Economic ordering policy for deteriorating items with a linearly increasing demand

Approximation of optimal order policy for deteriorating items with a linearly increasing demand

“…They proposed to obtain the optimal replenishment times of the inventory system by solving the first partial derivaties. According to equation (5) of [2), we know that if there are n replenishments over [0, H), then the total relevant cost of the system during His Here, we recall their proof. Chung & Ting considered that { T; =0, ti, Tt, ... , t;t_j, T,~_ l' t~ = H} is an optimal replenishment policy, Taking one component, say t;, Chung and Ting evaluated ~L( ...,ti + s, .. " ) -~L( ...,ti, ... ).…”

“…They mentioned the two inequalities in Proposition 1 in [2] can be used as a pair of .upper and lower bound to search for (a) T/. when t; and Ti.…”

“…Chung & Ting considered that { T; =0, ti, Tt, ... , t;t_j, T,~_ l' t~ = H} is an optimal replenishment policy, Taking one component, say t;, Chung and Ting evaluated ~L( ...,ti + s, .. " ) -~L( ...,ti, ... ). First dividing by E, then taking the limit as E -')0 O+, they derived the equation (6) of [2] ( ~l + C J ( eO(t; -T;.I) -1 ) ~ C 2 (1j* -tj). (2) By the same method, with s < 0, evaluating Wn( ... , t; + s, .. , ) W ( ... , ti,... ).…”

“…First dividing by E, then taking the limit as E -')0 O+, they derived the equation (6) of [2] ( ~l + C J ( eO(t; -T;.I) -1 ) ~ C 2 (1j* -tj). (2) By the same method, with s < 0, evaluating Wn( ... , t; + s, .. , ) W ( ... , ti,... ). dividing by E (the inequality will change the direction), …”

“…In [2], Chung and Ting considered the inventory system with assumptions that the demand rate is deterministic and linear (positive) trend, that the rate of deterioration is constant, and that shortages are allowed during the fixed finite planning horizon (shortages are not allowed in the last period). They proposed to obtain the optimal replenishment times of the inventory system by solving the first partial derivaties.…”