Information Technologies, Methods, and Techniques of Supply Chain Management by Wang John

Author:Wang, John...
Language: eng
Format: epub
Published: 2013-10-30T11:02:04.301000+00:00

Equation (9) is a first order price dynamics. By manipulating it into time domain price dynamics, Laplace domain price dynamics is obtained as follows

(10)

Equation (10) is formed by excluding in (9) and a step response (1/s), which represents demand variety, can be attached to (10) so that we have. This Laplace domain is finally converted to time domain price dynamics as follows

(11)

At a steady state, the price function can be simplified to be

The result of equation (10) is used by the supplier to set his selling price to retailers as the following relationship

(12)

By combining (6) and (12) then we have

(13)

(14)

Equation (14) describes a strong relationship among product substitutability (γ), retailer´s quantity and supplier price setting. We can see that supplier price is a concave function of product substitutability (γ).

Model Description for Production Postponement

Consider a Bertrand duopoly model with price function (see Gibbon, 2002; Kristianto & Helo, 2009) for retailers given by

(15)

Whereandis price of product 1 and 2.

In the Bertrand game firms choose their own price to maximize their profit by taking their opponent’s price as a given. We thus propose a methodology which is similar to the previous Cournot game, except that we take into account the quantity at infinite time in order to optimize the postponed decision resulting from the presence of long term price contract

This game decides the equilibrium price first before capacity and it can be described as follows:

Figure 2 is taken from waterflow analogy. Inflow describes a steady price state and it is assumed to be constant. The managerial price related decision is located at the output and it is assumed to be dynamic. Quantity automatically follows, whatever the price pattern, as the water level is also controlled by its flow in a storage tank. These two situations are identical to one another.

Figure 2. Dynamic quantity postponement

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