Base stock list price policy in continuous time

Alain Bensoussan; Sonny Skaaning

doi:10.3934/dcdsb.2017001

Article Contents

2017, Volume 22, Issue 1: 1-28. Doi: 10.3934/dcdsb.2017001

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Base stock list price policy in continuous time

Alain Bensoussan^, and
Sonny Skaaning

International Center for Decision and Risk Analysis, Jindal School of Management, University of Texas -Dallas, Richardson, TX 75080-5298, USA

* Corresponding author: Alain Bensoussan
* Corresponding author: Alain Bensoussan

Received: December 31, 2015

Revised: May 31, 2016

Published: November 2017

Alain Bensoussan is also with the department of Systems Engineeringand Engineering Management, the City University of Hong Kong :Research supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region (City U 500111)

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Abstract

We study the problem of inventory control, with simultaneous pricing optimization in continuous time. For the classical inventory control problem in continuous time, see [5], as a recent reference. We incorporate pricing decisions together with inventory decisions. We consider the situation without fixed cost for an infinite horizon. Without pricing, under very natural assumptions, the optimal ordering policy is given by a Base stock, which we review briefly. With pricing, the natural generalization is the so called "Base Stock list price" (BSLP) term coined by E. Porteus, see [36], and was shown in discrete time by A. Federgruen and A. Herching to be the optimal strategy, see [14]. We extend the concept to continuous time which not only complicates the dynamics of the problem, which has never been considered before.

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Mathematics Subject Classification: Primary:58F15, 58F17;Secondary:53C35.

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Figure 1. Finding the value of $S$

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Figure 2. $H_\epsilon$ with value of $S_\epsilon$ for $b=20$

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Figure 3. $H_\epsilon$ with value of $S_\epsilon$ for $b=30$

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Figure 4. $H_\epsilon$ with value of $S_\epsilon$ for $b=100$

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Figure 5. $H_\epsilon$ with value of $S_\epsilon$ for $b=250$

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Figure 6. $H_\epsilon(x)$ for decreasing epsilon

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Figure 7. $H_S(x)$ with value $S$ for $b=30$

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Figure 8. Price depending on Inventory Level

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