Uitleg aan de hand van veel voorbeelden!
Onderwerpen die behandeld zijn:
- Terminology
- EOQ Models
- Lead Time (constant and stochastic)
- EOQ with quantity discounts
- Continuous Rate EOQ Model
- Newsboy Problem
- (r,q) In Case Of Backlogging
- Determine TC(q,r) (Holding Cost, Shortage ...
There are 2 ways of approaching models, deterministic and stochastic models
o (Ch. 15 & 16 respectively)
Deterministic models (based on real input data, absence of randomness)
o Constant demand (continuous review)
Economic Order Quantity (ch. 15.2)
EOQ with quantity discounts (ch. 15.3)
Continuous rate EOQ/EBQ (ch. 15.4)
EOQ with backorders allowed (ch. 15.5) (During this year 23/24, this is not asked in
exam, so it is also not covered in this summary)
o Nonconstant demand (periodic review)
Wagner-Whitin, Silver-Meal (ch. 18.7) (Discussed earlier)
Stochastic models (includes randomness and uncertainty)
o Single-period inventory models
Newsboy problem
o Continuous review models
Cost based (r,q) and (s, S) models
Service level based
o Periodic review models
(R, S) models
Terminology
o 𝒒 = 𝒐𝒓𝒅𝒆𝒓 𝒒𝒖𝒂𝒏𝒕𝒊𝒕𝒚
o 𝑲 = 𝒐𝒓𝒅𝒆𝒓𝒊𝒏𝒈 𝒄𝒐𝒔𝒕𝒔
o 𝒉 = 𝒉𝒐𝒍𝒅𝒊𝒏𝒈 𝒄𝒐𝒔𝒕𝒔
o 𝑫 = 𝒅𝒆𝒎𝒂𝒏𝒅
o 𝒓 = 𝒓𝒆𝒐𝒓𝒅𝒆𝒓 𝒑𝒐𝒊𝒏𝒕
o 𝑬𝑶𝑸 = 𝒆𝒄𝒐𝒏𝒐𝒎𝒊𝒄 𝒐𝒓𝒅𝒆𝒓 𝒒𝒖𝒂𝒏𝒕𝒊𝒕𝒚
o 𝑳 = 𝒍𝒆𝒂𝒅 𝒕𝒊𝒎𝒆
28
, Julian Klep
OR Models for Pre-Master IEM
Winston Ch. 1, 3, 9, 15, 16, 18, 20
BASIC EOQ MODEL
For any order, ordering and setup cost K
Cost per unit per year of inventory is h
o Given directly or as percentage of purchasing price
Unit purchase price p
Assumptions
o Repetitive ordering
o Constant demand
o Continuous ordering
o Zero lead time (instantaneous delivery)
Find q that minimizes total annual cost (q*)
𝑻𝑪(𝒒) = 𝒐𝒓𝒅𝒆𝒓𝒊𝒏𝒈 𝒄𝒐𝒔𝒕
+ 𝒑𝒖𝒓𝒄𝒉𝒂𝒔𝒊𝒏𝒈 𝒄𝒐𝒔𝒕
+ 𝒉𝒐𝒍𝒅𝒊𝒏𝒈 𝒄𝒐𝒔𝒕
, Julian Klep
OR Models for Pre-Master IEM
Winston Ch. 1, 3, 9, 15, 16, 18, 20
EXAMPLE 17 – ORDERIN G CAMERAS (P.854)
Deterministic – stochastic model
Given is the following
o Demand D = 10000 cameras per year
o Ordering cost K = $5
o Cost price = $100
o Capital opportunity cost hd = 20%
Calculations
o ℎ = 𝑝 ⋅ ℎ = 100 ⋅ 0.20 =
20 (ℎ𝑜𝑙𝑑𝑖𝑛𝑔 𝑐𝑜𝑠𝑡)
⋅ ⋅
o 𝐸𝑂𝑄 = = = √5000 =
70
70.71 =
71
Remarks
o 𝐸𝑂𝑄 → ℎ𝑜𝑙𝑑𝑖𝑛𝑔 𝑐𝑜𝑠𝑡 = 𝑜𝑟𝑑𝑒𝑟𝑖𝑛𝑔 𝑐𝑜𝑠𝑡
o 𝑇𝐶(𝑞) is reasonable flat around the EOQ
o Small variations in K, D, h have little effect on EOQ
NONZERO LEAD TIME
DEFINITION S
Safety stock is inventory buffer against uncertainty in demand and supply (Stochastic)
o Actual demand deviates from forecast
o Timing of supply shows unpredictable variation (Lead Time variation)
o Quantity of supply shows unpredictable variation
On-Hand stock or physical stock always ≥ 0 [𝑂𝐻𝐼(𝑡)]
Stockout
o Event that D > OHI
Backorders or backlog
o Amount of unfilled demand waiting to be filled when replenishment order arrives [𝐵(𝑡)]
Net stock or inventory
o 𝐼(𝑡) = 𝑂𝐻𝐼(𝑡) − 𝐵(𝑡)
o In deterministic cases
There are no shortages, so 𝐼(𝑡) = 𝑂𝐻𝐼(𝑡)
Economic inventory = 𝑂𝐻𝐼(𝑡) + On-order inventory
30
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 julian19. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $3.43. You're not tied to anything after your purchase.
