Question

2. The MacBig fast-food Company stocks custom-printed wrappers that are used nor h sandwiches. The wrappers are needed throughout the 52-week year; the stores never close. Assume that wrappers are used at a constant daily rate. All wrapper inventory is held at MacBig's head office, and shipped to each store as needed. The Operations Manager collected the following data. Item Number of MacBig stores to be supplied600 Average daily demand (wrappers per store) 3000 Operating days (per week) Holidays-stores are closed (per year)0 Holding cost (costS/year) Ordering cost Number of items in a box Minimum order allowed Cost of item (per box of 10000) Wrapper 15% $100 10000 1 box $10 a. Develop an inventory control system for the wrappers b. An alternative is for each stor e to keep its own inventory. Calculate the cost of this alternative and indicate your recommended course of action. c. If you knew each store's individual demand, what would you do differently? d. IfMacBig experiences head-office warehouse shrinkage of 5% per month, but 1% er month shrinkage at the stores, will the inventory decision be different? (Note: e" is loss from theft, damage and misplacement of products.]

Answer 1

(a)

D = annual demand = 600 x 3000 x 7 x 52 = 655,200,000 wrapppers = 65520 boxes
S = ordering cost = $100
C = cost per box = $10
H = carrying cost per box per year = $10 x 15% = $1.5

Economic Order Quantity, Q* = SQRT(2*D*S/H) = SQRT(2*65520*100/1.5) = 2,956 boxes

Reorder point, R = average lead time demand, is unknown as the lead time of rder receiving is not given.

So, the policy is to order 2,956 boxes at a time.

(b)

For individual stores,

d = annual demand = 3000 x 7 x 52 = 1092000 wrapppers = 109.2 boxes
S = ordering cost = $100
C = cost per box = $10
H = carrying cost per box per year = $10 x 15% = $1.5

q* = SQRT(2*d*S/H) = SQRT(2*109.2*100/1.5) = 121 boxes

Total cost at each store = (d/q*)*S + (q*/2)*H = (109.2/121)*100 + (121/2)*1.5 = $181
Total cost at 600 stores = $181 x 600 = $108,600

Total cost for the central warehouse = (D/Q*)*S + (Q*/2)*H = (65520/2956)*100 + (2956/2)*1.5 = $4,434

Therefore, by pooling the inventory, the savings that can be achieved = $108,600 - $4,434 = $104,166. So, it is better to keep the inventory at the central location.

(c)

Even if we knew the individual demand, there will be always cost advatages in terms of inventory pooling at central location due to reduction is variability and aggregate ordering. However, with individual store's demand available, the total dmenad and hence the Q* estimate could have been estimated more accurately.

(d)

Total losses = Demand x shrinkage = 65520 x 5% x $10= $32,760 for the central warehouse

= 65520 x 1% x $10 = $6,552 for the indvidual warehouses.

But still, the difference does not balance savings achieved which is $104,166. So, the central warehouse is still a better option.