scholarly journals Optimal control policy to production and inventory system with promotion effort dependent demand in segmented market

2020 ◽  
pp. 40-40
Author(s):  
Sunita Mehta ◽  
Kuldeep Chaudhary
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Control Policy ◽  
Control Problems ◽  
Demand Rate ◽  
Segmented Market ◽  
Production Strategy ◽  
Numeric Data ◽  
Promotion Effort ◽  
Dependent Demand

Increased competition in market leads to the interaction between marketing and production of a firm in segmented market. This paper considers the problem of finding an optimal promotion and production strategy, where the consumer demand rate depends on differentiated and mass promotion efforts. Differentiated promotions can reach each segment independently and mass promotion reaches it with a fixed segment-spectrum. Under reasonable conditions, two optimal control problems are formulated. The first one considers a single source inventory and multi-segmented demand problem. In the second, a multi-segmented inventory and demand problem is considered, where it is assumed that the firm chooses an inventory directed to each segment. The solution to both problems is obtained by using Pontryagin's maximum principle. Numerical examples are provided to illustrate the applicability of proposed models. The discretized version of the problem is formulated and solved on some numeric data.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

Sign in / Sign up

Export Citation Format

Share Document