Logistics Management: Car Max company discussion I must create original quantitative questions. Each quantitative problem should have a clearly stated prob
Logistics Management: Car Max company discussion I must create original quantitative questions. Each quantitative problem should have a clearly stated problem description and be followed by a sample solution. I have attached the slides as well as an exercises sheet that you can refer to for the assignment. I need 3 problems with their solutions.You can refer to both but can use the same wording or numbers, so you can rephrase the questions and change the company names for example. Chapter 11
10.
Harley purchases components from three suppliers. Components purchased from Supplier
A are priced at $5 each and used at the rate of 20,000 units per year. Components purchased
from Supplier B are priced at $4 each and are used at the rate of 2,500 units per year.
Components purchased from Supplier C are priced at $5 each and used at the rate of 900 units
per year. Currently, Harley purchases a separate truckload from each supplier. As part of its
JIT drive, Harley has decided to aggregate purchases from the three suppliers. The trucking
company charges a fixed cost of $400 for the truck with an additional charge of $100 for each
stop. Thus, if Harley asks for a pickup from only one supplier, the trucking company charges
$500; from two suppliers, it charges $600; and from three suppliers, it charges $700. Suggest
a replenishment strategy for Harley that minimizes annual cost. Assume a holding cost of 20
percent per year. Compare the cost of your strategy with Harleys current strategy of ordering
separately from each supplier. What is the cycle inventory of each component at Harley?
(a) We first consider the case of ordering separately:
For supplier A:
Order quantity (Q) =
2(20000)( 400 + 100)
= 4,472 units/order
(0.2)(5)
Total cost = order cost + holding cost = (20000/4472)(500) + (4472/2)(0.2)(5) = $4,472
Similarly, for suppliers B and C the order quantities are 1768 and 949 and the associated total
costs are $1,414 and $949, respectively.
So, the total costs are $6,835
(b) In using complete aggregation, we evaluate the order frequency (n*) as follows:
So, n* of the case is =
D A hC A + DB hC B + DC hCC
2S *
S* = 400 + 3(100) = $700
So, n* =
20000(0.2)(5) + 2500(0.2)( 4) + 9000(0.2)(5)
= 4 orders/year
2(700)
Annual Ordering costs = (4 orders per year)*($700 per order) = $2,800.
Holding Costs:
For supplier A:
Q = D/n = 20000/4 = 5000 units/order ? cycle inventory = 5000/2 = 2,500 units
Holding cost = (5000/2)(0.2)(5) = $2,500
For supplier B:
Q = D/n = 2,500/4 = 625 units/order ? cycle inventory = 625/2 = 312.5 units
Holding cost = (625/2)(0.2)(4) = $250
For supplier C:
Q = D/n = 900/4 = 225 units/order ? cycle inventory = 225/2 = 112.5 units
Holding cost = (225/2)(0.2)(5) = $112.5
Total costs = Ordering costs + Holding costs = $2,800 + ($2,500 + $250 + $112.5) = $5,662.50
Costs savings from aggregation = TC (ordering separately) TC (complete aggregation)
= $6,835 – $5,662.50 = $1,172.50
19. SuperPart, an auto parts distributor, has a large warehouse in the Chicago region and is
deciding on a policy for the use of TL or LTL transportation for inbound shipping. LTL
shipping costs $1 per unit. TL shipping costs $800 per truck plus $100 per pickup. Thus, a
truck used to pick up from three suppliers costs 800 + 3 ? 100 = $1,100 . A truck can carry up
to 2,000 units. SuperPart incurs a fixed cost of $100 for each order placed with a supplier.
Thus, an order with three distinct suppliers incurs an ordering cost of $300. Each unit costs
$50, and SuperPart uses a holding cost of 20 percent. Assume that product from each supplier
has an annual demand of 3,000 units.
a. What is the optimal order size and annual cost if LTL shipping is used? What is the time
between orders?
b. What is the optimal order size and annual cost if TL shipping is used with a separate truck
for each supplier? What is the time between orders?
(a) LTL costs with one supplier per truck:
Optimal order quantity QLTL =
2(3000)(100)
= 245 units
(0.2)(50)
? 245 ?
?12 = 0.98 months
? 3000 ?
Time between orders = ?
