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Single Facility Lot Size Model Elsp

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Single Facility Lot Size Model Elsp

1. 1. Single Facility Lot Size Model Producing n items on a single machine
2. 2. <ul><li>Notation </li></ul><ul><ul><li>λ j : Demand rate for product j </li></ul></ul><ul><ul><li>P j : Production rate for product j </li></ul></ul><ul><ul><li>h j : holding cost per unit per unit time for product j </li></ul></ul><ul><ul><li>K j : Set up cost for product j </li></ul></ul><ul><li>Facility should have enough capacity to satisfy the demand of all products </li></ul>
3. 4. Example data 20 0.003 80 10,000 1000 D 5 0.005 120 50,000 5000 C 15 0.002 70 5,000 2000 B 10 0.001 50 10,000 3000 A Variable cost/unit Setup time Setup cost Production rate Annual demand Product
4. 5. Optimal Solution <ul><li>T min = Σ s j /(1- Σ ( λ j /P j ) = 0.011/0.10 = 0.11 years </li></ul><ul><li>T* =((2)(320)/15,900)^0.5=0.20 </li></ul><ul><li>Since T*> T min cycle length = 0.20 years </li></ul><ul><li>Q 1 =T* λ 1 =0.20 x 3000 = 600 </li></ul><ul><li>Q 2 =T* λ 2 =0.20 x 2000 = 400 </li></ul><ul><li>Q 3 =T* λ 3 =0.20 x 5000 = 1000 </li></ul><ul><li>Q 4 =T* λ 4 =0.20 x 1000 = 200 </li></ul><ul><li>Cost = 108,190 </li></ul>