Forecast horizon of dynamic lot size model for perishable inventory with minimum order quantities

Fuying Jing; Zirui Lan; Yang Pan

doi:10.3934/jimo.2019010

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2020, Volume 16, Issue 3: 1435-1456. Doi: 10.3934/jimo.2019010

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Forecast horizon of dynamic lot size model for perishable inventory with minimum order quantities

1.
University of Electronic Science and Technology of China, Chengdu 611731, China
2.
School of Economic and Management, Tianjin University of Science and Technology, Tianjin 300222, China

^* Corresponding author: Zirui Lan
^* Corresponding author: Zirui Lan

Received: February 28, 2018

Revised: August 31, 2018

Early access: March 2019

Published: March 2020

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Abstract

We consider the dynamic lot size problem for perishable inventory under minimum order quantities. The stock deterioration rates and inventory costs depend on both the age of the stocks and their periods of order. Based on two structural properties of the optimal solution, we develop a dynamic programming algorithm to solve the problem without backlogging. We also extend the model by considering backlogging. By establishing the regeneration set, we give a sufficient condition for obtaining forecast horizon under without and with backlogging. Finally, based on a detailed test bed of instance, we obtain useful managerial insights on the impact of minimum order quantities and perishability of product and the costs on the length of forecast horizon.

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Mathematics Subject Classification: Primary: 90C39, 90C90; secondary: 90B05.

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Figure 1. Median forecast horizon as a function of minimum order quantities

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Figure 2. Median forecast horizon as a function of lifetime

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Figure 3. Median forecast horizon as a function of backlogging cost

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Figure 4. Median forecast horizon as a function of inventory holding cost

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Table 1. Summary of Computations of Example 1

$ t $	$ 1 $	$ 2 $	$ 3 $	$ 4 $	$ 5 $	$ 6 $	$ 7 $
$ d_t $	$ 6 $	$ 8 $	$ 9 $	$ 12 $	$ 11 $	$ 7 $	$ 26 $
$ x_t^\ast $	$ 25 $
$ x_t^\ast $	$ 25 $	$ 0 $
$ x_t^\ast $	$ 25 $	$ 0 $	$ 0 $
$ x_t^\ast $	$ 35 $	$ 0 $	$ 0 $	$ 0 $
$ x_t^\ast $	$ 25 $	$ 0 $	$ 0 $	$ 25 $	$ 0 $
$ x_t^\ast $	$ 25 $	$ 0 $	$ 0 $	$ 32 $	$ 0 $	$ 0 $
$ x_t^\ast $	$ 25 $	$ 0 $	$ 0 $	$ 32 $	$ 0 $	$ 0 $	$ 26 $
$ C(t) $	$ 263 $	$ 285 $	$ 289 $	$ 399 $	$ 544 $	$ 607 $	$ 837 $

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