3000
(100) = $1225
245
Annual trucking cost = 3000(1) = $3000
245
(10) = $1225
Annual holding cost =
2
Annual order cost =
Total Cost for LTL = $5449 per supplier
(b) TL costs with one supplier per truck:
Optimal order quantity QTL =
2(3000)(1000)
= 775 units
(0.2)(50)
? 775 ?
?12 = 3.1 months
? 3000 ?
Time between orders = ?
3000
(100) = $387
775
3000
(900) = $3486
Annual trucking cost =
775
775
(10) = $3873
Annual holding cost =
2
Annual order cost =
Total Cost for TL = $7746 per supplier
22. Crunchy, a cereal manufacturer, has dedicated a plant for one major retail chain. Sales at the
retail chain average about 20,000 boxes a month and production at the plant keeps pace with
this average demand. Each box of cereal costs Crunchy $3 and is sold to the retailer at a
wholesale price of $5. Both Crunchy and the retailer use a holding cost of 20 percent. For
each order placed, the retailer incurs an ordering cost of $200. Crunchy incurs the cost of
transportation and loading that totals $1,000 per order shipped.
a. Given that it is trying to minimize its ordering and holding costs, what lot size will the
retailer ask for in each order? What is the annual ordering and holding cost for the retailer
as a result of this policy? What is the annual ordering and holding cost for Crunchy as a
result of this policy? What is the total inventory cost across both parties as a result of this
policy?
b. What lot size minimizes the inventory costs (ordering, delivery, and holding) across both
Crunchy and the retailer? How much reduction in cost relative to (a) results from this
policy?
c. Design an all unit quantity discount that results in the retailer ordering the quantity in (b).
(a) From the retailers standpoint, the optimal order quantity is:
Q=
2(240000)( 200)
= 9798 units/order
0.2(5)
Retailer costs:
Order costs = (240000/9798)(200) = $4,899
Holding costs = (9798/2)(0.2)(5) = $4,899
Retailer total cost = $9,798
Crunchys costs:
Order costs = (240000/9798)(1000) = $24,495
Holding costs = (9798/2)(0.2)(3) = $2,939
Crunchy total cost = $27,434
Total cost = $37,232
(b) In jointly optimizing the order quantity is:
Q=
2(240000)( 200 + 1000)
= 18974 units/order
0.2(5) + 0.2(3)
Retailer costs:
Order costs = $2,530
Holding costs = $9,487
Retailer total cost = $12,017
Crunchys costs:
Order costs = $12,649
Holding costs = $5,692
Crunchy total cost = $18,341
Total cost = $30,358
(c) The retailer costs increase from $9,798 (retailer optimization) to $12,017 (SC optimization)
? an increase of $2,219. Thus the minimum discount per unit that Crunchy must offer is
$2,219/240,000 = $0.00917 in order to entice the retailer to order in lots of 18,974 units.
So the price schedule from Crunchy to the retailer could be as follows:
$5 per unit for order sizes of 0 units to 18,973 units
$5 – $0.00917 = $4.99083 per unit for order sizes of 18,974 units.
24. The Orange company has introduced a new music device called the J-Pod. The J-Pod is sold
through Good Buy, a major electronics retailer. Good Buy has estimated that demand for the JPod will depend on the final retail price p according to the demand curve
Demand D = 2, 000, 000 ? 2, 000 p
The production cost for Orange is $100 per J-Pod.
a. What wholesale price should Orange charge for the J-Pod? At this wholesale price, what
retail price should Good Buy set? What are the profits for Orange and Good Buy at
equilibrium?
b. If Orange decides to discount the wholesale price by $40, how much of a discount should
Good Buy offer to customers if it wants to maximize its own profits? What fraction of the
discount offered by Orange does Good Buy pass along to the customer?
(a) Profit function for Good Buy: (p c) (2,000,000 2,000p)
Profit function for The Orange Company: (c 100) (2,000,000 2,000p)
Optimizing price (p) for Good Buy: p = (2,000,000/(2,000(2)) +(c/2) = 500 + 0.5c
Substituting Good Buys optimizing price, p, into Orange Companys profit function:
(c 100) (2,000,000 2,000 (500+.5c)) = (c 100) (1,000,000 1,000c)
Optimizing the wholesale cost for Orange company:
c = (1,000,000/(1,000(2)) + (100/2) = 500 + 50 = $550 ? c = $550 (wholesale price)
Substituting c into Good Buys optimal pricing function:
p = 500 + 0.5(550) = $775 ? p = $775 (optimal retail price for Good Buy)
Profit for Good Buy: (775 550) (2,000,000 2,000(775)) = $101,250,000
Profit for Orange Company: (550 100) (2,000,000 2,000(775)) = $202,500,000
(b) If Orange offers a $40 discount to Good Buy, then the new wholesale price, c, would be $510 (i.e.
