IDIS 344 – Spring 2010 Assignment 2 solution

Practice problems 1) The local supermarket buys lettuce each day to ensure really fresh produce. Each morning any lettuce that is left from the previous day is sold to a dealer that resells it to farmers who use it to feed their animals. This week the supermarket can buy fresh lettuce for $4.00 a box. The lettuce is sold for $10.00 a box and the dealer that sells old lettuce is willing to pay $1.50 a box. Past history says that tomorrow's demand for lettuce averages 250 boxes with a standard deviation of 30 boxes. How many boxes of lettuce should the supermarket purchase tomorrow? Solution: Newsboy model Cu = Cost of shortage (Stock out or Lost sale) = $10 - $4 = $6 Co = Cost of overage (Overstock) = $4 - $1.50 = $2.50

7059.650.2

6=

+=

+≤

uo

u

CCC

P

From Z- table (Normal Curve) For Probability 0.7059 (closest is 0.70884), Z value is 0.55

Therefore the supermarket should purchase 250 + 0.55 (30) = 266.5 or 267 boxes of lettuce.

2) Jill's Job shop buys two parts (Tegdiws and Widgets) for use in its production system from two different suppliers. The parts are needed throughout the entire 52-week year. Tegdiws are used at a relatively constant rate and are ordered whenever the remaining quantity drops to the reorder level. Widgets are ordered from a supplier who stops by every three weeks. Data for both products are as follows:

Item Tegdiw Widget Annual demand 10,000 5,000

Holding cost (% of item cost) 20% 20% Setup or order cost $150.00 $25.00

Lead time 4 weeks 1 week Safety stock 55 units 5 units

Item cost $10.00 $2.00

a) What is the inventory control system for Tegdiws? (reorder quantity and reorder point)

Tegdiws – Fixed Order Quantity Model

)10(20.150)10000(22* ==

HDSQ = 1224.74 → 1225 units

ssdLR += = (10000/52)(4) + 55 = 824.23 → 824 units

Note: Here d is weekly demand, since safety stock and lead time are defined in weeks. Also 4 weeks is not 1 month, i.e. you cannot compute dL as 10,000/12, it is 10,000/13.

b) What is the inventory control system for Widgets?

Widget – Fixed Time period model

Let I be the current (on-hand) inventory. Since it is not given, assume it to be zero

IssLTdq −++= )( = (5000/52)(3+1) + 5 – 0 = 390

Therefore the current inventory system for widgets is to order 390, based on current inventory. (Reorder point – Every Three Weeks! When the supplier drops by)

3) Dunstreet's department store would like to develop an inventory ordering policy of a 95% probability of not stocking out. To illustrate your recommended procedure, use as an example the ordering policy for white percale sheets.

Demand for white percale sheets is 5000 per year. The store is open 365 days per year. Every two weeks (14 days) inventory is counted and a new order is placed. It takes 10 days for the sheets to be delivered. Standard deviation of demand for the sheets is five per day. There are currently 130 sheets on hand. How many sheets should you order?

D = 5000 per year, d = daily demand = 5000/365 = 13.70 sheets T = time between orders (review) = 14 days L = Lead time = 10 days σ d = Standard deviation of daily demand = 5 per day

I = Current Inventory = 150 sheets

Service Level P = 95% (Probability of not stocking out) IzLTdq LT −++= +σ)(

)1014(5)( +=+=+ LTdLT σσ = 24.495

From Standard normal distribution, z = 1.64 for 95% Service Level (or 5% Stock out) 130)495.24(64.1)1014(*70.13 −++=q = 238.97 → 239 sheets