1. 1 Capacity Planning in a General Supply Chain with Multiple Contract Types Stephen C. Graves and Xin Huang May 2008

2. Copyright Stephen C. Graves 2008 All Rights Reserved 2 Motivation Prior research has developed algorithms and software for modeling and optimizing the inventory across a supply chain – “strategic inventory placement model” Impetus for current research – develop and deploy a tactical model to provide decision support for determining capacity levels across a supply chain

3. Copyright Stephen C. Graves 2008 All Rights Reserved 3 Intent Develop a framework to support capacity planning decisions in a supply chain with −Multiple products −Each product requires multiple processes (or components) −Each resource provides capacity for one or more processes Need to determine the right level and type of capacity investments Need to account for network interrelationships, demand uncertainty, multiple time periods, & different capacity contracts.

4. Copyright Stephen C. Graves 2008 All Rights Reserved 4 Work to Date Developed framework for structuring models Developed and tested algorithms for determining the amount, type and timing of capacity investments across a complex multi-product supply chain Implementation of user-friendly software is underway

5. Copyright Stephen C. Graves 2008 All Rights Reserved 5 Model assumptions Given demand forecast and contract prices, we first make capacity decisions: −For each resource how much capacity to reserve and with what type of contract Then we learn what the actual demand is and decide how to allocate capacity to meet demand as best as possible Objective is to maximize revenue net of capacity costs

6. Copyright Stephen C. Graves 2008 All Rights Reserved 6 Example 1 Laptop A Chip Set A Foundry 1 Display A A & T Foundry 3CM 1

7. Copyright Stephen C. Graves 2008 All Rights Reserved 7 Example 1: Sample Input Data Laptop A Mean2200 STD200 Sales price$700 Table 1: Table of Product Information Fixed Unit PriceUnit Reservation PriceUnit Exercise Price Foundry 1908510 Foundry 320016050 CM 111525100 Table 2: Table of Resource Price Inputs

8. Copyright Stephen C. Graves 2008 All Rights Reserved 8 Example 1: Model Outputs Fixed-price CapacityOption CapacityTotal Foundry 122110 Foundry 320401712211 CM 119542572211 The Expected Total Profit: $ 601,623 Mean – Laptop A: 2200

9. Copyright Stephen C. Graves 2008 All Rights Reserved 9 Example 1: Performance Statistics Fixed-price Capacity UtilizationOption Capacity Utilization Foundry 12131/2211 = 96.4%-- Foundry 32018/2040 = 98.9%112/171 = 65.5% CM 11945/1954 = 99.5%185/257 = 72.0% Units soldLost sales Average # of213075

10. Copyright Stephen C. Graves 2008 All Rights Reserved 10 Example 3 Laptop ALaptop B Chip Set A Foundry 1 Display A A & TChip Set BDisplay BA & T Foundry 3 Foundry 4CM 1CM 2 Foundry 3 CM 1 Foundry 2

11. Copyright Stephen C. Graves 2008 All Rights Reserved 11 Example 3: Sample Input Data Laptop ALaptop B Mean22001000 STD200100 Sales price$700$1000 Table 5: Table of Product Information Fixed Unit PriceUnit Reservation Price Unit Exercise Price Foundry 1CS -A908510 Foundry 2CS A/B1008030 Foundry 3Display20016050 Foundry 4CS - B987828 CM 1A&T – A/B11525100 CM 2A&T - B1103090 Table 6: Table of Resource Price Inputs

12. Copyright Stephen C. Graves 2008 All Rights Reserved 12 Questions of Interest Which suppliers should the manufacturer choose? What types of contract should we use for each supplier? Only fixed-price contract? Only option contract? Or Both. How much capacity should we buy?

