiable). A holding cost is incurred and when it is negative, a shortage cost is incurred, rendering the objective function nonsmooth (nondifferentiable) They use linear terms in their objective function.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
