The Economic Order Quantity (EOQ) model is a classical mode used for controlling

Question

The Economic Order Quantity (EOQ) model is a classical mode used for controlling inventory and satisfying demand. Costs included in the mode are holding cost per unit, ordering cost and the cost of goods ordered. The assumptions for that model are only a single item is considered: the entire quantity ordered arrives at one time: the demand for the item is constant over time: no shortages are allowed. Suppose we relax the first assumption and allow for multiple items which are independent except for a budget restriction. The following model describes this situation: Let D_j = annual demand for item j C_j = unit cost of item j S_j = cost per order placed for item j i = inventory carrying charge as a percentage of the cost per unit B = the maximum amount of investment in goods N = number of items The decision variables are Q_i, the amount of item j to order. The model is: Minimize sigma^N [C_j D_j + S D /Q + iC_j Q_i/2] s.t. sigma^N_j = 1 C_j Q_j lessthanorequalto B Q_j greaterthanorequalto 0 j = 1, 2,...N In the objective function, the first term is the annual cost of goods, the second is the annual ordering cost (D /Q is the number of orders) and the last term is the annual inventory holding cost (Q /2 is the average amount of inventory). Set up spreadsheet model for the following data: B = $25,000 i = 0.3 Solve the problem using Excel Solver. If required, round your answers to two decimal places. Optimal Solution: Q_1 = 52.22 Q_2 = 70.06 Q_3 = 64.20 If required, round your answer to the nearest dollar. Total cost = $ 20823.41

Explanation / Answer

Q1 = 127.96

Q2 = 148.67

Q3 =104.71

Total Cost = 374858

Item 1 Item 2 Item 3 Annual Demand 2000 2000 1500 Dj Item Cost 80 50 70 Cj Order Cost 160 135 125 Sj i 0.3 B 25000 127.9578 148.6735 104.71 Z 374857.5 365000 6107.544 3750 25000 25000

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