Optimal Models for Aggregate Planning Assignment Help

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Optimal Models for Aggregate Planning

Linear programming

The linear programming model is one of the optimal models used to formulate aggregate plans. The optimal plan for minimizing costs is identified by the linear programming procedure. The number of units to be produced, the total number of shifts for which the plan should operate in the planning time horizon, and the amount of inventory that has to be carried in each time period, are specified by the identified plan. Linear programming is used to allocate scarce resources to strategic alternatives when the costs of various resources are linear functions of their quantities. 

The linear programming model is useful when the cost and variable relationships are linear, and demand can be forecasted exactly. Optimal solutions can be derived using the simplex and transportation methods.

Linear decision rules (LDRs)

Linear Decision Rules (LDRs) are a set of equations for calculating the optimal workforce, aggregate output rate and inventory level for each time period in a planning horizon. Similar to linear programming, this method guarantees an optimal solution and eliminates trial-and-error computations. It also overcomes the limitation of linear programming by taking into account non-linear cost relationships. This model determines the actual costs incurred due to the changes in the inventory level, production rate, and workforce size, and fits them in the form of nonlinear equations. These equations are simplified to obtain two linear equations: for production rate, and workforce size, using calculus to minimize the total cost. These two equations can be used to determine the required workforce size and production rate (for a month) as a function of the demand forecast, the current workforce, and inventory. One of the drawbacks of LDRs is that they must be tailored to fit each organization's specific requirements. Further, to derive proper LDRs for a particular company, extensive mathematical analysis has to be carried out. Finally, any changes in the cost relationships like increase in wages will require redoing the whole process to derive new LDRs.              

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