1. Bonus Round Assembly Line Scheduling Assume Assembly Line is used for multiple products 1

2. The problem 2 t ij = time to process (set-up) product j if it immediately follows product i Minimize makespan: traveling salesman problem. shortest set-up time (SST) heuristic: 1. select a product arbitrarily. 2. choose the product not already in the sequence with the smallest set-up time when following the given product. 3. add it to the sequence and repeat until all products are sequenced.

3. Minimize Set-up times - Example 3 Product abcd a-574 b3-108 c74-5 d268- some examples: a – d – b – c - a: 4 + 6 + 10 + 7 = 27 b – a – d – c – b: 3 + 4 + 5 + 4 = 16 c – b – a – d – c: 4 + 3 + 4 + 8 = 19

4. Minimize Set-up times - Example 4 Prodabcd a-574 b3-108 c74-5 d268- Prodabcd a-574 b3-108 c74-5 d268- start Prodabcd a-574 b3-108 c74-5 d268- a – d – b – c – a: 4 + 6 + 10 + 7 = 27

5. Minimize Set-up times - Example 5 Prodabcd a-574 b3-108 c74-5 d268- start b – a – d – c – b: 3 + 4 + 8 + 4 = 19

6. Minimize Set-up times –a regret algorithm 6 ProdABCD A-345 B3-46 C16-2 D547- Prod ABCD MIN A-345 3 B3-46 3 C16-2 1 D547- 4 SUM 11 Prod ABCD SUM A-012 B0-13 C05-1 D103- MIN0011 2 Prod ABCD A-001 B0-02 C05-0 D102- D – B – A – C – D 4 + 3 + 4 + 2 = 9

7. General Search Methods 7 neighborhood search: 1. generate seed – initial schedule 2. generate neighbors from seed 3. approaches: a. if improvement keep neighbor b. generate all neighbors and keep best c. evaluate neighbors until 10 percent improvement given sequence 1-2-3-4-5-6-7-8 Adjacent pairwise interchange (API): exchange adjacent Products i and j in sequence:1-2-4-3-5-6-7-8 n-1 neighbors to evaluate Pairwise interchange (PI): exchange products i and j in sequence 1-2-7-4-5-6-3- 8 n(n-1)/2 neighbors to evaluate Insertion (INS): insert jobs k between products i and j 1-2-3-4-7-5-6-8 (n-1) 2 neighbors to evaluate

8. General Search Methods – Example (API) 8 Prod12345 t i 15397 d i 2781311 initial seed: SPT: 1 – 3 – 2 – 5 – 4N T = 3 neighbors: 3 – 1 – 2 – 5 –4 N T = 4 1 – 2 – 3 – 5 – 4N T = 3 1 – 3 – 5 – 2 – 4N T = 2* 1 – 3 – 2 – 4 – 5N T = 3 Objective Min N t seed: 1 – 3 – 5 – 2 – 4N T = 2 neighbors: 3 – 1 – 5 – 2 - 4N T = 3 1 – 5 – 3 – 2 – 4N T = 3 1 – 3 – 2 – 5 – 4N T = 3 1 – 3 – 5 – 4 – 2N T = 2*

9. An Unsolicited Testimonial I am a big advocate of the nearest neighbor heuristics when sequencing our products on the assembly line. It consistently gives us a good reduction in setup times thus allowing us to increase our value added time.