Dynamic-pricing models

L. M. A. Chan, D. Simchi-Levi, and J. L. Swann. Dynamic pricing models for manufacturing with stochastic demand and discretionary sales. Working Paper, 2002. 

For consequence analysis, we have developed a dynamic simulation model of the refinery SC, called Integrated Refinery In-Silico (IRIS) (Pitty et al., 2007). It is implemented in Matlab/Simulink (MathWorks, 1996). Four types of entities are incorporated in the model external SC entities (e.g. suppliers), refinery functional departments (e.g. procurement), refinery units (e.g. crude distillation), and refinery economics. Some of these entities, such as the refinery units, operate continuously while others embody discrete events such as arrival of a VLCC, delivery of products, etc. Both are considered here using a unified discrete-time model. The model explicitly considers the various SC activities such as crude oil supply and transportation, along with intra-refinery SC activities such as procurement planning, scheduling, and operations management. Stochastic variations in transportation, yields, prices, and operational problems are considered. The economics of the refinery SC includes consideration of different crude slates, product prices, operation costs, transportation, etc. The impact of any disruptions or risks such as demand uncertainties on the profit and customer satisfaction level of the refinery can be simulated through IRIS. 

The model presented in Figure 12.2 integrates the dynamic schema model developed by Price (2002) with the traditional Beckian model of stress (Beck 1987 Beck et al. 1985) outlined in Chapter 1 and Young s schema-focused model (Young et al. 2003) presented earlier in this chapter. The model places particular emphasis on the re-enactment of early maladaptive schemata (EMS) and behavioural coping strategies in the context of the workplace in the causation and maintenance of occupational stress. 

The dynamic programming modeling concepts presented in this chapter are iUustrated with an example, which is both a multiperiod extension of the single-period newsvendor problem of Section 2 as weU as an example of a dynamic pricing problem. 

In the HIM model, the processes for the bond price and the spot rate are not independent of each other. As an arbitrage-free pricing model, it differs in crucial respects from the equilibrium models presented in the previous chapter. The core of the HIM model is that given a current forward rate curve, and a function capturing the dynamics of the forward rate process, it models the entire term structure. 

From oiu understanding of derivatives, we know that option pricing models such as Black-Scholes assume that asset price returns follow a lognormal distribution. The dynamics of interest rates and the term structure is the subject of... 

Bernstein, F. and A. Federgruen. 2002. Dynamic inventory and pricing models for competing retailers. Forthcoming in Naval Research Logistics. 

Alpem and Snower [4] analyze a dynamic pricing and inventory control model with learning, where they assume upper and lower bounds on the initial uncertainty in the price-dependent demand function. They assume that the firm chooses a sequence of price-quantity combinations through time. The firm infers the position of its demand curve by observing its inventory level. 

A second pricing model that is increasingly popular for e-commerce applications is dynamic pricing, where the price of an item may change over time. This may used as a tool to manage variability in supply of product or components, or variability of customer demand, or as a reaction to competitors. 

S. Kachani and G. Perakis. A fluid model of dynamic pricing and inventory management for make-to-stock manufacturing systems. Working Paper, MIT, 2002. 

Z. K. Weng and M. Parlar. Price-incentive and stocking decisions for seasonal products A dynamic programming model. Working Paper, University of Wisconsin, 2000. 

In 2001, Hanke, Price and Lynden-BelP were the first to conduct an atomistic simulation of compovmds that can be called ionic liquids under our definition. They used molecular dynamics to model the crystalline state of 1,3-dimethylimidazolium chloride ([Cimim][Cl]), 1,3-dimethylimidazolium hexafluorophosphate ([CimimllPFg]), l-ethyl-3-methylimidazolium chloride ([C2mim][Cl]), and l-ethyl-3-methylimidazolium hexafluorophosphate ([C2 mimJlPFg]). They also modeled the liquid state of [Cimim][Cl] and [Cimim] [PFg], both of which are relatively high melting substances. Because of this (and the need to speed dynamics and thus limit computation times), the liquid simulations were carried out at temperatures between 400 and 500 K. The form of the potential function they used was... 

Before we can discuss in detail the simulation of adsorption and diffusion in zeolites using atomistic simulation we must ensure that the methods and potentials are appropriate for modelling zeolites. The work of Jackson and Catlow reviewed in the previous section shows the success of this approach. Perhaps the most critical test is to apply lattice dynamics and model the effect of temperature as any instability will cause the calculation to fail. Thus we performed free energy minimization calculations on a range of zeolites to test the methodology and applicability to zeolites. As noted in Section 2.2, the extension of the static lattice simulation technique to include the effects of pressure and temperature leading to the calculations of thermodynamic properties of crystals and the theoretical background to this technique have been outlined by Parker and Price [21], and this forms the basis of the computer code PARAPOCS [92] used for the calculations. 

THE CHALLENGE OF STRATEGIC CUSTOMERS In reality, the dynamic pricing problem is more complicated because demand is unpredictable and customers behave strategically in that they may decide to delay their purchases if they know that prices wiU drop over time. An excellent discussion of models that can be used in this more complex setting can be found in Talluri and Van Ryzin (2004). 

The friction models used in the dynamic modeling of systems can be further divided into static models and dynamic models. In the dynamic friction models such as the so-called LuGre model [13], the friction force is dependent on additional state variables that are governed by nonlinear differential equations stemming from the model for the average deflection of the contacting surfaces. At the price of increased complexity of the overall system dynamics, these models are capable of reproducing various features of friction such as velocity and acceleration dependence, pre-slip displacement, and hysteresis effect... 

Cause-effect-relations of these dynamics in the value chain may still be obvious, when operating a simple value chain comprising few products, locations and production steps. Considering the global multi-stage, multilocation value chain network, price changes in raw materials cannot directly be related to intermediate or even sales products and their prices. This problem requires specific planning models and methods. 

These simple examples can only show the opportunity to further extend the value chain planning model usage for decision support integrated in simulation-based optimization architecture. There is an opportunity for further industry-oriented research to better understand production-price dynamics in different types of value chain networks. 

To date, the only applications of these methods to the solution/metal interface have been reported by Price and Halley, who presented a simplified treatment of the water/metal interface. Briefly, their model involves the calculation of the metal s valence electrons wave function, assuming that the water molecules electronic density and the metal core electrons are fixed. The calculation is based on a one-electron effective potential, which is determined from the electronic density in the metal and the atomic distribution of the liquid. After solving the Schrddinger equation for the wave function and the electronic density for one configuration of the liquid atoms, the force on each atom is ciculated and the new positions are determined using standard molecular dynamics techniques. For more details about the specific implementation of these general ideas, the reader is referred to the original article. ... 

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