... 0),(2≤∂∂∂tptpq and if 0),(>∂∂ttpq, then 0),(2≥∂∂∂tptpq. Proposition 4. 2. In intertemporal centralized pricing (4. 2)- (4. 3), (4. 5)- (4. 6) and (4. 7), if the supply chain is profitable, ... (4. 38) and (4. 41) dssqCtct)()(0111∫−=γ; dssqCtct)()(0222∫−=γ. (4. 49) Thus, if a solution, q1(t) and q2(t), of the system of two equations (4. 47) and (4. 48), is such that ... mmax()∫+Tdtttmtwqtm0),()()( (4. 4) s.t. m(t)≥ 0, (4. 5) q(w(t)+m(t),t)≥ 0. (4. 6) Formulations (4. 1)- (4. 6) assume non-cooperative behavior of the supply chain members which affects the overall supply chain performance....