1. © J. Christopher Beck 20051 Lecture 29: Supply Chain Scheduling 3

2. © J. Christopher Beck 2005 2 Outline Medium-term Planning Data is aggregated but still complex! Short-term Scheduling Medium-term/Short-term Integration

3. © J. Christopher Beck 2005 3 Supply Chain Scheduling

4. © J. Christopher Beck 2005 4 Supply Chain Decomposition Medium- term planning Short- term sched- uling Stage 1Stage 2Stage 3Stage 4

5. © J. Christopher Beck 2005 5 Medium-term Planning Assumptions: 4 week horizon 2 product families 3 stages: 2 factories, 1 DC, 1 customer Factories work 24/7 = 168 hours/week

6. © J. Christopher Beck 2005 6 Medium-term Planning Costs Production cost Storage cost Transportation cost Tardiness cost Non-delivery cost

7. Productionc p ij Cost to produce one unit of family j at factory i StoragehWeekly holding cost for one unit of any type at DC TransportationC m i2* Cost of moving one unit of any type from factory i to DC C m i*3 Cost of moving one unit of any type from factory i to the customer C m *23 Cost of moving one unit of any type from DC to the customer Tardinessw’’ j Cost per unit per week for an order of family i delivered late to DC w’’’ j Cost per unit per week for an order of family i delivered late to customer Non-delivery  Penalty cost for never delivering one unit of any product

8. © J. Christopher Beck 2005 8 Medium-term Planning Costs Production cost Storage cost Transportation cost Tardiness cost Non-delivery cost c p ij h C m i2* C m i*3 C m *23 w’’ j w’’’ j 

9. © J. Christopher Beck 2005 9 IP Objective: Minimize Production Costs x ijt = # units of family j produced at factory i in week t

10. © J. Christopher Beck 2005 10 IP Objective: Minimize Storage Costs q 2jt = # units of family j in storage at DC at end of week t

11. © J. Christopher Beck 2005 11 IP Objective: Minimize Transportation Costs y i2jt # of units of family j transported from factory i to DC in week t y i3jt # of units of family j transported from factory i to customer in week t z jt # of units of family j transported from DC to customer in week t

12. © J. Christopher Beck 2005 12 IP Objective: Minimize Tardiness Costs v 2jt = # units of family j tardy at DC at end of week t v 3jt = # units of family j tardy at customer at end of week t

13. © J. Christopher Beck 2005 13 IP Objective: Minimize Non-delivery Costs v 2j4 = # units of family j not delivered to DC at end of horizon v 3j4 = # units of family j not delivered to customer at end of horizon

14. © J. Christopher Beck 2005 14 Production Constraints Estimate processing time for 1 unit of family j at factory i Total weekly hours # units of family j produced at factory i in week t Plus storage constraints, transportation constraints, tardiness constraints, and non-delivery constraints (see P p. 189-190)

15. © J. Christopher Beck 2005 15 Medium-term Planning Computes: Production amounts Storage amounts Transportation amounts

16. © J. Christopher Beck 2005 16 Short Term Scheduling Production schedule at factories what products on what machines and when? Transportation schedule between factories, DC, and customers what products on what trucks and when?

17. © J. Christopher Beck 2005 17 Short Term Scheduling For each week we know the number of items of each family that need to be produced (from x ijt ) However, that number was based on an estimate of the processing time required! In reality each product has a process plan including release date, due date, quantity, and set-ups!

18. © J. Christopher Beck 2005 18 Looks Like a “Normal” Scheduling Problem (like we’ve been studying all along) But … you are faced with the modeling problem How much of the “real world” do you represent?

19. © J. Christopher Beck 2005 19 This is Your Factory – How Do You Model It?

20. © J. Christopher Beck 2005 20 Possible Models & Components Flowshop with 5 tasks and parallel resources? Single machine? Sequence dependent setups? Buffer capacity?

21. © J. Christopher Beck 2005 21 FSP with Parallel Machines Minimize Hard problem! Setup cost if job k follows job j on machine i Weighting parameters

22. © J. Christopher Beck 2005 22 Single Machine Schedule really depends on a single bottleneck machine if the bottleneck schedule is fixed, everything else is easy May be a much easier problem in practice!

23. © J. Christopher Beck 2005 23 The Modeling Problem It is an open research question of how you take a real factory (or call centre) and create a “model” of it with optimization tools What’s the best level of detail? What can you ignore?