07_Lot Sizing in Job Shops Flashcards
Planning task of Lot Sizing and Scheduling
- determine capacity load and production schedule
- over a short-term horizon e.g. 1 week
Process plan inputs
- production tasks
- processing times
- sequence of tasks
- set up time e.g. changing setting on machine
PPM
Product Process model
(+) Product structure of MRP
(+) Process Plan [e.g. Turning, Drilling inspection]
Forward Scheduling
vs.
Backward Scheduling
Forward Scheduling
- determine EFS [earliest feasible start date] and EFE [earliest feasible end date]
- start from the first task required
Backward Scheduling
- start from the final task required using the due date
- calculate backwards using LFS, LFE
Buffer Time
in context of forward and backward scheduling
- due date - EFE
- **EFS is dependent on latest EFE of all predecessors **
Relevance of Lot Sizing
for types of production system
- Job Shop: High
- Flow Shop: 0
- Cellular manufacturing: Medium
**Relevance of compliance time with cycle time **
for the different production systems
- Job Shop: 0
- Flow Shop: high
- Cellular Manufacturing: Medium
Relevance of minimization of work-in-process and throughput times
for different production systems
- Job Shop: High
- Flow Shop: 0
- Cellular manufacturing: medium
Releavance of Determination of the order/product sequence
for different production systems
- Job Shop: medium
- Flow Shop: high
- Cellular Manufacturing: medium
Lot Sizing
in Job Shop production
- F.W. Harris (1913): “How many parts to marke at once?”
- frequent product changeover on the same machine
- setup operation before commencing production activities
- often batch-wise production on stock
- **trade-off between setup and inventory holding cots **
Lot Size = quantity of product manufactured without interruption
EOQ Model
Classic lot size model (Economic Order Quantity Model)
- single product
- single period
- constant and deterministic demand
- only setup and inventory holding costs
Simplifying Assumptions of EOQ
Economic Order Quantity Model
- constand demand per time (static modelling)
- deterministic demand
- infinite production or delviery speed
- only setup and holding costs considered
- no stockouts
- no capacity limits
**- single-product model - single-level product**
EOQ
Cost Function
C(q) = s x (D/q) + h x (q/s)
with s = setup costs
h = inventory holding costs per unit and period
D = Demand
q = lot size (variable)
EOQ model
Optimum lot size
Formula
**q(opt) = √[(2 x D x s) / h]
**
- derived from derivative of cost function dC(q) / d(q)
3 Methods for Lot Size Determination
Heuristic Procedures
- Dynamic: Silver/Meal Heuristic
Optimizing procedures
- static: Classic lot size model
- dynamic: Wagner/Within Algorithm