Planning with limiting factors Part2

ACCA F5 - Performance Management 

Deciding optimal production mix in situations with multiple limiting factors:

Factors: For the case to exist production in functional or divisional unit should pass through more than one factors (E.g. capital, labor, machine1, machine2) out of which there should at least two limiting factors for example ( i.e. machine1, and machine2)  or any other combination which limits production.

Objective function: Objective function simply maximizes benefit (reduce cost / increase output / increase contribution / increase NPV in case of investment appraisal) from total available units of decision variables. Decision variables relate to goal/objective.

Constraints: All constraints are coded into linear inequalities equations, which represent the sharing of know value of each available factor in between decision variables. Constraints can take myriad of forms. They are: Typesof Constraints 

Ø  Lower and upper bounds on the values of decision variables. E.g x >= 10

Ø  Limitation constraints - relationship between decision variables which does not exceed factor limit (2X + 3Y  =< 500 hours)

Ø  Requirement constraints - relationship between decision variables which should satisfy minimum set requirements (X + Y >= 50 units)

Ø  Ratio constraints - Relationship can be <=, >=, or =, which compares value of two or more variables.   (X / Y >= 2)

Ø  Balance Constraints - model process where "inputs" must equal "outputs."

Graphical approach:

Ø  First straight line is traced in the graph, which means the balanced constraints for each inequality.

Ø  Then, section represented inequality is identified.

Ø  The process is repeated for all inequalities

Ø  This gives feasible reason

Ø  Finally, values of variables at intersections are fed into objective function and best decision is made or objective function isoline is drawn, projected and decision is made.

To maximise shareholders wealth and minimise the limitations imposed by soft capital rationing, managers use this tool to decide on optimal mix of projects which increase overall net present value (NPV) of combined projects.

Excel solver is a tool available in Microsoft Excel to deal problems related to limiting factors. Installation of Solver pack is essential for using Excel 2007 to calculate decision variables.

Ø  Office button > Excel option > Add-Ins > Excel Add-Ins > Go > Check - "Solver"

Then copy input values to excel sheet, go to Data Ribbon  > Analysis > Solver and fill in the inputs required.

ACCA Article: Linear Programming

CIMA Article: Graphical Linear Programming