Classification of machine occupancy models

The classification of machine usage models is a common scheme used in machine usage planning to classify the large number of existing models. The following representation is common:

${\displaystyle [\alpha |\beta |\gamma ]}$ With

${\displaystyle \alpha }$: Machine characteristics

${\displaystyle \beta }$: Order characteristics

${\displaystyle \gamma }$: Goal setting

${\displaystyle [IP|g_{j}=3|D]}$symbolizes, for example, a model with identical and parallel machines (IP) and its objective is to minimize throughput time (D). Each of the orders consists of exactly three work steps.

Machine characteristics

α ₁ : machine type and arrangement

• ${\displaystyle \circ }$: An available machine
• ${\displaystyle IP}$: Identical parallel machines
• ${\displaystyle UP}$: Uniform parallel machines (with different production speeds)
• ${\displaystyle F}$: Flow shop
• ${\displaystyle J}$: Job shop
• ${\displaystyle O}$: Open shop

α ₂ : number of machines

• ${\displaystyle \circ }$: Any number
• ${\displaystyle m}$: exactly m machines

Order characteristics

β ₁ : number of orders

• ${\displaystyle n=const}$: A certain number of orders is given. Often n = 2.
• ${\displaystyle \circ }$: Any number

β ₂ : interruptibility

• ${\displaystyle pmtn}$: Interruption (eng. Preemption) is possible
• ${\displaystyle \circ }$: No interruption
• ${\displaystyle nowait}$: After a work step has been carried out, the next work step must begin immediately.

β ₃ : order relationship

• ${\displaystyle prec}$: Fixed order in the form of a graph
• ${\displaystyle tree}$: Graph in the form of a tree
• ${\displaystyle \circ }$: no sequence relationships

β ₄ : Release date and follow-up time

• ${\displaystyle a_{j}}$: Different order release times
• ${\displaystyle n_{j}}$: Follow-up times are given. After completion of a work cycle, the order must wait a certain time before it can be processed further.
• ${\displaystyle \circ }$: all orders are available from the start and there are no follow-up times

β ₅ : processing time

• ${\displaystyle t_{j}}$or makes statements about the duration of the processing time of the entire order or the individual work steps ${\displaystyle t_{ij}}$
• ${\displaystyle \circ }$: any processing times

β ₆ : sequence-dependent set-up times

• ${\displaystyle \tau _{jk}^{i}}$: Sequence- dependent set-up time from order j to order k on machine i
• ${\displaystyle \tau b_{jk}^{i}}$: The orders can be grouped into families
• ${\displaystyle \circ }$: no sequence-dependent set-up times

β ₇ : resource constraints

• ${\displaystyle res}$ ${\displaystyle \lambda \sigma \rho }$
  • ${\displaystyle \lambda }$: Number of resources
  • ${\displaystyle \sigma }$: Availability of resources
  • ${\displaystyle \rho }$: Need for resources
• ${\displaystyle \circ }$: no resource restrictions

β ₈ : completion dates

• ${\displaystyle f_{j}}$: Completion dates are mandatory for every order
• ${\displaystyle \circ }$: no dates given

β ₉ : number of operations

• ${\displaystyle g_{j}}$: Each order consists of exactly / a maximum of n operations
• ${\displaystyle \circ }$: Any number of operations

β ₁₀ : storage restrictions

• ${\displaystyle \kappa ={\kappa _{1},...,\kappa _{m}}}$: Indicates the available interim storage facility for the i-th machine
• ${\displaystyle \circ }$: every machine has a warehouse with an infinitely large capacity

Goal setting

• ${\displaystyle D}$: Minimizing the lead time
• ${\displaystyle Z}$: Minimization of the cycle time / total processing time
• ${\displaystyle T}$: Minimizing the schedule deviation
• ${\displaystyle V}$: Minimizing the delay
• ${\displaystyle L}$: Minimizing idle time

literature

• Domschke, Scholl, Voß: Production Planning - Process Organizational Aspects , Berlin, Springer, 1993 pp. 283–299.