13. Copyright Stephen C. Graves 2008 All Rights Reserved 13 Example 3: Model Outputs Fixed-price Capacity Option Capacity Total Foundry 1CS -A20090 Foundry 2CS A/B3650 Foundry 4CS - B728110838 Foundry 3Display30231893212 CM 1A&T – A/B21212522373 CM 2A&T - B80038838 The Expected Total Profit: $ 1,183,981 Mean – Laptop A: 2200 Mean – Laptop B: 1000

14. Copyright Stephen C. Graves 2008 All Rights Reserved 14 Example 4 1 12a Compare the following four strategies 1.Plan the capacity as given in the figure without option capacity 2.Use a common process to replace process 2a and 2b 3.Add option capacity to process 2a and 2b 4.Combine strategy S2 and S3 12a 2 2b3 3 S1 1 1 1 2 23 23 S2 1 12a 1 2 2b3 3 S3 1 1 1 2 23 23 S4

15. Copyright Stephen C. Graves 2008 All Rights Reserved 15 Example 4: Data Both products have the same price: changes from 66 to 150 Demand information: −E[D_1] = 500, STD(D_1) = 100, E[D_2] = 500, STD(D_2) = 100 Fixed price contracts: −[p_1, p_2a, p_2b, p_3] = [10, 50, 50, 10] Option contracts: −Reservation Price = 5, Exercise Price = 50

16. Copyright Stephen C. Graves 2008 All Rights Reserved 16 Example 4 Profit Margin Extra Profit (%) S2/S1 S3/S1 (S2+S3)/S1 S4/S1

17. Copyright Stephen C. Graves 2008 All Rights Reserved 17 Example 5: Multi-period Planning A Supply Chain Network −2 Products, 3 Processes, and 12 Periods. Each process has 4 different types of contract −1 period, 3 periods, 6 periods, and 12 periods Each contract has 4 terms −Duration, Fixed-price, Option reservation price, and Option exercise price 1 1 1 2 32 32

18. Copyright Stephen C. Graves 2008 All Rights Reserved 18 Sample Demands 123456789101112 70100180210240 230180100706050 24023018010070605070100180210240 E [ D 1 ] E [ D 2 ]

19. Copyright Stephen C. Graves 2008 All Rights Reserved 19 Sample Prices Prices: −Product 1: 65; Product 2: 65. Costs: −All processes have the same price structure. Duration13612 Fixed Price109.598.5 Reservation Price 87.57.256.75 Exercise Price32.52.25

20. Copyright Stephen C. Graves 2008 All Rights Reserved 20 Results 123456789101112 Process 16999247 10572 Process 224223616611574 83110199217248 Process 3325

21. Copyright Stephen C. Graves 2008 All Rights Reserved 21 Results (cont.) Process 1Process 2 Process 3

22. Copyright Stephen C. Graves 2008 All Rights Reserved 22 Summary Have developed a framework to support capacity planning decisions for supply chain Have developed solution algorithms for single period and multi-period problems To do − develop a case study to test and validate approach −finalize prototype software with user friendly interface

23. Copyright Stephen C. Graves 2008 All Rights Reserved 23 Collaboration Opportunities Need a test case(s) to validate and refine framework −Are we looking at problem in right way? −Does the data exist to test model? −Can our algorithms result in better decisions? −What’s critical/non-critical in how we are viewing problem ? Interest in internships for LFM or SDM students for “beta testing” Contact Steve Graves (sgraves@mit.edu) or Xin Huang (xinhuang@mit.edu)sgraves@mit.edu

24. Copyright Stephen C. Graves 2008 All Rights Reserved 24 Example 2 Laptop B Chip Set B Foundry 4 Display B A & T Foundry 3CM 2

25. Copyright Stephen C. Graves 2008 All Rights Reserved 25 Example 2: Sample Input Data Laptop A Mean1000 STD100 Sales price$1000 Table 3: Table of Product Information Fixed Unit PriceUnit Reservation PriceUnit Exercise Price Foundry 4987828 Foundry 320016050 CM 21103090 Table 4: Table of Resource Price Inputs

26. Copyright Stephen C. Graves 2008 All Rights Reserved 26 Example 2: Model Outputs Fixed-price CapacityOption CapacityTotal Foundry 49371041041 Foundry 39101311041 CM 28701711041 The Expected Total Profit: $ 556,320 Mean – Laptop B: 1000

27. Copyright Stephen C. Graves 2008 All Rights Reserved 27 Example 2: Performance Statistics Fixed-price Capacity UtilizationOption Capacity Utilization Foundry 4920/937 = 98.2%55/104 = 52.9% Foundry 3900/910 = 98.9%75/131 = 57.3% CM 2866/870 = 99.5%109/171 = 63.7% Units soldLost sales Average # of97523