$550 – $40). Then Good Buy would set its sales price to 500 + 0.5(510) = $755. Thus, Good Buy
is only passing along $20 (i.e. $775 – $755) or 50% of the discount given to them as a discount to
their customers.
11
Managing Economies of Scale
in a Supply Chain
Cycle Inventory
PowerPoint presentation
to accompany
Chopra and Meindl
Supply Chain Management, 6e
Copyright © 2016 Pearson Education, Inc.
11 1
Learning Objectives
1. Balance the appropriate costs to choose the optimal
lot size and cycle inventory in a supply chain.
2. Understand the impact of quantity discounts on lot
size and cycle inventory.
3. Devise appropriate discounting schemes for a
supply chain.
4. Understand the impact of trade promotions on lot
size and cycle inventory.
5. Identify managerial levers that reduce lot size and
cycle inventory in a supply chain without increasing
cost.
Copyright © 2016 Pearson Education, Inc.
11 2
Role of Cycle Inventory
in a Supply Chain
Lot or batch size is the quantity that a stage of a
supply chain either produces or purchases at a time
Cycle inventory is the average inventory in a supply
chain due to either production or purchases in lot
sizes that are larger than those demanded by the
customer
Q: Quantity in a lot or batch size
D: Demand per unit time
Copyright © 2016 Pearson Education, Inc.
11 3
Inventory Profile
FIGURE 11-1
Copyright © 2016 Pearson Education, Inc.
11 4
Role of Cycle Inventory
in a Supply Chain
lot size Q
Cycle inventory =
=
2
2
average inventory
Average flow time =
average flow rate
Average flow time
cycle inventory Q
=
resulting from cycle =
demand
2D
inventory
Copyright © 2016 Pearson Education, Inc.
11 5
Role of Cycle Inventory
in a Supply Chain
lot size Q
Cycle inventory =
=
2
2
For lot sizes of 1,000 and daily demand of 100
average inventory
Average
flow
time =
Average
flow
time
Q
1,000
average
flow= rate
resulting from cycle =
=
5 days
2D 2´100
inventory
Average flow time
cycle inventory Q
=
resulting from cycle =
demand
2D
inventory
Copyright © 2016 Pearson Education, Inc.
11 6
Role of Cycle Inventory
in a Supply Chain
Lower cycle inventory has
Shorter average flow time
Lower working capital requirements
Lower inventory holding costs
Cycle inventory is held to
Take advantage of economies of scale
Reduce costs in the supply chain
Copyright © 2016 Pearson Education, Inc.
11 7
Role of Cycle Inventory
in a Supply Chain
Average price paid per unit purchased is a key
cost in the lot-sizing decision
Material cost = C
Fixed ordering cost includes all costs that do
not vary with the size of the order but are
incurred each time an order is placed
Fixed ordering cost = S
Holding cost is the cost of carrying one unit in
inventory for a specified period of time
Holding cost = H = hC
Copyright © 2016 Pearson Education, Inc.
11 8
Role of Cycle Inventory
in a Supply Chain
Following costs considered in lot sizing
decisions
Average price per unit purchased, $C/unit
Fixed ordering cost incurred per lot, $S/lot
Holding cost incurred per unit per year,
$H/unit/year = hC
Copyright © 2016 Pearson Education, Inc.
11 9
Role of Cycle Inventory
in a Supply Chain
Primary role of cycle inventory is to allow
different stages to purchase product in lot sizes
that minimize the sum of material, ordering,
and holding costs
Ideally, cycle inventory decisions should
consider costs across the entire supply chain
In practice, each stage generally makes its own
supply chain decisions
Increases total cycle inventory and total costs
in the supply chain
Copyright © 2016 Pearson Education, Inc.
