2- Production planning models and systems Flashcards
What are the three classical production planning model?
1) Single-item uncapacited lot-sizing model (LS-U)
2) Master Production Schedule (MPS)
3) Material Requirement Planning (MRP)
General properties of Uncapacitated Lot-Sizing Model (LS-U)
Single-item, single-level, uncapacitated
Minimize total cost
Production cost (fixed + variable)
Inventory cost per unit in inventory at the end of each period
Satisfy all demand
Backlogging not allowed
No production capacity (infinite)
State the LS-U
Sets:
T = {0, . . . ,t, . . . , n}: discrete time periods
Parameters:
pt
: unit production cost in period t
qt
: fixed production cost in period t
ht
: unit inventory cost in period t
dt
: demand in period t
Decision variables:
xt
: production lot size in period t
yt
: binary variable for period t (yt = 1 if xt > 0)
st
: inventory at the end of the period t
(LS-U) min sum (pt xt + qt yt + ht st) for t∈T :t≥1
st−1 + xt = dt + st t ∈ T : t ≥ 1 (2)
s0 = sn = 0 (3)
xt ≤ Mt yt t ∈ T : t ≥ 1 (4)
xt ≥ 0 t ∈ T : t ≥ 1 (5)
st ≥ 0 t ∈ T (6)
yt ∈ {0, 1} t ∈ T : t ≥ 1 (7)
General properties of Master production scheduling Model (MPS)
Multi-item, single level, capacitated lot-sizing model
Production of a set of items (finished products)
Short-term horizon (at least total production cycle)
For each item, the model is the same as the LS-U
The items production plans are linked: capacity restrictions and common resources
State the Master production schedule (MPS)
General properties of the material requirement planning (MRP)
State the material requirement planning (MRP)
Make-to-stock (MTS)
Make-to-stock (MTS): independent demand must be already in stock
All procurement and production activities in anticipation of the demand (demand
forecasts)
Ideal for standard products, little variety or diversity (fast-moving consumer goods)
Make-to-order (MTO) or Assemble-to-order (ATO):
Some activities are performed after the external ordering
Delivery lead-time: time promised to customers for delivery
At the time of ordering: enough raw materials or semi-finished products in inventory
Remaining production lead-time ≤ commercial lead-time
Push phase (upstream)
Push phase (upstream) plans the procurement and production from raw materials up to
semi-finished products (demand forecast of semi-finished products)
Pull phase (downstream)
Pull phase (downstream) plans the production from semi-finished products (in
inventory) up to finished products (effective customer orders)
For which production policy is MRP used?
Customer-service leve
Customer-service level =% customer demand delivered on time
(minimal planning horizon length)
Total lead-time represents the required anticipation time in the planning process
(minimal planning horizon length)
Rolling-horizon approach:
the solution proposed for the early time periods is
implemented, the model parameters are updated, the model is solved again,…
Bill of materials (BOM) to compute dependent demand
Link BOM and MRP
Aspects of the MRP
1) Independent demand over the planning horizon d-i_t
2) Bill of materials (BOM) to compute dependent demand
3) Procurement and production lead-times (LTs)
4) Routing of components
5) Capacity of resources
6) Inventory records
7) Planning rules
Includes of the Independent demand over the planning horizon d
i_t
demand from customers
spare parts demand
demands from the distribution
System or other facilities
Procurement and production lead-times (LTs)
Procurement and production cannot be performed instantaneously: the BOM
includes LTs
Total time needed to complete orders, preparation, administration, waiting,
production, control tests, delivery (integer number of periods)
In MRP model, LTs constant over times and independent of the order size (input)
Link LTs and MRP
The procurement or production LT is modeled in (2) by γ
i
The number of time periods n ≥ the sum of γ
i
along any path in the BOM graph
γ
i
(planning)! = production lead-time
Routing of components and link to MRP
Link Capacity of resources to the MRP model
Link capacity of resources and MRP (1) – (8): The net capacity of resource k in
time period t is modeled in (5) by L
kt
Gross requirement:
total consumption (internal and external) of the components over
time
