Optimal Timing of Inventory Decisions with Price Uncertainty

Abstract

What is the optimal timing of inventory investment for a firm when its forecasts of demand and price improve with time but are correlated with the prices of traded assets in the financial markets? We consider this problem using a single period inventory model where demand is realized at time T and the stocking decision may be made at any time in the interval [0, T ]. The demand forecast evolves as a geometric Brownian motion, while the price forecase exhibits mean-reversion. The processes for the firm's value as well as that of the market evolve as geometric Brownian motions. We show that the right to make the optimal inventory decision is a modified American-style option. However, since the stochastic variables defining the forecasts of demand and price are not tradeable, we use a risk-adjusted valuation approach for incomplete markets to determine the optimal timing strategy.We derive the value of the inventory postponement option and the optimal exercise decision, that is, we present and analyze conditions under which early exercise of the inventory option takes place, and those under which postponement occurs. We also derive the comparative statics of optimal timing and stocking decisions relative to the key parameters: the market price of risk (and the cost of capital), the volatilities of price and demand, the correlation between these two variables and the return on the market portfolio, and the procurement cost.We illustrate the empirical validity of our model by testing it on firms in the gold mining industry. We show that our model performs well in explaining the variation in firm inventory as well as gross profit, and provides new evidence on the impact of price uncertainty on these variables.

Optimal Energy Procurement in Spot and Forward Markets

“…Various authors have considered the procurement of a commodity in forward and/or spot markets, including Kalymon (1971), Ritchken and Tapiero (1986), Williams (1986, p. 146), Williams (1987), Gurnani and Tang (1999), Gavirneni (2004), Seifert et al (2004), Berling and Rosling (2005), Gaur and Seshadri (2005), Gaur et al (2007), Goel and Gutierrez (2009), Nascimento and Powell (2009), Oum and Oren (2010), Berling and Martínez-de-Albéniz (2011), and Boyabatli et al (2011). Different from these authors, we analyze the impact of the correlation between the spot demand and nominal price on the optimal forward procurement quantity and the value of the forward procurement option, and we bring to light the near optimality of the demand forecast forward procurement policy.…”

“…Different from these authors, we analyze the impact of the correlation between the spot demand and nominal price on the optimal forward procurement quantity and the value of the forward procurement option, and we bring to light the near optimality of the demand forecast forward procurement policy. Ritchken and Tapiero (1986), Seifert et al (2004), and Oum and Oren (2010) maximize the expected utility of a risk averse procurement manager, while Gaur and Seshadri (2005), Gaur et al (2007), and Goel and Gutierrez (2009) model the risk aversion of economic agents via the risk neutral valuation approach (Luenberger 1998, Chapter 16, Seppi 2002. The risk neutral valuation approach does not admit the presence of transaction costs in security trading.…”

Flexible Capacity Investments and Product Mix: Optimal Decisions and Value of Postponement Options

“…The early influential work on the use of real options to study the impact of risk on capacity planning models, mostly for single-product firms and without any embedded switching and/or postponement options, is Birge (2000). Looking at inventory decisions of singleselling-season products as American options and quantifying the benefits of postponing the ordering decision to an a priori set time closer to the start of the selling season has been presented in a working paper by Gaur et al (2010). They also assume risk-averse investors and adopt the ICAPM model, but their analysis involves a single product and as a result does not consider embedded real options in capacity commitment as part of flexible capacity valuation.…”

An effective approach for optimization of a perishable inventory system with uncertainty in both demand and supply

“…One of the major inventory management challenges that needs more attention is supply uncertainty. Such uncertainty can be found in three aspects: uncertainty in supply lead time (Janakiraman et al., 2013; Muthuraman et al., 2014), uncertainty in supply quantity (Ciarallo et al., 1994; Wang and Gerchak, 1996; Jakšič, 2016), and uncertainty in purchase price (Tajbakhsh et al., 2007; Chen et al., 2015; Gaur et al., 2007). Uncertainty in supply quantity can be classified into three categories: random yield (the quantity ordered and the quantity received are not same), random supplier availability and random capacity (supplier's capacity is variable).…”