Using control theory to optimise profit in APVIOBPCS inventory systems

• The model uses data on production of RAM chips.
• Costs of production, inventory storage and lost sales are included.
• Cumulative profit is computed for existing inventory control and for PID control.
• This shows increased profit generated by suitable PID control over existing P control.
• The optimum level of desired inventory is obtained to maximise profit.

This paper describes an investigation of the effects on the variation of profitability with time caused by the choice of control formulation in a model for an Automatic Pipeline, Variable Inventory and Order Based Production Control System (APVIOBPCS) production system. The improvements are demonstrated using an example of electronic RAM production used by Deif and ElMaraghy [26]. The investigation using a SIMULINK™ model, includes varying the “order up to inventory” values, and “work in progress” values (WIP).Using Proportional, Integral and Derivative (PID) control elements to illustrate the profit gain from using control methods, the numerical results were optimised using MATLAB™ routines.The results show that using a range of PID gains for a controlled production system will increase profitability.The desired level of inventory also can increase profitability with a definite optimum value. The model shows increased production delays result in lower overall profit and cumulative profit is increased with increased PID gains up to a limit.Using the data published by Deif and Elmaraghy the model shows improvements in cumulative profitability by up to 30%.