Question No. 5

The production schedule at Mazda calls for 1,200 Mazdaz to be produced

during each of 22 production days in January and 900 Mazdas to be produced

during each of 20 production days in February. Mazda uses a kanban system

to communicate with Gesundheit, a nearby supplier of tires. Mazda purchases

four tires per vehicle from Gesundheit. The safety stock policy variable is 0.15.

The container (a delivery truck) size is 200 tires. The average waiting time plus

materials handling time is 0.16 day per container. Assembly lines are

rebalanced at the beginning of each month. The average processing time per

container in January is 0.10 day. February processing time will average 0.125

day per container. How many containers should be authorized for January?

How many for February?

Answer:

January

Problem Statement:

- d (average demand over some time period) = 1,200 (number of Mazda

required per day) x 4 (tire purchase per vehicle) = 4,800 tires per day

- L (lead time to produce parts) = 0.16 + 0.10 = 0.26 day per container

- dL = 4,800 x 0.26 = 1,248

- S (safety stock) = 0.15 dL = 0.15 x 1,248 = 187.2

- C (container size) = 200 tires

Solution:

Round up to 8 containers/day or 8 x 22 (production days) = 176 containers

in January (allow some slack)

OR

Round down to 7 containers/day or 7 x 22 (production days) = 154

containers in January (force productivity improvement)

2

N =

kanbans or containers

February

Problem Statement:

- d (average demand over some time period) = 900 (number of Mazda required

per day) x 4 (tire purchase per vehicle) = 3,600 tires per day

- L (lead time to produce parts) = 0.16 + 0.125 = 0.285 day per container

- dL = 3,600 x 0.285 = 1,026

- S (safety stock) = 0.15 dL = 0.15 x 1,026 = 153.9

- C (container size) = 200 tires

Solution:

Round up to 6 containers/day or 6 x 20 (production days) = 120 containers

in February (allow some slack)

OR

Round down to 7 containers/day or 5 x 20 (production days) = 100

containers in February (force productivity improvement)

N = k

anbans or containers

Question No. 7

Problem Statement

- Operating time: 52 weeks per year and 6 days per week

- Price of kitty litter = $11.70 per bag

- D (annual demand)= 90 x 52 = 4,680 bags per year

- Co(order cost) = $54/order

- Cc (annual holding cost) 27% of cost

- Desired cycle service level = 80%

- Lead time = 3 weeks (18 working days)

- Std. deviation of weekly demand = 15 bags

- Current on-hand inventory = 320 bags (no open orders or backorders)

Solution:

a) What is the EOQ? What would be the average time between orders (in

weeks)?

Cc = 0.27 x $ 11.70 = $ 3.16

Qopt=

Qopt = 399.93 bags or 400 bags (rounded up)

Order cycle time =Qopt/D

= 400/4680

= 0.08546 years = 4.44 weeks

b) What should R be?

R = demand during protection interval + safety stock

Demand during protection interval = 90 x 3 = 270 bags

Safety stock: zdLT

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

dLT = = = 25.98 or 26

Safety stock = 0.84 x 26 = 21.82 or 22 bags

R = 270 + 22 = 292

c) An inventory withdrawal of 10 bags was just made? Is it time to reorder?

Initial inventory position – OH + SR – BO = (320 + 0) – 10 = 310.

Because inventory positions remain above R (292), it is not yet time to

reorder.

d) The store currently uses a lot size of 500 bags. What is the annual holding

cost of this policy? Annual ordering cost? Without calculating the EOQ, how

can you conclude from these two calculations that the current lot size is too

large?

Annual holding cost

=

Annual ordering cost

When the EOQ is used, these two costs are equal. When Q = 500, the

holding cost is larger than the ordering cost, therefore Q is too large. Total

costs are therefore $789.75 + $505.44 = $1,295.19

e) What would be the annual cost size saved by shifting from the 500 bag lot size

to the EOQ?

Annual holding cost

=

Annual ordering cost

Total cost by using EOQ

$631.80 + $631.80 = $1,263.60

Annual cost saving compared to using 500 bags lot size

$1,295.19 - $ 1,263.60 = $31.59

Based on the above calculation, we can see that the annual holding cost

and annual ordering cost is equal when EOQ is used. Therefore, the total

cost of using EOQ is $1,263.60, which gives Sam’s Cat Hotel $31.59in

cost savings instead of using the 500 bags lot size.