Summary
Summary Operations Management
- Course
- Institution
Slides and lecture notes. Geslaagd in eerste zit.
[Show more]
Seller
Follow
tessacasier
Content preview
Inventory management subject todeterministic demand
Inventory management
• Focus on two questions:
o When should an order be placed?
o How much should be ordered?
1 BASIC EOQ MODEL
Relevant costs
• Holding cost
o = carrying cost or inventory cost
o costs proportional to the quantity of inventory held
o cost of keeping €1 in inventory for 1 year
o h = Ic
with item cost c and annual interest rate I
o Includes
▪ Physical cost of space
• Rent/investment, heat, light, equipment
▪ Taxes and insurance
▪ Breakage, spoilage and deterioration
▪ Opportunity C-cost of alternative investment (WACC)
• Order cost
o Cost of placing an order from a supplier
o K
o Includes:
▪ Administration and communication costs
▪ Receiving and quality inspection costs
▪ Fixed transportation costs
Sawtooth pattern:
Q = size of
the order
T = cycle length
1
Operations Management 2019-2020 Casier Tessa
,Minimizing total (annual) costs
• Average annual cost = annual order cost + annual purchase cost + annual holding cost
• EOQ = Q to minimize the average annual cost, G(Q)
𝐾 + 𝑐𝑄 ℎ𝑄
𝐺(𝑄) = + 𝑄
𝑇 2 𝑇 =
𝐾𝜆 ℎ𝑄 𝜆
𝐺(𝑄) = + 𝜆𝑐 +
𝑄 2
with λ the average demand rate
𝐾𝜆 ℎ
𝐺 ′ (𝑄) = − 2 + = 0
𝑄 2
• Economic order quantity (EOQ)
2𝐾𝜆
𝑄∗= √
ℎ
𝜆
This also determines the optimal number of orders per year 𝑄 and the optimal reorder
𝑄
interval 𝑇 ∗= 𝜆 .
• Costs
𝑄
o Average annual holding cost = ℎ 2
𝜆
o Average annual order cost = 𝐾 𝑄
o Average annual purchase cost = 𝜆𝑐
Economic Order Quantity model: trade-off between fixed order cost and holding costs
Assumptions
• Demand rate is deterministic and constant at λ units per unit time
• Shortages are not allowed
• Orders are received instantaneously
• Cost structure:
o Fixed order cost K
o Proportional purchase costs c
o Holding cost at h per unit held per time unit
Remarks:
• Q* is the order quantity for which annual order costs equal annual holding costs
• c does not appear explicitly in the expression for Q*, but c does affect the value of Q*
indirectly because h = Ic
• Even though the EOQ minimizes the yearly holding and setup costs, it could be infeasible,
e.g., space constraint, budget constraint
Robustness of the solution – sensitivity
• Total costs are relatively stable around Q*
• Often better to order a more convenient lot size (or with a more convenient reorder interval)
close to Q*, than the precise Q*
2
Operations Management 2019-2020 Casier Tessa
, • A greater penalty cost if you order too little than too much
𝐾𝜆 ℎ𝑄 2𝐾𝜆
𝐺(𝑄) = 𝑄
+ 2
and 𝑄 ∗= √ ℎ
𝐾𝜆
ℎ 2𝐾𝜆
𝐺∗ = + √
√2𝐾𝜆/ℎ 2 ℎ
𝐾𝜆ℎ
= 2√
2
= √2𝐾𝜆ℎ
𝐺(𝑄) 𝐾𝜆/𝑄 + ℎ𝑄/2
=
𝐺∗ √2𝐾𝜆ℎ
1 2𝐾𝜆 𝑄 ℎ
= √ + √
2𝑄 ℎ 2 2𝐾𝜆
𝑄∗ 𝑄
= +
2𝑄 2𝑄 ∗
1 𝑄∗ 𝑄
= [ + ]
2 𝑄 𝑄∗
The purchase cost λc is neglected because it is not influenced by Q
Inclusion of order lead time ≤ T
• ↔ Basic EOQ assumption: orders are received instantaneously
• Constant order lead time τ ≤ T
• Reorder point, R = level of on-hand inventory at the instant an order should be placed
(R = λτ)
3
Operations Management 2019-2020 Casier Tessa
, 2 EOQ WITH FINITE PRODUCTION RATE: EPQ
Motivation for holding inventories
• Basic EOQ:
o Fixed ordering cost → Economies of scale
CYCLE INVENTORY
• EPQ (Economic Production Quantity)
o Suppose that items are produced internally at a rate P (> λ, the consumption rate)
o There is a fixed setup time/cost per batch → Economies of scale
• Setup (or changeover) cost
o Planning the order
o Lost time (and capacity) due to changeover
o Initial (warm-up) losses after setup
𝐵𝑎𝑡𝑐ℎ 𝑠𝑖𝑧𝑒
𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑔𝑖𝑣𝑒𝑛 𝑏𝑎𝑡𝑐ℎ 𝑠𝑖𝑧𝑒 =
𝑆𝑒𝑡𝑢𝑝 𝑡𝑖𝑚𝑒 + 𝐵𝑎𝑡𝑐ℎ 𝑠𝑖𝑧𝑒 × 𝑇𝑖𝑚𝑒 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡
EOQ with finite production rate
𝑄 = 𝑃 × 𝑇1
𝐻 = (𝑃 − 𝜆) × 𝑇1
𝑄
𝐻 = (𝑃 − 𝜆) ×
𝑃
𝜆
𝐻 = 𝑄 × (1 − )
𝑃
𝐾 ℎ𝐻
𝐺(𝑄) = + + 𝜆𝑐
𝑇 2
𝐾𝑄 ℎ𝑄 𝜆
𝐺(𝑄) = + (1 − ) + 𝜆𝑐
𝜆 2 𝑃
• The optimal production quantity to minimize average annual holding and set up costs has the
same form as the EOQ
• Minimizing total (annual) costs
𝐾𝑄 ℎ𝑄 𝜆
𝐺(𝑄) = + (1 − ) + 𝜆𝑐
𝜆 2 𝑃
1−𝜆
with: h’ = ℎ
𝑃
𝐾𝜆 ℎ′
𝐺′(𝑄) = − 2 + = 0
𝑄 2
• Economic production quantity (EOQ)
2𝐾𝜆
𝑄 ∗= √
ℎ′
4
Operations Management 2019-2020 Casier Tessa
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller tessacasier. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $4.87. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
60281 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now