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Kathryn E. Stecke Xuying Zhao University of Texas at Dallas

Production and Transportation Integration for a Make-to-Order Manufacturing Company with a Commit-to-Delivery Business Mode. Kathryn E. Stecke Xuying Zhao University of Texas at Dallas Texas A&M Monday, Feb 27, 2006. Outline . Problem and motivation Literature review

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Kathryn E. Stecke Xuying Zhao University of Texas at Dallas

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  1. Production and Transportation Integration for aMake-to-Order Manufacturing Company with aCommit-to-Delivery Business Mode Kathryn E. Stecke Xuying Zhao University of Texas at Dallas Texas A&M Monday, Feb 27, 2006

  2. Outline • Problem and motivation • Literature review • Problem settings • Analysis when partial delivery is allowed • Analysis when partial delivery is not allowed • Extensions • Conclusions

  3. Ship and Delivery Dates • Ship date: the date when a manufacturing company gives products to a logistics company to deliver to a customer. • Delivery date: the date when the logistics company delivers products to a customer.

  4. Two Business Modes • Commit-to-ship • the manufacturing company commits a ship date for an order. • Customerspre-specify a shipping mode, e.g., overnight shipping. • Commit-to-delivery • the manufacturing company commits a delivery date for an order. • The ship mode can be decided dynamically by the company.

  5. Commit-to-ship at Dell

  6. Profit increase opportunity in Dell • Dell ships 95% of customer orders within eight hours. • Based on this fact, Dell could increase profit by adopting commit-to-delivery. For example: • Customers pay $450 for a computer and $160 for overnight shipping. • Dell gets $450 in commit-to-ship. • Dell promises a 5-days-later ship date. The logistics company gets $160. • Dell gets $510 in commit-to-delivery. • Dell could ship the order within eight hours by adjusting the production schedule. Then a slow ship mode can be adopted. The logistics company gets $100. Dell gets $450+$60. • Profit increases over 10%.

  7. Problem Description • Production schedule is important when adopting a commit-to-delivery mode. • A good production schedule saves shipping costs. • A bad production schedule incurs expediting costs. • How to schedule production for accepted orders so that • All orders meet their delivery due dates. • The total shipping cost is reduced as much as possible.

  8. Literature Review Our research is related to two literature streams: 1. Production scheduling • Pinedo (2000), … 2. Integration between transportation and production • Bhatnagar, Chandra, and Goyal (1993),Thomas and Griffin (1996), and Sarmiento and Nagi (1999), Chen and Vairaktarakis (2005)

  9. Production Environment • Finished products are assembled from partly-finished products and customized components. • Differences among orders exist in different models/types of components. • Switching production from one order to another order rarely incurs any extra production costs.

  10. Production Schedule Setting • We specify the production schedule for n new, just arrived orders with delivery due dates. • A manufacturer can wait for customer orders to accumulate as long as its master production schedule is notempty. • The schedule for the n new orders will be added to the end of the current master production schedule.

  11. Transportation Setting • Outsourced to a third party logistics company, e.g., FedEx • The logistics company comes to collect products at the end of each day.

  12. Shipping Cost Setting

  13. Shipping Cost Setting • The shipping cost is a general function of shipping time and the quantityof computers shipped. • From the table in the previous slide, shipping cost is convex decreasing in shipping time. • From the table in the previous slide, shipping cost is linearly increasing with shipping weight. • Since all computers’ weights are similar, shipping cost is linearly increasing with the quantity of computers shipped.

  14. Problem Settings Summary • Orders • There are n orders to be scheduled for production; • Each order Oihas a production due date di and requires quantity Qi. • Production • The production planning horizon is m days • Daily production capacity is c products • Single machine or a paced assembly line • Transportation • Outsourced to a third party logistics company, e.g., FedEx • The logistics company comes to collect products at the end of each day.

  15. Table of Notation

  16. r1=1 O1 Process Timeline d1 r1=0 Production Planning Horizon O1 … 2 m 3 1 0 t1=1 t1=2 Ship cost for one order i: G(ri, Qi), convex decreasing with ri and linearly increasing with Qi

  17. Feasibility Condition where denotes a set of orders having a production due date on or before production day j in the planning horizon.

  18. When Partial Delivery is Allowed Quantity produced in day j for order i MIP-PD: Ship date is the same as the production date Order i is produced before its due date Daily production capacity constraint

  19. When Partial Delivery is Allowed • MIP-PD • Totally unimodular • ILOG CPLEX • Algorithm • Nonpreemptive Earliest Due Date Schedule (NEDD) : orders are sorted according to earliest due date first and processed nonpreemptively and continuously without idle time. Production Planning Horizon … O1 O2 O3 O4 O5 … 0 1 2 m 3 d1=1 d2=d3=2 d4= d5=3

  20. When Partial Delivery is Not Allowed Yij=1 means that the last product in order i is produced in day j. MIP-NPD: The ship date is the last product’s production date.

  21. When Partial Delivery is Not Allowed

  22. When Partial Delivery is Not Allowed Cj: number of products which are produced in day j but shipped in day j+1 or later. C1=150 C2=160 Production Planning Horizon … O1 O2 O3 … (100) (150) (90) (160) (100) 2 m 1 0 (100) (150+90)

  23. When Partial Delivery is Not Allowed • Algorithm NPD: try to reduce each Cj as much as possible. • Get an initial feasible schedule by NEDD. • Start reducing Cm-1 by producing smaller orders first. • Reduce each Cj the same way. • The algorithm stops when C1 is reduced. Cm-1 O5 O1 O2 O3 O4 Cm-1 O5 O3 O1 O2 O4 Day m Day m-1

  24. Algorithm Performance When n=5 and m=5

  25. Algorithm Performance When n=8 and m=8

  26. Performance of Lower Bounds When n=5 and m=5

  27. Performance of Lower Bounds When n=8 and m=8

  28. Algorithm Performance When n=500 and m=15

  29. Extensions • Considering customer locations in the shipping cost function • Considering quantity discounts in the shipping cost function

  30. Shipping Cost Varies with Customer Locations

  31. Considering Customer Locations in Models • When partial delivery is allowed. • When partial delivery is not allowed

  32. Considering Quantity Discounts • Some 3PL companies offer quantity discounts when multiple items are sent in a batch. • When partial delivery is allowed, there exists a tradeoff. • We propose another MIP to consider this tradeoff … O1 … (150) (150) 2 m 1 0 (0) (300) (150) (150)

  33. Conclusions • We analyzed a production and transportation integration problem for make-to-order industries. • When partial delivery is allowed, NEDD provides the optimal production schedule. • Mixed integer programming model: MIP-PD • Totally unimodular • ILOG CPLEX • When partial delivery is not allowed, an effective and efficient heuristic algorithm is provided. • Mixed integer programming model: MIP-NPD • Heuristic algorithm NPD

  34. Thank You!

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