Q2 10 points facility operates 52 weeks per year 6 days per

Q2 (10 points) facility operates 52 weeks per year, 6 days per week, and uses a continuous review inventory system. It purchases kitty litter for $11.70 per bag. The following information is available about these bags Demand- 90 bags/week Order cost-$54/order Annual holding cost- 27 percent of cost Desired cycle-service level-80 percent Lead time 3 weeks (18 working days) Standard deviation of weekly demand 15 bags Current on-hand inventory is 320 bags, with no open orders or backorders. a. What is the EOQ? What would be the average time between orders (in weeks)? b. What should be? c. An inventory withdrawal of 10 bags was just made. Is it time to reorder? d. What would be the annual cost saved by shifting from the 500-bag lot size to the E 0Q?

Solution

d = 90 bags/week

D= 90 bags/week)*(52 weeks/yr) = 4,680

S= $54 and price is $11.7

so, H = (27%)($11.70) = $3.16 (holding cost)

EOQ = sq root(2DS/H)

putting the above values, we get

EOQ= 399.93 or 400 bags

Time between orders in weeks is Q/D = 400/4680= .08547 years= 4.44 weeks

b) R = demand during protection interval + safety stock

Demand during protection interval = L = 90 * 3 = 270 bags

When the desired cycle-service level is 80%, z is 0.84

safety stock is 0.84*15*sqroot (3) = 21.82= 22 bags

so, R= 270+22 = 292

c) Initial inventory = = 320 + 0 – 0

Withdawal of 10 bags 320 – 10 = 310.­

Because inventory remains above 292, it is not yet time to place an order

d) Annual holding cost is QH/2 = 500*(27%)($11.7)/2 = $789.75

Annual ordering cost is DS/Q = 4680*($54)/500 = $505.44

At EOQ, these two costs are equal

When Q is 500 ,Total costs = $(789.75+505.44) = $1295.19