2. Strategic Production Planning Now showing at your local university

3. Production planning is the activity of establishing production goals over a future time period called the planning horizon. The objective is to plan the optimal use of resources to meet stated production requirements.

4. A Framework Strategic –which products? –How many of each? –what factories? –where located? –what capacities? –which technologies? –time period in years –focus on profit –static or dynamic Tactical –how many workers? –what inventory levels? –what production rates? –number of shifts/overtime? –contracting out? –time period in months –focus on costs –dynamic

5. A Hierarchy of Production Planning Forecast product demand for t periods in the planning horizon Determine product mix, plant utilization & capacity Determine work force levels and production rates Establish schedule and job sequencing by item by time period Production tracking and control Material Requirements Planning Two workers discussing the company’s production planning system. Years Months Weeks/days

6. Three Levels of Planning Strategic –Everything subject to change Tactical –Infrastructure (e.g. factories, warehouses, products) remains fixed –Resources (e.g. machinery, raw material, labor) may change Operational –Infrastructure and resources are fixed –Basic question is how best to utilize them

7. Aggregate Planning Macro production planning Products lumped together to form an aggregate product Aggregated products and capacity expressed in terms of an average item if similar If items are different, then money, production hours, or weight (e.g. tons of steel) may be used Translate demand forecasts into a blueprint for planning staff and production levels Can be applied to strategic or tactical planning

8. Spreadsheet Methods Zero inventory strategy –produce to meet monthly demand –no inventories –work force fluctuates Level production strategy –maintain constant production rate –inventory fluctuates –constant work force

9. Production Strategies time cumulative number of units constant production rate demand curve variable production rate

10. Production Strategy - Example Excel

11. Optimal Strategy Use Solver to minimize total cost (target cell) Change labor force each month (changing cells) Excel

12. A Static Strategic Planning Model Assumptions deterministic –all input parameters are known selling price is fixed unit cost does not vary with production levels (no learning curve effect) demand is over a fixed planning horizon (static)

13. A Static Strategic Planning Model Let x ijk = the number of units of product i manufactured in factory j using technology (process) k R i = selling price of product i c ijk = cost of producing one unit of product i in factory j using technology k D i = forecasted demand for product i over planning horizon a iL = number of units or resource L required to produce one unit of product i F jL = capacity of resource L at factory j Static - demand rate of each product is constant over time.

14. I – product J – factory K – process L - resource

15. Let y ijm = the number of units of product i manufactured at factory j and sent to customer m t jm = unit transportation cost from factory j to customer m D im = demand for product i by customer m How can we work the Supply chain problem into this plan?

16. This model is becoming quite interesting. How can I throw a fixed startup cost into this? Let z ij = 1 if product i is to be produced at factory j; 0 otherwise f ij = fixed cost of producing product i at factory j

17. The Breakeven Point - B ij Isn’t there some way we can account for the break-even point?

18. The Makit Company Our very first example… The Makit Company makes a variety of products. They currently have excess capacity within two of their factories and are interested in introducing three new products: a gas trimmer, a gas driven edger, and a gas driven snow blower. Selling prices are estimated to be $200, $180, and $298 respectively. Determine the annual production levels that will maximize profit. I think we need more information to solve this problem?

19. Makit Company ProductProd 1 Prod 2 Prod 3 Factory location DaytonTijuanaDaytonTijuana Dayton Tijuana Per unit data Process A Process B Production cost $25201812363032 Material cost$403024 18 16 Labor hr12 23 186 Machine hr22665115 Fixed setup cost 10000150005000600010001200008000

20. Plant Capacities Labor hours per year Machine hrs per year Dayton8200055000 Tijuana6000015000 ProductEastern region Central region Western region Trimmer100145234 Edger200120285 Snowblower125280362 More Data Annual Demand

