Question: 4. In the teaching material for the deterministic model with storage (Inventory_3.pptx), there is optimal formula for the optimal order quantity and optimal maximum shortage

4. In the teaching material for the deterministic

4. In the teaching material for the deterministic model with storage (Inventory_3.pptx), there is optimal formula for the optimal order quantity and optimal maximum shortage level. The following notations are used. D: Annual Demand S: Setup (ordering) cost C : Annual Production capacity H: Inventory holding cost Shortage cost per unit short, independent of the duration of the shortage t: Shortage cost per unit short per year A(A) Maximum (Average) inventory B(B): Maximum (Average) shortage Q Order quantity Cycle time t: Production run time TT . T From the total cost formula, 2 B TBD SD TC(Q,B) = Q + #(@(1-) B) 20(1-2) + 2(1-92 and from OTC(Q.B) ag = 0 and aTC(Q.B) aB = 0, we have the following formula. 2 SD (D) H+ (HQ*-AD)(1-2 Q* = and B* H(1-7 #(H++) H+R Please derive the optimal formula of Q* and B*. 4. In the teaching material for the deterministic model with storage (Inventory_3.pptx), there is optimal formula for the optimal order quantity and optimal maximum shortage level. The following notations are used. D: Annual Demand S: Setup (ordering) cost C : Annual Production capacity H: Inventory holding cost Shortage cost per unit short, independent of the duration of the shortage t: Shortage cost per unit short per year A(A) Maximum (Average) inventory B(B): Maximum (Average) shortage Q Order quantity Cycle time t: Production run time TT . T From the total cost formula, 2 B TBD SD TC(Q,B) = Q + #(@(1-) B) 20(1-2) + 2(1-92 and from OTC(Q.B) ag = 0 and aTC(Q.B) aB = 0, we have the following formula. 2 SD (D) H+ (HQ*-AD)(1-2 Q* = and B* H(1-7 #(H++) H+R Please derive the optimal formula of Q* and B*

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