11 10
Key Point
Cycle inventory exists in a supply chain
because different stages exploit
economies of scale to lower total cost. The
costs considered include material cost,
fixed ordering cost, and holding cost.
Copyright © 2016 Pearson Education, Inc.
11 11
Role of Cycle Inventory
in a Supply Chain
Economies of scale exploited in three
typical situations
1. A fixed cost is incurred each time an order
is placed or produced
2. The supplier offers price discounts based
on the quantity purchased per lot
3. The supplier offers short-term price
discounts or holds trade promotions
Copyright © 2016 Pearson Education, Inc.
11 12
Estimating Cycle Inventory Related
Costs in Practice
Ordering Cost
Buyer time
Transportation costs
Receiving costs
Other costs
Inventory Holding Cost
Obsolescence cost
Handling cost
Occupancy cost
Miscellaneous costs
Theft, security, damage, tax, insurance
Copyright © 2016 Pearson Education, Inc.
11 13
Economies of Scale
to Exploit Fixed Costs
Lot sizing for a single product (EOQ)
Annual demand of the product
Fixed cost incurred per order
Cost per unit
Holding cost per year as a fraction of product
cost
Basic assumptions
Demand is steady at D units per unit time
No shortages are allowed
Replenishment lead time is fixed
D
S
C
h
=
=
=
=
Copyright © 2016 Pearson Education, Inc.
11 14
Economies of Scale
to Exploit Fixed Costs
Minimize
Annual material cost
Annual ordering cost
Annual holding cost
Copyright © 2016 Pearson Education, Inc.
11 15
Lot Sizing for a Single Product
Annual material cost = CD
D
Number of orders per year =
Q
æ Dö
Annual ordering cost = ç ÷ S
èQø
æQ ö
æQö
Annual holding cost = ç ÷ H = ç ÷ hC
è2ø
è2ø
æ Dö
æQ ö
Total annual cost, TC = CD + ç ÷ S + ç ÷ hC
èQø
è2ø
Copyright © 2016 Pearson Education, Inc.
11 16
Lot Sizing for a Single Product
FIGURE 11-2
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11 17
Lot Sizing for a Single Product
The economic order quantity (EOQ)
2DS
Optimal lot size, Q* =
hC
The optimal ordering frequency
D
n* =
=
Q*
Copyright © 2016 Pearson Education, Inc.
DhC
2S
11 18
EOQ Example
Demand for Deskpro computer at Best Buy is 1,000 units per month.
Best Buy incurs a fixed order placement, transportation and receiving
cost of $4,000 each time an order is placed. Each computer costs Best
Buy $500 and the retailer has a holding cost of 20 percent. Evaluate
the number of computers that the store manager should order in each
replenishment lot.
Annual demand, D = 1,000 x 12 = 12,000 units
Order cost per lot, S = $4,000
Unit cost per computer, C = $500
Holding cost per year as a fraction of unit cost, h = 0.2
2 ´12,000 ´ 4,000
Optimal order size = Q* =
= 980
0.2 ´ 500
Copyright © 2016 Pearson Education, Inc.
11 19
EOQ Example
Q * 980
Cycle inventory =
=
= 490
2
2
D
Number of orders per year =
= 12.24
Q*
æ Q *ö
D
Annual ordering and holding cost =
S +ç
÷ hC = $97,980
Q* è 2 ø
Q*
490
Average flow time =
=
= 0.041 = 0.49 month
2D 12, 000
Copyright © 2016 Pearson Education, Inc.
11 20
Key Point
Total ordering and holding costs are
relatively stable around the economic
order quantity. A firm is often better
served by ordering a convenient lot size
close to the EOQ rather than the precise
EOQ.
Copyright © 2016 Pearson Education, Inc.
11 21
EOQ Example
Lot size reduced to Q = 200 units
æQ ö
D
Annual inventory-related costs = S + ç ÷ hC = $250,000
Q
è2ø
Copyright © 2016 Pearson Education, Inc.
11 22
Lot Size and Ordering Cost
If the lot size Q* = 200, how much should
the ordering cost be reduced?
Desired lot size, Q* = 200
Annual demand, D = 1,000 × 12 = 12,000 units
Unit cost per computer, C = $500
Holding cost per year as a fraction of inventory value, h = 0.2
hC(Q*)2 0.2 ´ 500 ´ 2002
S=
=
= $166.7
2D
2´12,000
Copyright © 2016 Pearson Education, Inc.
