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

Haiying Liu; Wenjie Bi; Kok Lay Teo; Naxing Liu

doi:10.3934/jimo.2018050

Article Contents

2019, Volume 15, Issue 2: 445-464. Doi: 10.3934/jimo.2018050

This issue Previous Article A potential reduction method for tensor complementarity problems Next Article Higher-order weak radial epiderivatives and non-convex set-valued optimization problems

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

Received: June 2017

Revised: January 2018

Early access: April 2018

Published: January 2019

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.

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Abstract

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.

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Mathematics Subject Classification: Primary: 1201; Secondary: 120100.

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Figure 1. Production inventory system

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Figure 2. Attention function

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Figure 3. Truncation function

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Figure 4. The influence of ${\hat p_1}$ on $\lambda$

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Figure 5. The influence of ${\hat p_2}$ on $\lambda$

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Figure 6. The influence of ${\hat \theta _1}$ on $\lambda$

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Figure 7. The influence of ${\hat p_1}$ on $q$

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Figure 8. The influence of ${\hat p_2}$ on $q$

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Figure 9. The influence of ${\hat \theta _1}$ on $q$

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Figure 10. The influence of ${\hat \theta _2}$ on $q$

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Figure 11. The influence of ${\hat p_1}$ on $s$

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Figure 12. The influence of ${\hat p_2}$ on $s$

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Figure 13. The influence of ${\hat \theta _2}$ on $s$

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