Title: An optimal inventory pricing and ordering strategy subject to demand dependent on stock level and price

Authors: A. Tsoularis

Addresses: Business Rose Bowl, Portland Gate, Leeds Metropolitan University, Leeds, LS1 3HB, UK

Abstract: This article considers the deterministic singular optimal control problem of profit maximisation for inventory replenished at a variable rate and depleted by demand which is assumed to vary with price and stock availability. Optimal policies for the product order rate and price are derived using the maximum principle. Several initial inventory regions are identified as potential inventory states for feasible profit optimisation. Bounds on the maximum price for maximising net profit or minimising loss are obtained. Numerical simulations accompanied by phase diagrams are performed to support the theoretical findings.

Keywords: optimal control; Hamiltonian; maximum principle; transversality condition; costate variable; bang-bang control; optimisation; inventory pricing; ordering strategy; dependent demand; stock levels; prices; inventory control; inventory management; profit maximisation; product order rate; numerical simulation; phase diagrams.

DOI: 10.1504/IJMOR.2015.071283

International Journal of Mathematics in Operational Research, 2015 Vol.7 No.5, pp.595 - 608

Received: 07 Nov 2013
Accepted: 14 Jun 2014
Published online: 19 Aug 2015 *

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