11 23
Production Lot Sizing
The entire lot does not arrive at the same time
Production occurs at a specified rate P
Inventory builds up at a rate of P D
QP =
Annual setup cost
æ Dö
ç P ÷S
èQ ø
Copyright © 2016 Pearson Education, Inc.
2DS
(1 D / P)hC
Annual holding cost
æQP ö
(1 D / P) ç
÷ hC
è 2 ø
11 24
Lot Sizing with Capacity Constraint
If order size is constrained to K units
and Q > K,
Compare the cost of ordering K units and the EOQ
Optimal order size is the minimum of EOQ and
capacity K
Copyright © 2016 Pearson Education, Inc.
11 25
Aggregating Multiple Products
in a Single Order
Savings in transportation costs
Reduces fixed cost for each product
Lot size for each product can be reduced
Cycle inventory is reduced
Single delivery from multiple suppliers or
single truck delivering to multiple retailers
Receiving and loading costs reduced
Copyright © 2016 Pearson Education, Inc.
11 26
Key Point
Aggregating replenishment across
products, retailers, or suppliers in a single
order allows for a reduction in lot size for
individual products because fixed ordering
and transportation costs are now spread
across multiple products, retailers, or
suppliers.
Copyright © 2016 Pearson Education, Inc.
11 27
Lot Sizing with Multiple
Products or Customers
Ordering, transportation, and receiving
costs grow with the variety of products or
pickup points
Lot sizes and ordering policy that minimize
total cost
Di: Annual demand for product i
S: Order cost incurred each time an order is placed,
independent of the variety of products in the order
si: Additional order cost incurred if product i is included
in the order
Copyright © 2016 Pearson Education, Inc.
11 28
Lot Sizing with Multiple
Products or Customers
Three approaches
1. Each product manager orders his or her model
independently
2. The product managers jointly order every
product in each lot
3. Product managers order jointly but not every
order contains every product; that is, each lot
contains a selected subset of the products
Copyright © 2016 Pearson Education, Inc.
11 29
Multiple Products Ordered and
Delivered Independently
Best Buy sells three models of computers: Litepro
(12,000 units annual demand), Medpro (1,200
/year), and Heavypro (120/year). Each model
costs Best Buy $500. A fixed transportation cost
of $4,000 is incurred each time an order is
delivered. For each model ordered and delivered
on the same truck, an additional fixed cost of
$1,000 per model is incurred for receiving and
storage. Best Buy incurs a holding cost of 20
percent. Evaluate the lot sizes that the Best Buy
manager should order if lots for each product are
ordered and delivered independently. Also,
evaluate the annual cost of such a policy.
Copyright © 2016 Pearson Education, Inc.
11 30
Multiple Products Ordered and
Delivered Independently
Demand
DL = 12,000/yr, DM = 1,200/yr, DH = 120/yr
Common order cost
S = $4,000
Product-specific order cost
sL = $1,000, sM = $1,000, sH = $1,000
Holding cost
h = 0.2
Unit cost
CL = $500, CM = $500, CH = $500
Copyright © 2016 Pearson Education, Inc.
11 31
Multiple Products Ordered and
Delivered Independently
Litepro
Medpro
Heavypro
Demand per year
12,000
1,200
120
Fixed cost/order
$5,000
$5,000
$5,000
1,095
346
110
548
173
55
$54,772
$17,321
$5,477
11.0/year
3.5/year
1.1/year
$54,772
$17,321
$5,477
Average flow time
2.4 weeks
7.5 weeks
23.7 weeks
Annual cost
$109,544
$34,642
$10,954
Optimal order size
Cycle inventory
Annual holding cost
Order frequency
Annual ordering cost
Total annual cost = $155,140
Copyright © 2016 Pearson Education, Inc.
TABLE 11-1
11 32
Lots Ordered and Delivered Jointly
S* = S + sL + sM + sH
Annual order cost = S * n
DL hC L DM hCM DH hC H
Annual holding cost =
+
+
2n
2n
2n
DL hC L DM hCM DH hC H
Total annual cost =
+
+
+S*n
2n
2n
2n
n* =
DL hC L + DM hCM + DH hC H…
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