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Article Review: Time-dependent and Independent Control Rules

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2 Coordinated Production and Pricing The incorporation of random demand and the problems related to the manufacturing system model's yield has been on the watch over the past years. Different authors have described these problems in various ways, depending on how they analyze the situation. For instance, Yano and Lee (1995) came up with various models of random-yield lot-sizing problems. They include; single-stage models, assembly system, multiple stages models, and continuous-time models. They later classified Continuous-time dynamic models into two streams concerning their assumptions in product pricing. The first stream stated that price was not a decision variable; instead, it was a dependent price. This first stream used the stochastic equations widely and was majorly based on the Brownian motion theory, specifically the Wiener diffusion process (Herbon & Kogan, K, 2014). On the other hand, the product price is assumed to be a decision variable in the second research stream. This implies that it affects demand. Therefore, most studies that goes hand in hand with this second approach focus on coordinated dynamic inventory decisions, including price, product, and inventor control (Herbon & Kogan, K, 2014). Therefore, the document studies the effects of demand-related uncertainty on pricing decisions and coordinated dynamic production to focus on the Continuous-time stochastic formulations. To understand this better, we can use an example of the wholesaler's demands to the manufacturers depending on their price. The assumption made in this case is that demand is the downward linear function of the product price. The study also focuses on enterprise risk management (ERM), which aims at providing tools that can enable both public and private firms to manage risks that may come across a large variety of domains. Therefore, Enterprise Risk Management is the integrated process of identifying, analyzing, and accepting or mitigating the uncertainties related to

3 investment decision making (Herbon & Kogan, K, 2014). Under problem formulation, there are various methods derived and explained in detail how to handle different problems. An example of a formula that has been derived is the stochastic demand formula shown below: d D(t) = μadt − σadWa(t) − [μbdt + σbdWb(t)]p(t) where Wa(t) and Wb(t) represents the independent standard Wiener processes; μa and μb are the potential demand and customer price sensitivity, respectively; σa and σb represent the volatilities of the potential demand and customer price sensitivity, respectively. The assumption that comes with this method is, the customers are always charged when an order is placed; therefore, immediate sales are realized. Also, the drift components of demand are likely to affect the instantaneous revenue. Under closed-loop pricing and product control, the assumption made is that the production rate continuously adjusts concerning the number of stocks available. The derivation of the formula related to these problems is indicated in the document. Another formula derivation in the document is that one is loved in the optimal solution for zero-volatility of customer price sensitivity. The assumption made is that the volatility of the customer price sensitivity is negligible. The document further discusses the time-dependent control rule, which analyses various graphs in depth. It also compares the Time-independent and time-dependent controls. Finally, the conclusion summarizes the main ideas in the document.

4 Reference Herbon, A., & Kogan, K. (2014). Time-dependent and independent control rules for coordinated production and pricing under demand uncertainty and finite planning horizons. Annals of Operations Research, 223(1), 195-216....