Two-Period Planning for Hybrid Seed Corn: An Alternative Solution Procedure

Stuart J. Allen Reference: Jones, Philip C., Timothy J. Lowe, Rodney D. Traub, Greg Kegler. 2001. Matching Supply and Demand: The Value of a Second Chance in Producing Hybrid Seed Corn. Manufacturing & Service Operations Management. Vol. 3, No. 2, pp. 122-137. Introduction This is an attempt to fathom the approach of Jones, et al to the problem stated in the title. We assume that the reader has this reference at hand. We also wish to avoid the need for a solver such as What’s Best! as used in that study. Throughout we rely on the results from Jones, et al that the marginal profit functions are well behaved and that local optima are global. For the most part, we adopt the notation used in the Jones study. However, we will assume that the probability distributions for crop yield and demand are statistically independent, normal distributions with the same means and standard deviations used by Jones in his Managerial Insights section. In that section, he examined 9 combinations of variability for yield and demand: high, medium and zero, using symmetrical, discrete distributions. We will confine our attention to only 2 of these combinations: yield and demand at high variability ; yield and demand at medium variability. Some Notation i = 1,2 index for planning periods Ki = $900 , cost per acre ci = $10 , variable cost per bushel π = $27.50 , shortage cost per bushel v = $23.50 , salvage value per bushel p = $60 , price per bushel yi = yield in bushels per acre for period i, a random variable D = demand in bushels, a random variable μyi = 40 bushels per acre, mean yield