Advantages Of Linear Programming

Linear programming is a useful planning method, used for decisions with many different alternatives (Beneke & Winterboer, 1973). Producers do not have perfect information, thus bear income risk from fluctuating level of production as well as product prices. With linear programming there are four main techniques which incorporate risk when aiming for the efficient allocation of resources, where the ratio of output to input used of a particular resource is maximized. For linear programming risk is measured or captured by a variance in farm income (Hazell & Norton, 1986). The linear programming technique which captures risk by including the fluctuations in real gross margins or prices from the mean, over a particular time period is called MOTAD

These points are considered risk-efficient, as the plans given by the model are the ones with the least variance for a particular level of GM. When different risk efficient expected income points are plotted against the variance, an E-V curve is developed with each point on the E-V curve being a unique farm plan (Zia, 1998). The E-V boundary can be estimated with MOTAD. The set of risk efficient farm plans is generated by solving the model for different values of E and minimising risk. According to Hazell & Norton (1986), it is assumed that farmers aim to maximize utility, which is the function of expected income and income variance. From the combinations of expected income and income variance, points resulting in equal utility can be identified. When these points are plotted, they create a set of iso-utility curves. The utility maximizing farm plan occurs where the E-V touches one of the iso-utility curves (Hazell & Norton, 1986). However, reality is that it is difficult to determine an individual’s iso-utility curves (Zia, 1998). From MOTAD all results can be presented to the farmer so that the farmer decides which plan suits his/her risk preference and production

This method is closely related to MOTAD in a sense that it accounts for risk by including deviations in real prices from the mean over a certain time period. The difference between the two is that the risk aversion coefficient (θ) is known or can be estimated and included in the model (Hazell & Norton, 1987). The objective function seeks to maximize utility, where the risk is treated as a cost. The proportionality between risk preference and θ is direct, hence the diverse the resulting farm plan. Therefore, the more risk averse the farmer is, the larger the value of θ and the more diverse the resulting farm plan. In Baumol’ model, instead of generating a set of risk efficient farm plans and an E-V curve for the farmer to decide which plan best suits him/her because the exact level of risk is known. Thus a single risk efficient farm plan can be developed, which best suits the farmers’ risk aversion level, and maximizes his/her utility (Hazell & Norton,