The Impact of Yield-Dependent Trading Costs on Pricing and Production Planning Under Supply Uncertainty

Abstract

This paper studies the role of the yield-dependent trading cost structure influencing the optimal choice of the selling price and production quantity for a firm that operates under supply uncertainty in the agricultural industry. The firm initially leases farm space, but its realized amount of fruit supply fluctuates because of weather conditions, diseases, etc. At the end of the growing season, the firm has three options: convert its crop supply to the final product, purchase additional supplies from other growers, and sell some (or all) of its crop supply in the open market without converting to the finished product. We consider the problem both from a risk-neutral and a risk-averse perspective with varying degrees of risk aversion. The paper offers three sets of contributions: (1) It shows that the use of a static cost exaggerates the initial investment in the farm space and the expected profit significantly, and the actual value gained from a secondary (emergency) option for an agricultural firm is lower under the yield-dependent cost structure. (2) It proves that although the risk-neutral firm does not benefit from fruit futures, a sufficiently risk-averse firm can benefit from the presence of a fruit futures market. The same risk-averse firm does not purchase fruit futures when it operates under static costs. Thus, fruit futures can only add value under yield-dependent trading costs. (3) Contrary to the results presented for the newsvendor problem under demand uncertainty, the firm does not always commit to a lower initial quantity (leased farm space) under risk aversion. Rather, the firm might lease a larger farm space under risk aversion.

Hedging demand and supply risks in the newsvendor model

“…Finally, through a numerical illustration with the exponential utility function, they illustrate that using fruit futures has an impact on the optimal decisions. The ideas presented by the numerical illustration in Kazaz and Webster (2011) are very much related to our ideas since they also address the effect of risk hedging. However, as mentioned above, the fact that the cash flows are not related is a significant difference.…”

“…The models, analysis, results and the corresponding cash flows are completely different. Regarding risk hedging, there is a resemblance to our model in Kazaz and Webster (2011) where the authors discuss the value of using fruit futures in mitigating the supply risk in their model. Assuming that there is a futures market for the fruit, they show that fruit futures do not have an impact on firm's profitability in the risk-neutral case due to the implicit assumption on no arbitrage in the futures market.…”

“…A model with supply uncertainty and risk hedging using futures is discussed in Kazaz and Webster (2011). They consider a specific problem in agriculture involving a two-stage decision process where the manager decides on the amount of land to rent in the first stage when the product yield of the land is random.…”

Coordination of perishable crop production using auction mechanisms

“…They do not consider any interactions among agents, but rather assume centralized control by one single planner. Some examples of these models of expanded scope include Widodo et al (2006), Rantala (2004), Kazaz (2004), Kazaz and Webster (2011), Ahumada, Villalobos and Mason (2012), and Ahumada and Villalobos (2009b), whose contributions vary from perishability modeling to plant location and production planning. These models are generally tactical in nature and therefore are of particular relevance to our approach.…”

Supply Uncertainty in Food Processing Supply Chain: Sources and Coping Strategies

“…High uncertainty until delivery [17], weather induced variability [18], whey, generated with cheese, has low margin [2] Variation in individual bird weights which can result in varying proportions of heavier and lighter birds [19], some parts of the chicken have higher demand then others [2] Crop yield uncertainty due to weather conditions, contagious bacterial diseases [20], fresh produce heavily exposed to environment [21] Supply quality, product size and type Uncertainty depending on periods and biology [1,16,22], Temperature sensitive [16], quality degradation depends on microbial growth [22] High contamination risk [23] High and variable mortality, weight or fat variability, poor lairage control at abattoir affecting pig quality [24], variable quality of beasts and microbial growth [22,25] High uncertainty from environment (air, soil, water, insects, rodents, etc.) and manual manipulation and thus intrinsically potentially heavily contaminated [21,26] …”