Optimal production and pricing strategies in a dynamic model of monopolistic firm

被引:2
|
作者
Rokhlin, Dmitry B. [1 ]
Mironenko, Georgii [1 ]
机构
[1] Southern Fed Univ, Inst Math Mech & Comp Sci, Milchakova Str 8a, Rostov Na Donu 344090, Russia
关键词
Production; Pricing; Inventory; State constraints; Constrained viscosity solution; Non-convex production cost;
D O I
10.1007/s13160-016-0235-7
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider a deterministic continuous time model of monopolistic firm, which chooses production and pricing strategies of a single good. Firm's goal is to maximize the discounted profit over infinite time horizon. The no-backlogging assumption induces the state constraint on the inventory level. The revenue and production cost functions are assumed to be continuous but, in general, we do not impose the concavity/convexity property. Using the results from the theory of viscosity solutions and Young-Fenchel duality, we derive a representation for the value function, study its regularity properties, and give a complete description of optimal strategies for this non-convex optimal control problem. In agreement with the results of Chazal et al. (Nonlinear Anal. Theor. 54(8):1365-1395, 2003), it is optimal to liquidate initial inventory in finite time and then use an optimal static strategy. We give a condition, allowing to distinguish if this strategy can be represented by an ordinary or relaxed control. General theory is illustrated by the example of a non-convex production cost, proposed by Arvan and Moses (University of Illinois at Urbana-Champaign, Working paper No. 756, 1981, p.31).
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页码:557 / 582
页数:26
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