Summary
Samenvatting Fundamentals of Operations Management (1CV00)
- Course
- Institution
Summary for the fundamentals of operations management exam of the weeks 1 - 7
[Show more]
Seller
Follow
jbtue
Content preview
1CV00 – fundamentals ofoperations management
Week 1:
Linear programming:
MAX (or MIN): f 0 (X 1 , X 2 , … , X n )
Constraints: f 1 ( X 1 , X 2 , … , X n ) ≤b 1
f k ( X 1 , X 2 , … , X n ) ≥b k
f m ( X 1 , X 2 , … , X n )=bm
Plot the constraints, optimal solution occurs where constraints intersect.
Inventory control:
Relevant costs:
Holding costs
Order and production costs
Shortage costs
Details on relevant costs:
Order costs = average number of order per time unit * costs per order
Purchasing costs = average number of orders per time unit * number of products
bought per order * cost per unit of product
Holding costs = average number of products on stock * holding costs per product per
time unit
Costs per cycle:
h∗Q
∗Q
2
K +cQ+
D
One fixed order cost (K)
Buy Q products (cQ)
Average inventory (Q/2)
Cycle duration (Q/D)
,Costs per year:
( )
h∗Q
∗Q
D 2 K∗D h∗Q
G ( Q )= ∗ K + cQ+ = + cD+
Q D Q 2
Demand D
D/Q orders
Average inventory Q/2
Optimal order quantity: Q¿ =±
√ 2 KD
h
Optimal order quantity when shortages are allowed: Q¿ =
√ 2 KD ( h+ s )
sh
Lagrange approach when multiple products have to fit in one warehouse: Q i =
¿
√ 2 K i Di
hi +2 θ c i
with θ (>0) such that the total capacity fits exactly: ∑ ci Qi=C
i
n
If the constraint is active: Q =m EOQ i where m=C / ∑ ( c i EOQi )
¿
i=1
Optimal annual costs: G ( Q )= √ 2 hKD +cD
¿
Production with finite production rate P:
D 1Q Q
Annual costs: G ( Q )= ( K + cQ+h ( P−D ) ), where D/Q is # cycles, cQ is production
Q 2P D
costs, h*1/2 is holding costs, Q/P(P-D) is maximum inventory and Q/D is cycle length.
Optimal size production run: Q=
√ 2 KD
h '
' D
where h =h(1− ) and P> D
P
Annual holding and set-up costs: √ 2 KDh '
Ordering multiple products: same cycle
2
T T
Costs per cycle:C ( T )= A+ ∑ (¿ a i+ hi Qi )=A + ∑ ( ai +hi D i )¿
i 2 i 2
A+ ∑ ai
Costs per time unit: C ( T ) = i
+ ∑ hi D i
T
T T i 2
Minimum costs at: T =√ 2 ¿¿ ¿
, Ordering multiple products: different cycles
Suppose product i is ordered every mi cycles:
Minimum costs are achieved at: T =√ 2 ¿¿ ¿
Week 2:
Lot sizing
In periodic lot sizing we consider the problem that a supplier meets in situations where
demand for products is not simply delivered from stock, but where some processing steps
have to be done before the shipment. Demand is fully known for a number of periods, the
so-called horizon, and no information is available for periods after the horizon. Two types of
costs are balanced: production set-up costs and the inventory holding costs.
Definitions and standard assumptions:
Y(t) = inventory position at the end of period t
D(t) = total demand in period t
Q(t) = production order quantity in period t
H = the number of known demand periods (horizon)
A = the fixed setup or replenishment costs
h = the carrying costs per unit of inventory per period
Rules based upon average demand
If the average demand level is D per period, the quantity is given by: EOQ = √ (¿ 2 AD /h) ¿
Rule 1: fixed quantity EOQ rule
We first determine the EOQ quantity, usually with the D-level based upon the average
demand during H periods of known demand. This quantity is rounded to the nearest integer
Qf.
Rule 2: EOQ rule
We first determine the EOQ quantity, usually with the D-level based upon the average
demand during H periods of known demand. Now, every time we produce, we will try to get
as close as possible to this quantity.
Rule 3: TEOQ fixed cycle rule (POQ)
We first determine the EOQ quantity, usually with the D-level based upon the average
demand during H periods of known demand. When we divide the EOQ quantity by the
average demand, we obtain the average time between two replenishments TEOQ. This is
rounded to the nearest integer. Every time we produce, we produce the demand for this
number of periods.
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 jbtue. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.61. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
62890 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now