A company wishes to plan its production of two items with seasonal demands over a 12-month period. The monthly demand of item1 is 100 units during the months of October, November and December; 10 units during the months of January, February, March and April; and 30 units during the remaining months. The demand of item2 is 50 units during the months of September through December and 15 units during the remaining months. Suppose that the unit product cost of item1 and item2 is 5000 TL and 8000 TL, respectively, if they are manufactured before June. After June, the unit costs are reduced to 4500 TL and 7000 TL because of the installation of an improved manufacturing system. Item1 requires 1 unit of a key component and item2 requires 2 units. The availability of this key component is 120 units per month during January- September and 150 units per month during October-December. Furthermore, each unit of item1 occupies 2 m3 and each item2 occupies 4 m3 of inventory. Suppose that the maximum inventory space allocated to these items is 200 m3 and that the holding cost during any month is 100 TL/m3. Formulate a linear programming model which will represent this system. Define the decision variables, state the objective function, and specify all the constraints.
A company wishes to plan its production of two items with seasonal demands over a 12-month period. The monthly demand of item1 is 100 units during the months of October, November and December; 10 units during the months of January, February, March and April; and 30 units during the remaining months. The demand of item2 is 50 units during the months of September through December and 15 units during the remaining months. Suppose that the unit product cost of item1 and item2 is 5000 TL and 8000 TL, respectively, if they are manufactured before June. After June, the unit costs are reduced to 4500 TL and 7000 TL because of the installation of an improved manufacturing system. Item1 requires 1 unit of a key component and item2 requires 2 units. The availability of this key component is 120 units per month during January- September and 150 units per month during October-December. Furthermore, each unit of item1 occupies 2 m3 and each item2 occupies 4 m3 of inventory. Suppose that the maximum inventory space allocated to these items is 200 m3 and that the holding cost during any month is 100 TL/m3.
Formulate a linear programming model which will represent this system. Define the decision variables, state the objective function, and specify all the constraints.
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