Optimization model

If the check box Display model is selected before the algorithm is launched, the data used by the algorithm are displayed. The variables and constraints are defined by indices corresponding to the type of item (Family item or Resource item) and to the time period.

Variables

The variables associated with the Family items are the following for the successive periods:

•      V_subcontracting: quantity produced via a subcontractor,

•      V_Production: quantity produced with the production resources

•      V_Stock: quantity in inventory at the end of each period

•      V_Stockout: stockout quantity at the end of each period

The variables associated with the Resource items are the following for the successive periods:

•      V_Capacity_coefficient : capacity coefficient for the resource (in the period)

•      V_Capacity_increase : Capacity increase with respect to the previous period

•      V_Capacity_decrease : Capacity decrease with respect to the previous period

•      V_Over_capacity : quantity produced in excess with respect to the available capacity

Constraints

The constraints associated with the Family items are the following for the successive periods:

•      C_Max_subcontracting : the maximal quantity that can be subcontracted

•      C_Min_inventory : lower bound for the admissible inventory at the end of each period (defined as a fraction of the next demand)

•      C_Max_inventory : upper bound for the admissible inventory at the end of each period (defined as a fraction of the next demand)

•      C_Stockout : upper bound for the admissible stockout for each period (defined as a fraction of the next demand)

•      C_Inventory_equation : classical inventory equation :

V_Stock _p,i-1 – V_Stock _p,i - %Backlog_p * V_Stockout_p,i-1 + V_Stockout_p,i + V_Production_p,i + V_subcontracting_p,i - Demand_p,i = 0

The constraints associated with the Resource items are the following for the successive periods:

•      C_Min_value : lower bound for the admissible resource coefficient

•      C_Max_value : upper bound for the admissible resource coefficient

•      C_Capacity_increase  : upper bound for the admissible capacity coefficient increase with respect to the previous period

•      C_Capacity_decrease  : upper bound for the admissible capacity coefficient decrease with respect to the previous period

•      C_Over_Capacity : maximum produced quantity (in addition to the nominal capacity)

•      C_Resource_equation : classical resource capacity conservation equation

V_Capacity_coefficient_r,i-1 - V_Capacity_coefficient_r,i + V_Capacity_increase_r,i - V_Capacity_decrease_r,i = 0

The additional constraints are the following:

•      C_Capacity : classical periodic resource capacity constraint

Σ_r (C_p,r * V_Production_p,i) <= CoefCap_r,i * V_Capacity_coefficient_r,i + CoefCapr,i * V_Over_capacity_r,i

•      C_Max_inventory : upper bound for the global inventory value

Σ_p V_Stock_p,i <= Maximal value

Objective function

As stated above, two different objective functions can be selected (Files menu, Preferences window, S&OP panel):

•    the total cost over the horizon has to be minimized,

•    or the total gross margin over the horizon has to be maximized.