21. PlantEastern region Central region Western region Dayton5810 Tijuana, Mexico 1276 Distribution Costs $ per unit

22. X ijk = number of units of product i produced at plant j using process k Y ijl = number of units of product i produced at plant j and sent to region l Z ij = fixed cost of producing product i at plant j MAX Profit: z = - 10000 Z11 - 15000 Z12 - 5000 Z21 - 6000 Z22 - 1000 Z311 - 12000 Z312 - 8000 Z32 + 135 X11 + 150 X12 + 138 X21 + 144 X22 + 244 X311 + 250 X312 + 250 X32 -5 Y111 - 8 Y112 - 10 Y113 - 12 Y121 - 7 Y122 - 6 Y123 -5 Y211 - 8 Y212 - 10 Y213 - 12 Y221 - 7 Y222 -6 Y223 - 5 Y311 - 8 Y312 - 10 Y313 - 12 Y321 - 7 Y322 - 6 Y323 The Formulation

23. SUBJECT TO Regional demands: 2) Y111 + Y121 = 100 3) Y211 + Y221 = 200 4) Y311 + Y321 = 125 5) Y112 + Y122 = 145 6) Y212 + Y222 = 120 7) Y312 + Y322 = 280 8) Y113 + Y123 = 234 9) Y213 + Y223 = 285 10) Y313 + Y323 = 362 Plant capacities: 11) 12 X11 + 23 X21 + 18 X311 + 6 X312 <= 82000 12) 12 X12 + 23 X22 + 18 X32 <= 60000 13) 2 X11 + 6 X21 + 5 X311 + 11 X312 <= 55000 14) 2 X12 + 6 X22 + 5 X32 <= 15000 Eastern Central Western

24. Fixed costs: 15) - 10000 Z11 + X11 <= 0 16) - 10000 Z21 + X21 <= 0 17) - 10000 Z311 + X311 <= 0 18) - 10000 Z312 + X312 <= 0 19) - 10000 Z12 + X12 <= 0 20) - 10000 Z22 + X22 <= 0 21) - 10000 Z32 + X32 <= 0 Production – Distribution dependency: 22) - X11 + Y111 + Y112 + Y113 = 0 23) - X21 + Y211 + Y212 + Y213 = 0 24) - X311 - X312 + Y311 + Y312 + Y313 = 0 25) - X12 + Y121 + Y122 + Y123 = 0 26) - X22 + Y221 + Y222 + Y223 = 0 27) - X32 + Y321 + Y322 + Y323 = 0 END INT Z11 Z12 Z21 Z22 Z311 Z312 Z32

25. ProductProd 1 Prod 2 Prod 3 Factory location Dayt on Tijua na Dayt on Tijua na Dayton Tijua na Process A Process B Units produced 479 605767 Distribution Eastern region 100 200125 Central region 145 120280 Western region 234 285362 The Solution – Max Profit = $309,064

26. A “Solver” Solution Let me show you what solver can do with this problem.

27. Another Example? Could you share with us another example?

28. Production Planning – Strategic A manufacturer produces four household products fabricated from sheet metal. The production system consists of five production centers at two plants: stamping, drilling, assembly, finishing (painting and printing), and packaging. For a given month, the manufacturer must decide how much of each product to manufacture, and to aid in this decision, he has assembled the data shown in the following Tables. Furthermore, he knows that only 1000 square feet of the type of sheet metal used for products 2 and 4 will be available at each plant during the month. Product 2 requires 2.0 square feet per unit and product 4 uses 1.2 square feet per unit.

29. TABLE 1 Production Data PRODUCTION RATES IN HOURS PER UNIT production Department prod 1 prod 2 prod 3 prod 4 hours available Plant 1 Plant 2 Stamping0.030.150.050.10 150 250 Drilling0.060.12-0.10 200 200 Assembly0.050.100.050.12 300 200 Finishing0.040.200.030.12 175 275 Packaging0.020.060.020.05 300 100

30. TABLE 2 Product Data NET SELLINGVARIABLE SALESPOTENTIAL ProductPRICE/UNITCOST/UNIT MINIMUMMAXIMUM Plant 1 Plant 2 110 $6 5 10006000 225 $15 13 -500 316 $11 10 5003000 420 $14 12 1001000

31. TABLE 3 distribution costs Plant /warehouse Warehouse 1 Warehouse 2 Plant 1$21 Plant 2 34 Demands – as a percent of 40 % 60 % above sales potential

