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
Dynamic vs Static model
Heuristic vs. Optimizing Procedures
Lot Sizing Procedures
Static
- constant demand per time unit
Dynamic
- fluctuating demand
Heuristic Procedures
- approaching optimal soluation through structured search and stopping criteria
- in general no global optimum solution found
Optimizing Procedure
- optimum solution with respect to a specific objective function
Dynamic Models for Lot Sizing
- Silver/Meal Heuristic [heuristic]
- Wagner/Within Algorithm [optimizing]
Dynamic lot sizing heuristics
General
**- adjustment to discrete timeframe of MRP
- consideration of demand fluctuations
- Basic Principle: Geneartion of lot sizes through combination fo demand from adjacent periods
- Determin Range of coverage ie. number of periods for which the lot size covers demand
Dynamic lot sizing
Algorithm
3 Steps
- Start with range of coverage of one period
- Increase range of voverage stepwise until underlying cost function reaches the first local minimum
- The lot size corresponds to total demand of all periods supplied by the range of coverage
How are inventory holding costs calculated in dynamic lot size heuristics?
- on the final inventory of a period
Silver/Meal heuristic
vs.
Wagner/Within Algorithm
Silver/Meal Heuristic
- Minimization of average costs per period
vs.
Optimum solution to dynamic lot size problem
- **no capacity limits **
- only one single product considered
- final inventory costs considered
range of coverage
in context of dynamic lot sizing heuristics
- number of periods for which the lot size covers demand [∑ of t]
- e.g. period 3-4 -> 𝜏 = 2
Wagner/Within Algorithm
Procedure
!!Don’t forget final step E!!
- Determine setup and holding costs for all paths
- Construct from to Matrix starting with first column
- when first optimum is calculated continue next column with smallest cost
- final costs are considered when arriving at E
