Name the Motivations for holding inventory.
Economies of Scale (large batches due to high set-up costs)
Uncertainties (buffer)
Speculation (rise on value)
Transportation (in transit goods)
Smoothing (irregular demand)
Logistical system constraints e.g. truck needs to be full —> req. inventory
Reduced control costs
Protection against process errors
Outline the Characteristics of inventory systems
Demand:
Constant vs. variable
known vs. random
Lead Time:
External: Time between order & arrival
Internal: Production duration
Review Time:
Constant vs. Periodic
Excess demand
Backlog —> Lost Demand
Describe the major Questions in Inventory Management and the Balances or trade-offs between targets. Name also the relevant Costs for inventory models.
Major Questions:
How often should the inventory status be determined?
When should a replenishment order be placed?
How large should the replenishment order be?
Inventory Management balancing the trade-offs between the following cost types while obeying additional restrictions (e.g. lead time, capacities)
Balances
Set-up costs <—> Holding Costs
Holding Costs <—> Penalty Costs
Relevant Costs:
A: Fixed Costs
c: Variable costs (Stückkosten)
h: Holding Costs
p: Penalty Costs
Neus Model: EOQ-Model (Constant Demand)
Economic Order Quantity
Name the Assumptions of the EOQ-Model.
Assumptions:
Demand known
Shortages not permitted
No lead time
Instant replenishmend
Zero Inventory
Name the relevant Variables for the EOQ-Model
Q: Order quantity
T: Cycle time between orders
D: Demand per time unit t
l(t): Inventory level
Name the following Forumlas for the EOQ-Model (constant demand).
Develop the following formulars from the giben formulars or name them only.
Given:
Name the sensitivity and the Problems of the EOQ-Model with constant demand
Sensitivity:
EOQ is relative insensitive to deviations from optimal Q*
e.g. ordering 2*EOQ = 25% cost increase
Problems:
Storage capacity not considered
Selling price not considered
Neues Model: Extension of the EOQ (Discounts) with constant demand.
Name the possibe Scenarios for a quantity discount.
All unit discount
Discount is applied to all units
Incremental discount
Discount is applied to additional units
Present the All unit discount Model and bring in the prive breaks qj.
Describe the solution of the EOQ Model with All unit discount and give the algorithmus with an example
Describe the finite production rate R from the Extension of the EOQ with constant demand.
Neues Model: Extension of the EOQ (Finite production rate R) with constant demand
Name the following Formulars fpr the finite production rate R.
Develop the following Forumulars from the previous formulars and analyses the ratio of D/R
Neues Model: Multi-Item-Models (Ressource Constraints) with Constant Demand
Name the importance of Multi-Item Models and explain the different Restrictions between Multi-Item Models with Resource constraints and coordinated ordering.
Important because:
Most companies stock many different items
Restrictions for
Resource constraints:
Warehouse capacities
Budget constraints
Coordinated ordering:
Reduction of high order fixed costs (setup costs)
Realiziation of quantitys discounts
Joint transports
Name the Assumptions and the problem of the Multi-Item-Models with Resource Constraints and constant demand.
Problem:
Show the Lagrange-Multiplier Approach fpr the linear constraint. When we are we using the Lagrange multiplier approach
We are using it wehen solution is infeasible > M
Give the two types of solutions fot the Multi-Item- Model:
Scaling
Trial & Error
Was sind die Assumptions beim Multi-Idem-Model with (Coordinated ordering)
Neues Modell: Multi-Idem-Models (Coordinated ordering)
Give a short summery of the important formulas and a solution approach for the Multi Item Model.
Neues Modell: Multi-Idem-Models (Coordinated ordering): Übung 2, Aufgabe 1 a) & b)
Gib die Bezeichnungen der wichtigen Variablen an (Multi-Idem-Models (Coordinated ordering)
Gib die Formeln für folgende Begriffe an:
Gib den Algorithmus für Multi-Idem-Models (Coordinated ordering) an.
Neues Modell: Wagner Within (Time varying demand): Übung 2, Aufgabe 4 & 5
Gib die Assumptions an (Wagner Within (Time varying demand))
Gib die Variablen und die Problemformulierung an (Wagner Within (Time varying demand)).
Was sind die Eigenschaften des Modells? (Wagner Within (Time varying demand))
Gib die Formel zur Lösung an (Wagner Within (Time varying demand)).
Gib den Algorithmus an (Wagner Within (Time varying demand)).
Neues Model: Multi-Item- Models (Time varying demand)
Which generalization is the time varying demand multi-item model?
Name the Problem and the important variables for the Multi-item-Model fpr time varyying demand
Fehler hier fehlt das i beim c —> c_i
Give the different interaction models für Multi-Item mode with time varying demand an and the important variables. What type of variable was ignoried and why?
Give the Assumptions fpr Capacitated lot sizing problem (CLSP) and the problem formulation (Big Bucket Model).
—> Fehler bei A. —> A ist eigentlich abhängig von j also vom Produkt
Give the Assumptions and the model of the Disrete lot sizing & scheduling problem (DLSSP).
Aus Vorlesung: Wie lässt sich das System in einer Nebenbedingung auf zwei Maschinen erweiter: Ganz einfach man könnte z_j,t <= 2 einfach machen und es wäre möglich zwei maschinen parallel zu fahren.
Kommentar:
we compute here how much we can produce von from product in i.e. half an hour.
Wir habenm z.b. 30 min verfügbar (qt) und das Produkt benötigt 5 min. Dann können wir 6 Stück produzieren. ( bei Qt/aj)
das model wird benutzt weil es sich schneller berechnen lässt. Wir haben hier im gegensatz zu dem CSLSP kein Xjt. Deshalb haben wir wesentlich weniger Variablen.
Give the Assumptions of the Continous setup lot sizing problem (CSLSP) and give the model.
Hier immer noch fehler!!!! bei A fehlt ein j —> Aj
x ist demand und wir beschränken die Menge die Produzieren wir produzieren wollen.
Give the Assumptions for time variying multi-item model with joint fixed (setup) costs.
Advanced MIP approach —> nochmal anschauen
Neues Thema: Inventory Models mit Stochastic demand
Gib die verschiedenen Klassifikationen des Lagerbestands an bei Inventory Models mit stochastic demand
Welche Unsicherheiten gibt es bei Inventory Models mit stochastic demand?
Gib die verschiedenen Modelltypen an, die Vor - und Nachteile und das Ziel der Zielfunktion von Inventory Models mit stochastic demand.
Gib die verschiedenen Service-Levels an für Inventory Models mit stochastic demands.
Neues Model: Newsvendor Problem (Stochastic Demand)
Gib die Modellannahmen des Newsvendor Problem (Stochastic Demand) wieder.
Welche wichtigen Variablen gibt es im Newsvendor Problem (Stochastic Demand)?
Gib die Formeln des Newsvendor Problem (Stochastic Demand) für folgende Ausdrücke an:
Gib mir die Herangehensweise der Problemlösung für Normal Verteilte Nachfrage und Diskret Verteilte Nachfrage.
Welche Möglichen Erweiterungen gibt es beim Newsvendor Model (stochastic Demand)?
Mit Anfangslagerbestand
Mehrere Planungsperioden
Neues Model: Reorder Point - Lot size system (stochastic demand)
Gib das komplette Modell der Reorder Point - Lot size system (stochastic demand) wieder.
Zuletzt geändertvor einem Jahr
