Scheduling of industrial production processes

• US 20070088447A1
• Filed: 10/26/2006
• Published: 04/19/2007
• Est. Priority Date: 04/27/2004
• Status: Abandoned Application

• Current Assignee: ABB Research Ltd. (ABB Ltd.)
• Original Assignee: ABB Research Ltd. (ABB Ltd.)
• Inventors: Stothert, Alec, Poncet, Andreas
• Application Number:
  US11/586,713
• Publication Number:
  US 20070088447A1
• Time in Patent Office: Days
• US Class Current: 700/36
• CPC Class Codes: G05B 13/04 involving the use of models or simulators
• CPC Class Codes: Y02E 20/16 Combined cycle power plant [CCPP], or combined cycle gas turbine [CCGT]

Abstract

A rescheduling problem can be reformulated as a multi-parametric (mp-QP) optimization problem which can be solved explicitly. The subsequent exploitation of this algebraic solution is computationally inexpensive.

Claims

1. A production scheduler for scheduling an industrial production process determined by

a decision variable (u) and constraints (A, b) on the decision variable (u);

parameter variables (b, c, p) representing generalized limits, costs and revenues;

a positive semi-definite cost matrix (Q);

an objective function depending quadratically, via the cost matrix (Q), on the decision variable (u) and depending bilinearly on the decision variable (u) and the parameter variables (b, c, p), wherein the scheduler comprises;

computing means for calculating an optimal production schedule u* for a given set of parameter values; and

computing means for evaluating an algebraic expression for the production schedule u*(b, c, p) as a function of the parameter variables (b, c, p).

2. The production scheduler according to claim 1, wherein the algebraic expression for the production schedule u*(b, c, p) is obtained by

a) formulating a multi-parametric quadratic programming (mp-QP) problem, including:

a QP-variable (z) being defined based on the decision variable (u) and the parameter variables (b, c, p);

the objective function being rewritten in general quadratic form (eq. 1.1, eq. 2.1) in the QP-variable (z);

linear constraints on the QP-variable (z) (eq. 1.2, eq. 2.2) being defined based on the constraints (A, b) on the decision variable (u) and the parameter variables (b, c, p);

b) solving the mp-QP problem for an algebraic expression of the QP-variable z as a function of the parameter variables (b, c, p); and

c) deriving the algebraic expression for the production schedule u*(b, c, p) from the algebraic expression of the optimal QP-variable z*.

3. A method of optimizing a production schedule of an industrial production process determined by

a decision variable (u) and constraints (A, b) on the decision variable (u);

parameter variables (b, c, p) representing generalized limits, costs and revenues;

a positive semi-definite cost matrix (Q);

an objective function depending quadratically, via the cost matrix (Q), on the decision variable (u) and depending bilinearly on the decision variable (u) and the parameter variables (b, c, p), wherein an algebraic expression for the optimal production schedule u*(b, c, p) as a function of the parameter variables (b, c, p) is obtained by a method comprising;

a) formulating a multi-parametric quadratic programming (mp-QP) problem, including;

a QP-variable (z) being defined based on the decision variable (u) and the parameter variables (b, c, p);

the objective function being rewritten in general quadratic form in the QP-variable (z); and

linear constraints on the QP-variable (z) being defined based on the constraints (A, b) on the decision variable (u) and the parameter variables (b, c, p);

b) solving the mp-QP problem for an algebraic expression of the QP-variable z* as a function of the parameter variables (b, c, p); and

c) deriving the algebraic expression for the production schedule u*(b, c, p) from the algebraic expression of the QP-variable z, wherein the algebraic expression for the production schedule u*(b, c, p) obtained is evaluated as a function of the parameter variables (b, c, p).

4. The method according to claim 3, wherein the algebraic expression for the production schedule u*(b, c, p) is evaluated on-line upon a change in the value of a parameter variable (b, c, p).

5. The method according to claim 3, wherein the QP-variable (z) has the twofold dimension as the decision variable (u) and is obtained by augmenting the decision variable (u) with an augmenting parameter variable (P) equal to a difference between the parameter variables (c−

p), and wherein constraints on the QP-variable (z) constrain the augmenting parameter variable (P) to its given value.

6. The method according to claim 3, wherein the matrix Q is positive definite, wherein the QP-variable (z) has the same dimension as the decision variable (u) and is obtained by mapping the parameter variables (c, p) on the decision variable (u).

7. The method according to claim 3, wherein the mp-QP problem is of a form

8. The method according to claim 5, wherein:

9. A computer implemented method for scheduling an industrial production process comprising:

receiving a decision variable and constraints on the decision variable;

receiving parameter variables representing generalized limits, costs and revenues;

calculating a production schedule for a given set of the parameter values using a positive semi-definite cost matrix and an objective function depending quadratically, via the cost matrix, on the decision variable and depending bilinearly on the decision variable and the parameter variable; and

evaluating an algebraic expression for the production schedule as a function of the parameter variables.

10. The method according to claim 9, wherein the algebraic expression for the production schedule is evaluated on-line upon a change in the value of a parameter variable.