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 orderc) what is the length of an order cycled) What is the total cost

Assignment; Basic Inventory Model

What is the Optimal Order Quantity

D = 32000, H = .6, S = 24

H

DSEOQ

2

16006.

)24)(32000(2EOQ

How many times should we order

Annual demand for a product is 32000D = 32000Economic Order Quantity is 1600EOQ = 1600Each 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

SQDHQTC )/()2/(

)1600/32000(24)2/1600(6. TC

960TC

480480 TC

The economic order quantity is 1600

The total cost of any policy is computed as

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 carriyng cost including cost of capital, storage, and obsolescence is 20% of the purchasing cost. Assume 52 weeks per year.

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

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

Assignment; Problem 2

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 systeme) 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.

Assignment; Problem 2

a) Annual demand = 30(52) = 1560Number of orders/yr = D/Q = 1560/300 = 5.2(D/Q) S = 5.2(225) = 1,170/yr.Average inventory = Q/2 = 300/2 = 150H = 0.2(150) = 30Annual 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

smallerWhyc) Total annual costs = 1170+4500 = 5670

Problem 6.3flow unit = one dressflow rate d = 30 units/wkcostost C = $150/unitfixed order cost S = $225H = 20% of unit cost.lead time L = 2 weeksten weeks supply Q = 10(30) = 300 units.52 weeks per year

Current Policy

30

225)1560(22

H

DSQ* = EOQ = = 153 units.

e) What is the ordering interval under optimal ordering policy?We order D/Q = 1560/153 = 10.2 timesA year is 52 weeks.Therefore we order every 52/10.2 = 5.1 weeks

Optimal Policy

d) Compute EOQ

His annual cost will be 4,589

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 unitswhich 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.

Optimal Policy

Inventory Turns

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

Inventory turns = yearly demand / Average inventoryAverage 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

Flow time

h) Compute the flow time under the two policies.Average inventory = cycle inventory = I = Q/2 Current average inventory = 300/2 = 150Throughput?R?R= DR= 30 /weekCurrent flow timeRT= I30T= 150 T= 5 weeksOptimal average inventory = 153/2) = 76.5Optimal flow time RT=I 30T= 76.5T = 2.55 weeksDid 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.

Assignment; Problem 3

Decentralized ordering: If each outlet orders individually.Centralized ordering: If all outlets order together as a single

order.a) Compute EOQ in decentralized orderingb) Compute the cycle inventory for one outlet and for all

outlets. c) Compute EOQ in the centralized orderingd) Compute the cycle inventory for all outlets and for one

outlete) Compute the total holding cost + ordering cost (not

including purchasing cost) for the decentralized policyf) Compute the total holding cost plus ordering cost for the

centralized policy

Assignment; Problem 3

Four outletsEach outlet demandD = 4000(50) = 200,000S= 900C = 200H = .2(200) = 40If all outlets order together

in a centralized ordering, then S= 1800

Decentralized Policy

H

DSQ

2

40

)900)(200000(2 =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.

40

)9002)(2000004(2 EOQ =8485

and a cycle inventory of 4242.5.

Total holding & ordering costs under the two policies

)2/()/( QHQDSTC

Decentralized

)2/8485(40)8485/800000(1800 TC

339411169700169711 TC

)2/3000(40)3000/200000(900 TC

1200006000060000 TC

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

Centralized

339411 compared to 480000 about 30% improvement