1. Supply Chain Management Part II Supply chain management is the combination of art and science that goes into improving the way a company finds the raw components it needs to make a product or service, manufactures that product or service and delivers it to customers. Managing the flow of goods and services.

2. A Supply Chain Model Objective: Determine the least-cost configuration and activity levels among suppliers, factories, and distributors. I need a model of a supply chain to free me of this.

3. The Book’s Approach Use the transportation problem to model distribution of a single product from plants to warehouse Generalized somewhat with the transshipment problem Neither integrates suppliers – factories – warehouses – customers nor addresses multi- resources and products A broken supply chain

4. A “Real” Supply Chain Model - the variables Let X i,j,k = the number of units of resource i (raw material, parts, etc.) shipped from supplier j to factory k Let Y l,k,m = the number of units of product l manufactured in factory k for customer m (warehouse, retail store, region, etc.) A model prisoner supplied with a chain.

5. A Supply Chain Model – the cost coefficients Let c i,j,k = the cost of purchasing resource i from supplier j and shipping to factory k Let d l,k,m = the cost of manufacturing product l in factory k and shipping to customer m The objective function:

6. A Supply Chain Model – the first set of parameters a i,l = the number of units or resource i needed to produce one unit of product l b i,j = number of units of resource i available from supplier j Ship each factory needed resources Each supplier has limited resources

7. A Supply Chain Model – the second set of parameters f l = number of production units (machine hrs, labor hrs, assembly time, etc.) needed to produce one unit of product l F k = number of production units available at factory k production constraint Note: There may be more than one production constraint at a factory.

8. A Supply Chain Model – the third set of parameters D l,m = demand for product l by customer m I have a big demand for product l.

9. A Request… Could you make your so called supply chain model come alive with a real world example? My brother, Thomas Maytow, is owner of a cannery. What can your model do for him? Pat Maytow, a fruit picker.

10. A Real World Example The T. Maytow Company* produces three types of tomato products: a tomato paste, (condensed) tomato soup, and tomato juice. They operate two canning facilities. One is located in Kokomo, Indiana and the other is located in Santa Fe, New Mexico. Final product is distributed to three major distribution centers located in Pittsburgh, PA, Chicago, IL, and San Diego, CA. *Owned and operated by Thomas Maytow

11. The Suppliers There are three varieties of tomatoes used in production: Roma tomatoes Plum tomatoes Beefsteak tomatoes There are two major suppliers: Taste of the World (Morristown, New Jersey) imported from tomato fields near Naples, Italy Sierra Quality Canners from California's central valley

12. Tomato Distribution A typical tomato truck holds 50,000 pounds of tomatoes, which is about 300,000 tomatoes. (6 X 50,000)

13. Supplier Costs TypeNJ to Kokomo NJ to Santa Fe CA to Kokomo CA to Santa Fe Roma1215-- Plum1014158 Beefstk810129 Purchase and shipping cost per 1,000 pounds

14. Supplier Output TypeRomaPlumBeefstk NJ140100140 CA-120150 1,000 pounds per week

15. Production & Distribution Costs Kokomo Paste Santa Fe Paste Kokomo Soup Santa Fe Soup Kokomo juice Santa Fe juice Pgh8967910 Chi101189 12 SD1210 81312 $ per canner load

16. Tomato Production Tomato Paste - an average of 35 pounds of tomatoes is needed per canner load of 7 quarts; an average of 21 pounds is needed per canner load of 9 pints. A bushel yields 10 to 12 quarts of sauce. Tomato Soup - an average of 26 pounds of tomatoes is needed per canner load of 7 quarts; an average of 18 pounds is needed per canner load of 9 pints. A bushel yields 12 to 14 quarts of sauce. Tomato Juice - An average of 23 pounds of tomatoes is needed per canner load of 7 quarts, or an average of 14 pounds per canner load of 9 pints. A bushel yields 15 to 18 pounds per canner load of 9 pints. A bushel yields 15 to 18 quarts of juice.

17. Production Requirements* PasteSoupJuice Roma12-8 Plum8815 Beefstk1518- Total352623 Pounds of tomatoes per canner load (7 quarts) *The actual blends of tomato variety into finished product is proprietary

18. Plant Capacities PlantCapacity Kokomo10,000 Santa Fe14,000 capacity in canner loads (7 quarts) per week

19. Distribution Center Requirements PasteSoupjuice Pgh2,0003,000500 Chi1,0004,0001,500 SD5,0002,0003,000 canner loads (7 quarts) per week

20. The Decision Variables Let X i,j,k = the number of tomatoes in 1,000 pounds of type i shipped from supplier j to factory k i = roma, plum, beefsteak j = NJ, CA k = Kokomo, Santa Fe Let Y l,k,m = the number of canner loads of product l produced in factory k for distribution center m l = paste, soup, juice m = Pgh, Chi, SD

21. The Objective Function Min 12XR_NJ_K + 10XP_NJ_K+ 8XB_NJ_K + 15XR_NJ_S + 14XP_NJ_S + 10XB_NJ_S + 15XP_CA_K+ 12XB_CA_K + 8XP_CA_S+ 9XB_CA_S +8YP_K_PGH + 6YS_K_PGH + 9YJ_K_PGH +9YP_S_PGH + 7YS_S_PGH + 10YJ_S_PGH +10YP_K_CHI + 8YS_K_CHI + 11YJ_K_CHI +11YP_S_CHI + 9YS_S_CHI + 12YJ_S_CHI + 12YP_K_SD + 10YS_K_SD + 13YJ_K_SD +10YP_S_SD + 8YS_S_SD + 12YJ_S_SD

