Question

Problem 13-9 The Economic Order Quantity (EOQ) model is a classical model used for controlling inventory and satisfying demand. Costs included in the model 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,-annual demand for item j -unit cost of item j S- cost per order placed for item j wj space required for item j Wthe maximum amount of space available for all goods inventory carrying charge as a percentage of the cost per unit N-number of items The decision variables are Q, the amount of item j to order. The model is Minimize s.t. 2 03-1,2 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 (Q2 is the average amount of inventory) Set up a spreadsheet model for the following data: Item 1 Item 2 Item 3 2,500 2,500 1,500 100 $50 $80 165 $145 $125 Annual Demand Item Cost Order Cost Space Required (sq.ft. 50 25 40 W-6,000 -0.25 Solve the problem using Excel Solver. Hint: You will need to start with decision variable values that are greater than 0 for Solver to find a solution. If required, round your answers to two decimal places Optimal Solution: Q1 = Q2 Q3 = If required, round your answer to the nearest dollar. Total cost-

Answer 1

Item 1 Item2Item 3 2 Annul demandD 3000 3000 2000 53 1 10 Cost of Item Onder Cost, S 80 130 300 45 |Real optimal qumetty is taken as 1 becaue 6. Inventurycarminrcw.nmas)|20し125 75E left 13.7enk excel in cell 811,C11. 01 Q1 03 beauze of a o optimal quantity 10 Annual purchase cost Annual mering cast Annual holding cost Total cost 80 45 12 13 14 15 16 50000 90000 220000 10 5.6256.875 objective function 150090 900050.625 220061.875 1570202.50 Badget 180 22000 Solver Parameters

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Item1Item2 Item 3 Annual demand, D30003000 2000 80 150 45 300 Cost of Item Order Cost. S 10tal ta natty G Inventery carrying cost, H(0.25) 20 1125 13.75 o3. 6 cel! E11, С11. D11 01 92 197 denominator 89 optimal qunntity Annual purchave cost Annual holding cost1030 103 10 8865 4368.9 4568 52792 2471.9101 1108 125 8240 1895 12 Annual ordering cost 13 14 15 16 611.875Objective unction 13639 14541.6529 7978.753615937 Total cost 22000 Budget 22000 Tus, the cctimal quntiy for each itemihown abovE