# EOQ, lead time demand information;safety stock;reorder point

Given the following information, formulate an inventory management system. The item is demanded 50 weeks a year.

_________________________________________________________________

Item cost $10.00 Standard deviation of

Order cost $250.00 weekly demand 25 per week

Annual holding cost (%) 33% of item cost Lead time 1 week

Annual demand 25,750 Service probability 95%

Average demand 515 per week

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a. State the order quantity and reorder point.

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#### Solution Preview

See the attached file. Thanks

R Demand rate avg. (units per unit time) 25750

sR Demand rate std. dev. (units per unit time) 176.78 (converted to annual)

LT Leadtime avg. (time units) 0.02 (in terms of year = 1/50)

sLT Leadtime std. dev. (time units) 0

K Unit ordering/prod. cost ($ per order) $250.00 ...

#### Solution Summary

This post shows how to calculate EOQ, lead time demand information, calculate the safety stock based on S.L. and reorder point

Estimating Inventory Levels, Finding the EOQ, Total Cost and TBO , safety stock and reorder point

Can someone assist me with the attached Operations Management Problems?

Textbook is Foundations of Operations Management by Larry P. Ritzman and Lee J. Krajewski

Please see attached file for full problem description.

APPLICATION 10.1: ESTIMATING INVENTORY LEVELS

Management has decided to establish three DCs in its supply chain, located in different regions of the country, to save on transportation costs. For one of the products, the average weekly demand at each DC will be 50 units. The product is valued at $650 per unit. Average shipment sizes in to each DC will be 350 units per trip. The average lead time will be two weeks. Each DC will carry one week's supply as safety stock, as the demand during the lead time sometimes exceeds its average of 100 units (50 units/wk 2 wk). Anticipation inventory should be negligible.

1. How many dollars, on the average, of cycle inventory will be held at each DC?

2. How many dollars of safety stock will be held at each DC?

3. How many dollars of pipeline inventory, on the average, will be in transit for each DC?

4. How much inventory, on the average, will be held at each DC?

5. Which type of inventory is your first candidate for reduction?

APPLICATION 10.2: FINDING THE EOQ, TOTAL COST, AND TBO

Suppose that you are reviewing the inventory policies on an item stocked at a hardware store. The current policy is to replenish inventory by ordering in lots of 360 units. Additional information is:

D = 60 units per week, or 3120 units per year

S = $30 per order

H = 25% of selling price, or $20 per unit per year

a. What is the EOQ?

b. What is the total annual cost of the current policy (), and how does it compare with the cost with using the EOQ?

Current policy EOQ policy

Q = 360 units Q = 97 units

C = (________)(_____) + (_______)(____) C = (________)(_____) + (_______)(_____)

C = ________ + ________ C = ________ + ________

C = $ _______ C = $ _______

c. What is the time between orders (TBO) for the current policy and the EOQ policy, expressed in weeks?

APPLICATION 10.3: PLACING ORDERS WITH A CONTINUOUS REVIEW SYSTEM

The on-hand inventory is only 10 units, and the reorder point R is 100. There are no backorders and one open order for 200 units. Should a new order be placed?

Decision:

APPLICATION 10.4: SELECTING THE SAFETY STOCK AND R

Suppose instead that the demand during lead time is normally distributed with an average of 85 and.

a. Find the safety stock, and reorder point R, for a 95%cycle-service level.

Safety stock = zL = ______ (______) = ______ , or ______ units

R = Average demand during lead time + Safety stock

R = _______ + _______ = _______ units

b. Find the safety stock, and reorder point R, for an 85%cycle-service level.

Safety stock = zL = ______ (______) = ______ , or ______ units

R = Average demand during lead time + Safety stock

R = _______ + _______ = _______ units

APPLICATION 10.5: CONTINUOUS REVIEW SYSTEM: PUTTING IT ALL TOGETHER

The Discount Appliance Store uses a continuous review system (Q system). One of the company's items has the following characteristics:

Demand = 10 units/wk (assume 52 weeks per year)

Ordering and setup cost (S) = $45/order

Holding cost (H) = $12/unit/year

Lead time (L) = 3 weeks

Standard deviation in weekly demand = 8 units

Cycle-service level = 70%

a. What is the EOQ for this item?

D = _____ (_____) = units

b. What is the desired safety stock?

L= ______ = _____ units

Safety stock = zL = (_______) = ______ units

c. What is the desired reorder point R?

R = Average demand during lead time + Safety stock

= ( ) + ___ = _____ units

d. What is the total annual cost?

e. Suppose that the current policy is Q = 80 and R = 150. What will be the changes in average cycle inventory and safety stock if your EOQ and R values are implemented?

Cycle inventory reduction: ______ ______ = ______ units

Safety stock reduction: ______ ______ = ______ units

APPLICATION 10.6: PLACING ORDERS WITH A PERIODIC REVIEW SYSTEM

The on-hand inventory is 10 units, and T is 400. There are no back orders, but one scheduled receipt of 200 units. Now is the time to review. How much should be reordered?

DECISION:

APPLICATION 10.7: PERIODIC REVIEW SYSTEM: PUTTING IT ALL TOGETHER

Return to Discount Appliance Store (Application 13.8), but now use P system for the item.

a. Previous information

Demand = 10 units/wk (assume 52 weeks per year)

EOQ = 62 units (with reorder point system)

Lead time (L) = 3 weeks

Standard deviation in weekly demand = 8 units

z = 0.525 (for cycle-service level of 70%)

b. Reorder interval P, if you make the average lot size using the Periodic Review System approximate the EOQ.

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