32. Formulation Variable definitions: X ij = number of units of product i produced at plant j Y ijk = number of units of product i shipped from plant j to warehouse k Profit = selling price – variable cost – distribution costs MAX 4 X11 + 5 X12 + 10 X21 + 12 X22 + 5 X31 + 6 X32 + 6 X41 + 8 X42 - 2 Y111 - 2 Y211 - 2 Y311 - 2 Y411 - Y112 - Y212 - Y312 - Y412 - 3 Y121 - 3 Y221 - 3 Y321 - 3 Y421 - 4 Y122 - 4 Y222 - 4 Y322 - 4 Y422

33. Constraints Department processing constraints 2) 0.03 X11 + 0.15 X21 + 0.05 X31 + 0.1 X41 <= 150 3) 0.06 X11 + 0.12 X21 + 0.1 X41 <= 200 4) 0.05 X11 + 0.1 X21 + 0.05 X31 + 0.12 X41 <= 300 5) 0.04 X11 + 0.2 X21 + 0.03 X31 + 0.12 X41 <= 175 6) 0.02 X11 + 0.06 X21 + 0.02 X31 + 0.05 X41 <= 300 7) 0.03 X12 + 0.15 X22 + 0.05 X32 + 0.1 X42 <= 250 8) 0.06 X12 + 0.12 X22 + 0.1 X42 <= 200 9) 0.05 X12 + 0.1 X22 + 0.05 X32 + 0.12 X42 <= 200 10) 0.04 X12 + 0.2 X22 + 0.03 X32 + 0.12 X42 <= 275 11) 0.02 X12 + 0.06 X22 + 0.02 X32 + 0.05 X42 <= 100 Plant 1 Plant 2

34. warehouse upper/lower bounds 12) Y111 + Y121 >= 400 13) Y111 + Y121 <= 2400 14) Y211 + Y221 <= 200 15) Y311 + Y321 >= 200 16) Y311 + Y321 <= 1200 17) Y411 + Y421 >= 40 18) Y411 + Y421 <= 400 19) Y112 + Y122 >= 600 20) Y112 + Y122 <= 3600 21) Y212 + Y222 <= 300 22) Y312 + Y322 >= 300 23) Y312 + Y322 <= 1800 24) Y412 + Y422 >= 60 25) Y412 + Y422 <= 600 Warehouse 1 Warehouse 2

35. produce only what is to be shipped 26) - X11 + Y111 + Y112 = 0 27) - X21 + Y211 + Y212 = 0 28) - X31 + Y311 + Y312 = 0 29) - X41 + Y411 + Y412 = 0 30) - X12 + Y121 + Y122 = 0 31) - X22 + Y221 + Y222 = 0 32) - X32 + Y321 + Y322 = 0 33) - X42 + Y421 + Y422 = 0 sheet metal constraint 34)2 X21 + 1.2 X41 <= 1000 35)2 X22 + 1.2 X42 <= 1000

36. Solution Prod 1Prod 2 Prod 3 Prod 4 Plant 1 212 1 2 1 2 3333.3 1680 440 1000 1200 100 Warehouse 1 1680 200 1200 40 2 3333.3 240 1000 60 max profit = $25,120

37. Alternate Solution Prod 1Prod 2 Prod 3Prod 4 Plant 1 212 1 21 2 3333.3 880 440 1000 2000 100 Warehouse 1 880 200 1200 40 2 3333.3 240 1000 800 60 max profit = $25,120

38. Production Planning The Dynamic Case Look, we must consider the fact that demands are going to fluctuate significantly over the next several years

39. Let x ijt = number of units or product i produced by process j in period t s it = number of units of product i sold in period t I it = number of units of product i in inventory at the end of period t Decision Variables

40. Model Parameters r it = revenue from selling one unit of product i in period t c ijt = variable production cost of one unit of product i by process j in period t F it = maximum sales forecasted for product i in period t a ijk = units of resource k required for each unit of product i produced by process j. b kt = number of units of resource k available in time period t d it = inventory carrying cost for product i during period t h ijt = cost of changing production levels for product i using process j in period t

41. Resource constraints Inventory balance constraints Smoothing constraints Upper / lower bounds

42. Turn-in Problem #3 This is a great exercise for the student! Due Monday September 28 Web Submission