07_Lot Sizing in Job Shops Flashcards

1
Q

Planning task of Lot Sizing and Scheduling

A
  • determine capacity load and production schedule
  • over a short-term horizon e.g. 1 week
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2
Q

Process plan inputs

A
  • production tasks
  • processing times
  • sequence of tasks
  • set up time e.g. changing setting on machine
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3
Q

PPM

A

Product Process model

(+) Product structure of MRP
(+) Process Plan [e.g. Turning, Drilling inspection]

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4
Q

Forward Scheduling
vs.
Backward Scheduling

A

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

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5
Q

Buffer Time

in context of forward and backward scheduling

A
  • due date - EFE
  • **EFS is dependent on latest EFE of all predecessors **
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6
Q

Relevance of Lot Sizing
for types of production system

A
  1. Job Shop: High
  2. Flow Shop: 0
  3. Cellular manufacturing: Medium
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7
Q

**Relevance of compliance time with cycle time **
for the different production systems

A
  1. Job Shop: 0
  2. Flow Shop: high
  3. Cellular Manufacturing: Medium
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8
Q

Relevance of minimization of work-in-process and throughput times
for different production systems

A
  1. Job Shop: High
  2. Flow Shop: 0
  3. Cellular manufacturing: medium
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9
Q

Releavance of Determination of the order/product sequence
for different production systems

A
  1. Job Shop: medium
  2. Flow Shop: high
  3. Cellular Manufacturing: medium
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10
Q

Lot Sizing
in Job Shop production

A
  • 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
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11
Q

EOQ Model

A

Classic lot size model (Economic Order Quantity Model)
- single product
- single period
- constant and deterministic demand
- only setup and inventory holding costs

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12
Q

Simplifying Assumptions of EOQ

Economic Order Quantity Model

A
  • 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**
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13
Q

EOQ
Cost Function

A

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)

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14
Q

EOQ model
Optimum lot size

Formula

A

**q(opt) = √[(2 x D x s) / h]
**
- derived from derivative of cost function dC(q) / d(q)

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15
Q

3 Methods for Lot Size Determination

A

Heuristic Procedures
- Dynamic: Silver/Meal Heuristic

Optimizing procedures
- static: Classic lot size model
- dynamic: Wagner/Within Algorithm

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16
Q

Dynamic vs Static model
Heuristic vs. Optimizing Procedures

Lot Sizing Procedures

A

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

17
Q

Dynamic Models for Lot Sizing

A
  • Silver/Meal Heuristic [heuristic]
  • Wagner/Within Algorithm [optimizing]
18
Q

Dynamic lot sizing heuristics
General

A

**- 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

19
Q

Dynamic lot sizing
Algorithm

3 Steps

A
  1. Start with range of coverage of one period
  2. Increase range of voverage stepwise until underlying cost function reaches the first local minimum
  3. The lot size corresponds to total demand of all periods supplied by the range of coverage
20
Q

How are inventory holding costs calculated in dynamic lot size heuristics?

A
  • on the final inventory of a period
21
Q

Silver/Meal heuristic
vs.
Wagner/Within Algorithm

A

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

22
Q

range of coverage

in context of dynamic lot sizing heuristics

A
  • number of periods for which the lot size covers demand [∑ of t]
  • e.g. period 3-4 -> 𝜏 = 2
23
Q

Wagner/Within Algorithm
Procedure

A

!!Don’t forget final step E!!

  1. Determine setup and holding costs for all paths
  2. Construct from to Matrix starting with first column
  3. when first optimum is calculated continue next column with smallest cost
  4. final costs are considered when arriving at E