Table 1 Notations

\(\tilde {c}:\)

Unit manufacturing cost, an uncertain variable

\(\tilde {s}_{i}:\)

Unit sales cost of retailer i, an uncertain variable

w _i :

Unit wholesale price to retailer i, the manufacturer’s decision variable

r _i :

Unit markup price of retailer i, the retailer’s decision variable

p _i :

Unit retail price of retailer i, where p _i =w _i +r _i

\(\tilde {d}_{i}:\)

The market base of retailer i, an uncertain variable

π _m :

The profit of the manufacturer: \(\pi _{m}=\sum _{i=1}^{2}(w_{i}-\tilde {c})(\tilde {d}_{i}-\tilde {\beta } p_{i}+\tilde {\gamma } p_{3-i})\)

\(\pi _{r_{i}}\):

The profit of retailer i: \(\pi _{r_{i}}=(r_{i}-\tilde {s}_{i})(\tilde {d}_{i}-\tilde {\beta } p_{i}+\tilde {\gamma } p_{3-i})\)