# American Institute of Mathematical Sciences

April  2019, 15(2): 445-464. doi: 10.3934/jimo.2018050

## Dynamic optimal decision making for manufacturers with limited attention based on sparse dynamic programming

 1 School of Accountancy, Hunan University of Finance and Economics, Changsha 410205, China 2 Business School, Central South University, Changsha 410083, China 3 Department of Mathematics and Statistics, Curtin University, Australia

* Corresponding author: beenjoy@126.com (Wenjie Bi)

Received  June 2017 Revised  January 2018 Published  April 2018

Fund Project: This work is supported by National Natural Science Foundation of China, NO.91646115, 71371191, 71790615 71631008, and Natural Science Foundation of Hunan Province, NO.2018JJ3012.

In a fully competitive industry, the market demand is changing rapidly. Thus, it is important for manufacturers to manage their inventory effectively as well as to determine the best order quantity and optimal production strategy. In this paper, our concern is how shall a manufacturer with limited attention determine his optimal order quantity and optimal production strategy in an environment when many factors are volatile, such as the price of raw materials (respectively, finished goods) and attrition rate of inventory of raw materials (respectively, finished product). Under this environment, it is observed, according to various empirical studies, that decision makers tend to focus their attention on factors with major changes. Taking all these into account, our problem is formulated as a discrete-time stochastic dynamic programming. We propose a general approach based on the sparse dynamic programming method to solve this multidimensional dynamic programming problem. From the numerical examples solved using the proposed method, it is interesting to observe that decision makers with limited attention do not adjust their final decision when the volatility is small.

Citation: Haiying Liu, Wenjie Bi, Kok Lay Teo, Naxing Liu. Dynamic optimal decision making for manufacturers with limited attention based on sparse dynamic programming. Journal of Industrial & Management Optimization, 2019, 15 (2) : 445-464. doi: 10.3934/jimo.2018050
##### References:

show all references

##### References:
Production inventory system
Attention function
Truncation function
The influence of ${\hat p_1}$ on $\lambda$
The influence of ${\hat p_2}$ on $\lambda$
The influence of ${\hat \theta _1}$ on $\lambda$
The influence of ${\hat p_1}$ on $q$
The influence of ${\hat p_2}$ on $q$
The influence of ${\hat \theta _1}$ on $q$
The influence of ${\hat \theta _2}$ on $q$
The influence of ${\hat p_1}$ on $s$
The influence of ${\hat p_2}$ on $s$
The influence of ${\hat \theta _2}$ on $s$
 [1] Andrzej Nowakowski, Jan Sokolowski. On dual dynamic programming in shape control. Communications on Pure & Applied Analysis, 2012, 11 (6) : 2473-2485. doi: 10.3934/cpaa.2012.11.2473 [2] Jérôme Renault. General limit value in dynamic programming. Journal of Dynamics & Games, 2014, 1 (3) : 471-484. doi: 10.3934/jdg.2014.1.471 [3] Oliver Junge, Alex Schreiber. Dynamic programming using radial basis functions. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 4439-4453. doi: 10.3934/dcds.2015.35.4439 [4] Eduardo Espinosa-Avila, Pablo Padilla Longoria, Francisco Hernández-Quiroz. Game theory and dynamic programming in alternate games. Journal of Dynamics & Games, 2017, 4 (3) : 205-216. doi: 10.3934/jdg.2017013 [5] Rein Luus. Optimal control of oscillatory systems by iterative dynamic programming. Journal of Industrial & Management Optimization, 2008, 4 (1) : 1-15. doi: 10.3934/jimo.2008.4.1 [6] Qing Liu, Armin Schikorra. General existence of solutions to dynamic programming equations. Communications on Pure & Applied Analysis, 2015, 14 (1) : 167-184. doi: 10.3934/cpaa.2015.14.167 [7] Xianchao Xiu, Lingchen Kong. Rank-one and sparse matrix decomposition for dynamic MRI. Numerical Algebra, Control & Optimization, 2015, 5 (2) : 127-134. doi: 10.3934/naco.2015.5.127 [8] Shi'an Wang, N. U. Ahmed. Optimum management of the network of city bus routes based on a stochastic dynamic model. Journal of Industrial & Management Optimization, 2019, 15 (2) : 619-631. doi: 10.3934/jimo.2018061 [9] Ryan Loxton, Qun Lin. Optimal fleet composition via dynamic programming and golden section search. Journal of Industrial & Management Optimization, 2011, 7 (4) : 875-890. doi: 10.3934/jimo.2011.7.875 [10] Tengfei Yan, Qunying Liu, Bowen Dou, Qing Li, Bowen Li. An adaptive dynamic programming method for torque ripple minimization of PMSM. Journal of Industrial & Management Optimization, 2017, 13 (5) : 0-0. doi: 10.3934/jimo.2019136 [11] Amin Aalaei, Hamid Davoudpour. Two bounds for integrating the virtual dynamic cellular manufacturing problem into supply chain management. Journal of Industrial & Management Optimization, 2016, 12 (3) : 907-930. doi: 10.3934/jimo.2016.12.907 [12] Bruce D. Craven, Sardar M. N. Islam. Dynamic optimization models in finance: Some extensions to the framework, models, and computation. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1129-1146. doi: 10.3934/jimo.2014.10.1129 [13] Fuying Jing, Zirui Lan, Yang Pan. Forecast horizon of dynamic lot size model for perishable inventory with minimum order quantities. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-22. doi: 10.3934/jimo.2019010 [14] Matthew H. Henry, Yacov Y. Haimes. Robust multiobjective dynamic programming: Minimax envelopes for efficient decisionmaking under scenario uncertainty. Journal of Industrial & Management Optimization, 2009, 5 (4) : 791-824. doi: 10.3934/jimo.2009.5.791 [15] Martino Bardi, Shigeaki Koike, Pierpaolo Soravia. Pursuit-evasion games with state constraints: dynamic programming and discrete-time approximations. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 361-380. doi: 10.3934/dcds.2000.6.361 [16] Silvia Faggian. Boundary control problems with convex cost and dynamic programming in infinite dimension part II: Existence for HJB. Discrete & Continuous Dynamical Systems - A, 2005, 12 (2) : 323-346. doi: 10.3934/dcds.2005.12.323 [17] Guy Barles, Ariela Briani, Emmanuel Trélat. Value function for regional control problems via dynamic programming and Pontryagin maximum principle. Mathematical Control & Related Fields, 2018, 8 (3&4) : 509-533. doi: 10.3934/mcrf.2018021 [18] Haibo Jin, Long Hai, Xiaoliang Tang. An optimal maintenance strategy for multi-state systems based on a system linear integral equation and dynamic programming. Journal of Industrial & Management Optimization, 2020, 16 (2) : 965-990. doi: 10.3934/jimo.2018188 [19] Yeong-Cheng Liou, Siegfried Schaible, Jen-Chih Yao. Supply chain inventory management via a Stackelberg equilibrium. Journal of Industrial & Management Optimization, 2006, 2 (1) : 81-94. doi: 10.3934/jimo.2006.2.81 [20] Jian-Wu Xue, Xiao-Kun Xu, Feng Zhang. Big data dynamic compressive sensing system architecture and optimization algorithm for internet of things. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1401-1414. doi: 10.3934/dcdss.2015.8.1401

2018 Impact Factor: 1.025

## Tools

Article outline

Figures and Tables