This thesis is concerned with the determination of standard product sizes when customers' preferred sizes have a normal distribution. The probability of sale is assumed to be significantly affected by the degree to which standard size deviates from the customer's exact requirement.
The optimal standard size set is determined to maximize total expected profit during a planning horizon. It is an economic balance involving the lost sales resulting from failing to provide each segment of customers with their exact preference sizes versus economics of scale in producing standard size set.
Two cases of customer's preference are considered :
1. When the demands for a specific size are successfully substituted with larger standard size items within the acceptance range of size difference (however, lost sales occur beyond the range), an analytical formula is derived;
2. When the probability of sale linearly increases in proportion to the nearness to the preferred size, dynamic programming approach is used.
Some numerical examples are given to illustrate the solution methodology for each case.
