1. An optimal batch size for a JIT manufacturing System 指導老師：楊金山 博士 學生：黃惠卿 中華民國九十三年五月五日

2. Outline Abstract Introduction Model formulation –Assumptions –Case I : JIT delivery system –Case II: JIT Supply and delivery system Solution methodology –Problem I –Problem II Results and discussions Conclusions

3. Abstract Production batch sizes for a JIT delivery system. Incorporate a JIT raw material supply system. Compute the batch sizes for both manufacturing and raw material purchasing policies.

4. The manufacturing lot size is dependent on the retailer ’ s sales volume, unit product cost, set-up cost, inventory holding cost and transportation cost. The raw material purchasing lot size is dependent on raw material requirement in the manufacturing system, unit raw material cost, ordering cost and inventory holding cost. Introduction

5. Introduction (cont.)

6. Case I ： –The ordering quantity of raw material is assumed to be equal to the raw material required for one batch of the production system. –Can be fitted in the JIT supply system. Case II ： –Ordering quantity of a raw material to be n times the quantity required of one lot of a product, where n is an integer. –Is not favourable for the JIT environment.

7. 2.1 Assumptions –To simplify the analysis, we make the following assumptions: There is only one manufacturer and only one raw material supplier for each item. The production rate is uniform and finite. There are no shortages. The delivery of the product is in a fixed quantity at a regular interval. The raw material supply is available in fixed quantity whenever required. The producer is responsible to transport the product to the retailers ’ location. Model formulation

8. Model formulation (cont.)

9. 2.2 Case I ： JIT delivery system –The total cost function, for case I, can be expressed as follows ： where =ordering cost of raw materials =inventory holding cost of raw materials =set-up cost of finished products =inventory holding cost of finished products

10. Model formulation (cont.)

11. Using the relationship in Eq.(3),the total cost in Eq.(1) may be written as

12. Model formulation (cont.) 2.3 Case II ： JIT Supply and delivery system –The total cost function, for case II, can be expressed as follows ： where =set-up cost of finished products =inventory holding cost of finished products =ordering cost of raw materials =inventory holding cost of raw materials

13. Model formulation (cont.)

14. 3.1 Problem I Solution methodology

15. Solution methodology (cont.) Algorithm I: finding batch size –Step0 Initialize and store D P, P, A P, A r, H p and H r. –Step1 Compute the number of batch size using Eq.(9) –Step2 Compute If is an integer, then stop. –Step3 Compute TC 1 using Eq.(5) for –Choose the that gives minimum TC 1 –Stop

16. Solution methodology 3.2 Problem II –Substituting the integer variable, we can rewrite Eq.(7) as follow:

17. Solution methodology Algorithm II: finding batch size –Step0 Initialize and store D P, P, A P, A r, H p and H r –Step1 Compute the number of batch size using Eq.(11) –Step2 Compute. If is an integer, then stop. –Step3 Compute TC 2 using Eq.(7) for and Choose the that gives minimum TC 1 –Stop

18. Results and discussions

20. Conclusions A supplier to the JIT buyer is expected to synchronize his production capacity with the buyer ’ s demand so that the inventory in the supply pipeline is reduced and eventually eliminated. Total cost function is convex for a given. The quality of solution is discussed and sensitivity analysis is provided. In problem II, it is assumed that To generalize the problem, needs to be relaxed.the relation