22. Supplier constraints East Coast Supplier: XR_NJ_K + XR_NJ_S < 140 XP_NJ_K + XP_NJ_S < 100 XB_NJ_K + XB_NJ_S < 140 West Coast Supplier: XP_CA_K + XP_CA_S < 120 XB_CA_K + XB_CA_S < 150 Legend X variables first index R – Roma P – Plum JB– Beefsteak middle index NJ – New Jersey supplier CA – California supplier last index K – Kokomo plant S – Santa Fe plant units in 1,000 lb of tomatoes

23. Production constraints Roma: XR_NJ_K -.012YP_K_PGH -.012YP_K_CHI -.012YP_K_SD -.008YJ_K_PGH -.008YJ_K_CHI -.008YJ_K_SD >= 0 XR_NJ_S -.012YP_S_PGH -.012YP_S_CHI -.012YP_S_SD -.008YJ_S_PGH -.008YJ_S_CHI -.008YJ_S_SD >= 0 Plum: XP_NJ_K + XP_CA_K -.008YP_K_PGH -.008YP_K_CHI -.008YP_K_SD -.008YS_K_PGH -.008YS_K_CHI -.008YS_K_SD -.015YJ_K_PGH -.015YJ_K_CHI -.015YJ_K_SD >= 0 XP_NJ_S + XP_CA_S -.008YP_S_PGH -.008YP_S_CHI -.008YP_S_SD -.008YS_S_PGH -.008YS_S_CHI -.008YS_S_SD -.015YJ_S_PGH -.015YJ_S_CHI -.015YJ_S_SD >= 0 Beefsteak: XB_NJ_K +XB_CA_K -.015YP_K_PGH -.015YP_K_CHI -.015YP_K_SD -.018YS_K_PGH -.018YS_K_CHI -.018YS_K_SD >= 0 XB_NJ_S +XB_CA_S -.015YP_S_PGH -.015YP_S_CHI -.015YP_S_SD -.018YS_S_PGH -.018YS_S_CHI -.018YS_S_SD >= 0

24. Production Capacity constraints Kokomo: YP_K_PGH + YS_K_PGH + YJ_K_PGH + YP_K_CHI + YS_K_CHI + YJ_K_CHI + YP_K_SD + YS_K_SD + YJ_K_SD < 10000 Santa Fe: YP_S_PGH + YS_S_PGH + YJ_S_PGH + YP_S_CHI + YS_S_CHI + YJ_S_CHI+ YP_S_SD + YS_S_SD + YJ_S_SD < 14000 in canner loads

25. Distribution Center Requirements Pittsburgh: YP_K_PGH + YP_S_PGH > 2000 YS_K_PGH + YS_S_PGH > 3000 YJ_K_PGH + YJ_S_PGH > 500 Chicago: YP_K_CHI + YP_S_CHI > 1000 YS_K_CHI + YS_S_CHI > 4000 YJ_K_CHI + YJ_S_CHI > 1500 San Diego: YP_K_SD + YP_S_SD > 5000 YS_K_SD + YS_S_SD > 2000 YJ_K_SD + YJ_S_SD > 3000 Legend Y variables first index P – paste S – soup J – juice middle index K – Kokomo S – Santa Fe units in canner loads

26. The Glorious Solution Min Cost per week = $ 207,160.80 VARIABLE VALUE XR_NJ_K 49.777775 XP_NJ_K 92.055557 XB_NJ_K 140.000000 XR_NJ_S 86.222229 XP_NJ_S 0.000000 XB_NJ_S 0.000000 XP_CA_K 0.000000 XB_CA_K 0.000000 XP_CA_S 118.944450 XB_CA_S 141.999985 YP_K_PGH 2000.0000 YS_K_PGH 3000.0000 YJ_K_PGH 500.00000 YP_S_PGH 0.000000 YS_S_PGH 0.000000 VARIABLE VALUE YJ_S_PGH 0.000000 YP_K_CHI 1000.0000 YS_K_CHI 2277.778076 YJ_K_CHI 1222.221924 YP_S_CHI 0.000000 YS_S_CHI 1722.221924 YJ_S_CHI 277.778046 YP_K_SD 0.000000 YS_K_SD 0.000000 YJ_K_SD 0.000000 YP_S_SD 5000.00000 YS_S_SD 2000.00000 YJ_S_SD 3000.00000

27. More of the Glorious Solution Kokomo Paste Santa Fe Paste Kokomo Soup Santa Fe Soup Kokomo juice Santa Fe juice Pgh20003000500 Chi10002277.781722.221222.22277.78 SD500020003000 TypeNJ to Kokomo NJ to Santa Fe CA to Kokomo CA to Santa Fe Roma49.7886.22 Plum92.06118.94 Beefstk140142.0 Final Product (weekly canner loads): Resources (weekly 1,000 lb of tomatoes):

28. The End of the Supply Chain Model The bottom line: The supply chain locks in money! Goods and services flowing through the supply pipeline