580,000
27,750,000
An Integer Programming Model for Optimal Provision of Multiple Manufactures With Interior
Design of Provision Facilities
Ahmed Abdullah Bamousa
Abstract
Many practical problems are concerned with the provision of manufactured components;
the provision can be done using three different methods which are production, importing/storing and subcontracting. The total market demand can be estimated and also the total fixed and variable cost elements for each method can be evaluated. The problem is to make an optimum design for the production and importing facilities and to determine how many components of each type of manufactures should be provided using individual method with the aim to minimize the total cost of provision of the whole requirements.
A mathematical model for such a problem is formulated using the linear and integer programming model where the decision variables represent the number of components to be provided using different methods in various plants. The objective function is to minimize the total fixed and variable costs of provision of all needed components. A special (If-Then) form for the objective function is generated due to the addition of the fixed cost associated with some of the provision methods. Another (If-Then / Or) form for the objective function is generated due to the addition of the fixed cost associated with the provision using the subcontracting method. The problem constraints are provision of the total demand, maximum capacity constraints, overtime condition, more prevision lines constraints and subcontracting stepping prices constraints.
A real example with only one single component is presented. The model is solved and the optimal solution saves SR 580,000 compared to other solutions using only one method of provision. A second example is presented with two manufactured components and an optimal value of SR 83,693,080 is achieved. Also, by taking care of the optimal interior design of the provision systems for the second example, the optimal solution saves SR 24,228,958 which represents about 29 % of the previous total cost.