Draw the network diagram and (b) prepare the From-To table for this work system.

Question

Draw the network diagram and (b) prepare the From-To table for this work system. 02) Last year, the annual demand for a certain piece of merchandise that is inventoried at a department store warehouse was 13,688 units. The annual demand is expected to increase 10 percent in the next year. One unit of the product costs S8.75, and the selling price is S19 95 The holding cost rate-15%y-Cost to place an order for the merchandise is figured at S65. Determine the economic order quantity and the total inventory cost for this case

Explanation / Answer

Q.2:- ANNUAL DEMAND LAST YEAR = 13688 ,NEXT YEAR DEMAND (13688 X110)/100 =15056.8 UNITS

= 15057 UNITS

LET OPTIMUM ORDER SIZE TO MINIMIZE COST `Q`THEN ANNUAL ORDERING COST

= ( 15057/ Q)X 65 AS COST OF PLACING AN ORDER $65

ANNUAL HOLDING COST = COST OF STORINGPER ITEM X AVERAGENUMBER OF STOCK

= ($ 8.75 X15%) XQ/2 ( AVERAGE STOCK 0 TO Q I.E AVERAGE Q/2)

=(1.3125 Q )/2

TOTAL ANNUAL PURCHASING COST = 150567 X $8.75 = $ 131748.75

NOW TOTAL ANNUAL COST(TC) = (15057X65) /Q + (1.3125 Q)/2 + 131748.75 ......................(1)

DIFFERENCIATING W.R.T Q dc/dQ = -978705/Q2 + 1.3125/2 +0 PUTTING dC/dQ = 0

978705/Q2 = 0.65625 => Q2 = 978705/0.65625 = 1491360

=> Q = 1221.21 = 1221

d2C/dQ2  IS POSITIVE FOR THIS Q HENCE IT IS MINIMIZATION CASE.

HENCE OPTIMIZATION ORDER SIZE FOR MINIMUM COST Q = 1221

NOW TOTAL ANNUAL INVENTORY COST AT THIS LEVEL ,PUTTING VALUE OF Q IN EQUATION (1)

TOTAL COST = (15057X65) /1221 +( 1.3125 X 1221)/2 + 131748.75

= 801.56+ 801. 28 + 131748.25 = $ 133351.09 = $133351

  

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