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Assignment; Basic Inventory Model

- Problem 1: A toy manufacturer uses approximately 32000 silicon chips annually. The Chips are used at a steady rate during the 240 days a year that the plant operates. Annual holding cost is 60 cents per chip, and ordering cost is $24. Determine
- a) How much should we order each time to minimize our total cost
- b) How many times should we order
- c) what is the length of an order cycle
- d) What is the total cost

How many times should we order

Annual demand for a product is 32000

D = 32000

Economic Order Quantity is 1600

EOQ = 1600

Each time we order EOQ

How many times should we order ?

D/EOQ

32000/1600 = 20

what is the length of an order cycle

working days = 240/year

32000 is required for 240 days

1600 is enough for how many days?

(1600/32000)(240) = 12 days

What is the Optimal Total Cost

The total cost of any policy is computed as

The economic order quantity is 1600

This is the total cost of the optimal policy

- Victor sells a line of upscale evening dresses in his boutique. He charges $300 per dress, and sales average 30 dresses per week. Currently, Vector orders 10 week supply at a time from the manufacturer. He pays $150 per dress, and it takes two weeks to receive each delivery. Victor estimates his administrative cost of placing each order at $225. His inventory carriyngcost including cost of capital, storage, and obsolescence is 20% of the purchasing cost. Assume 52 weeks per year.
- Compute Vector’s total annual cost of inventory system (carrying plus ordering but excluding purchasing) under the current ordering policy?
- Without any EOQ computation, is this the optimal policy? Why?

c) Compute Vector’s total annual cost of inventory system (carrying plus ordering but excluding purchasing) under the optimal ordering policy?

d) Compute EOQ and total cost of the system

e) What is the ordering interval under optimal ordering policy?

f) When do you order?

g) What is average inventory and inventory turns under the original policy and under the optimal ordering policy? Inventory turn = Demand divided by average inventory. Average inventory = Max Inventory divided by 2. Average inventory is the same as cycle inventory.

h) Compute the flow time under the two policies.

flow unit = one dress

flow rate d = 30 units/wk

costost C = $150/unit

fixed order cost S = $225

H = 20% of unit cost.

lead time L = 2 weeks

ten weeks supply

Q = 10(30) = 300 units.

52 weeks per year

Current Policy

a) Annual demand = 30(52) = 1560

Number of orders/yr = D/Q = 1560/300

= 5.2

(D/Q) S = 5.2(225) = 1,170/yr.

Average inventory = Q/2 = 300/2 = 150

H = 0.2(150) = 30

Annual holding cost = H (Q/2) = 30(150) = 4,500 /yr.

b) Without any computation, is this the optimal policy?

Why?

Without any computation, is EOQ larger than 300 or smaller

Why

c) Total annual costs = 1170+4500 = 5670

d) Compute EOQ

= 153 units.

Q* = EOQ =

4,589

His annual cost will be

e) What is the ordering interval under optimal ordering policy?

We order D/Q = 1560/153 = 10.2 times

A year is 52 weeks.

Therefore we order every 52/10.2 = 5.1 weeks

f) When do you order(re-order point) ?

An order for 153 units two weeks before he expects to run out.

That is, whenever current inventory drops to

30 units/wk * 2 wks = 60 units

which is the re-order point.

Whenever inventory reaches 60 we order 153.

This process is repeated 10.2 times a year. Every 5.1 weeks.

g) What is average inventory and inventory turns under the original policy and under the optimal ordering policy?

Inventory turns = yearly demand / Average inventory

Average inventory = cycle inventory = I = Q/2

Current policy inventory turns = D/(Q/2)= 1560/(300/2)

Current policy Inventory turns = 10.4 times per year.

Optimal policy inventory turns = D/(Q/2)= 1560/(153/2)

Optimal policy inventory turns = = 20.4

turns roughly double

h) Compute the flow time under the two policies.

Average inventory = cycle inventory = I = Q/2

Current average inventory = 300/2 = 150

Throughput?

R?

R= D

R= 30 /week

Current flow time

RT= I

30T= 150 T= 5 weeks

Optimal average inventory = 153/2) = 76.5

Optimal flow time RT=I 30T= 76.5

T = 2.55 weeks

Did we really need this computations?

Complete Computer (CC) is a retailer of computer equipment in Minneapolis with four retail outlets. Currently each outlet manages its ordering independently. Demand at each retail outlet averages 4,000 per week. Each unit of product costs $200, and CC has a holding cost of 20% per annum. The fixed cost of each order (administrative plus transportation) is $900. Assume 50 weeks per year. The holding cost will be the same in both decentralized and centralized ordering systems. The ordering cost in the centralized ordering is twice of the decentralized ordering system.

- Decentralized ordering: If each outlet orders individually.
- Centralized ordering: If all outlets order together as a single order.
- Compute EOQ in decentralized ordering
- Compute the cycle inventory for one outlet and for all outlets.
- Compute EOQ in the centralized ordering
- Compute the cycle inventory for all outlets and for one outlet
- Compute the total holding cost + ordering cost (not including purchasing cost) for the decentralized policy
- Compute the total holding cost plus ordering cost for the centralized policy

Four outlets

Each outlet demand

D = 4000(50) = 200,000

S= 900

C = 200

H = .2(200) = 40

If all outlets order together in a centralized ordering, then S= 1800

=3000

With a cycle inventory of 1500 units for each outlet.

The total cycle inventory across all four outlets equals 6000.

With centralization of purchasing the fixed order cost is S = $1800.

=8485

and a cycle inventory of 4242.5.

Total holding & ordering costs under the two policies

Decentralized

Decentralized: TC for all 4 warehouses = 4(120000)=480000

Centralized

339411 compared to 480000 about 30% improvement

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