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This dissertation intends to use a mathematical model to
investigate the interrelationship between bonus scheme and
sales forces for the design of a reward system combining bonus
and commission. The firm is unable to foresee sales forces'
reaction to the bonus scheme during the design period.
Therefore, what can be done is to analyze the sales forces with
some basic assumptions according to the existing circumstances.
First of all, the firm owns several sales forces the aims of
which are all searching for the optimization of their own
rewards. Second, sales forces are permitted to decide the
prices of the product by themselves. The firm is unable to
predict the complicated interrelationship of practical selling
behavior among the sales forces. Therefore, the firm can only
figure out a reasonable situation based on the general
principles of demand. Besides, each sales force has its own
particular market segment the size of which will influence the
sales force's policy toward bonus scheme. This dissertation
attempts to construct both sales forces' reward models when
they face firm's bonus scheme and firm's reward model,
mathematically by using the calculus of variation to derive the
optimal solution. Through the characteristics of the optimal
solution of the model, the policy type of sales forces and the
factors which influence the firm's design bonus scheme can be
found. Moreover, this dissertation studies the differences of
sales forces' market segment rate, their influences on bonus
scheme and the characteristics of bonus scheme under different
demand states.
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