Strategic Production Planning Now showing at your local university

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.

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

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

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

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

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

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

Production Strategy - Example Excel

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

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)

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.

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

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?

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

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

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?

Makit Company ProductProd 1 Prod 2 Prod 3 Factory location DaytonTijuanaDaytonTijuana Dayton Tijuana Per unit data Process A Process B Production cost $ Material cost$ Labor hr Machine hr Fixed setup cost

Plant Capacities Labor hours per year Machine hrs per year Dayton Tijuana ProductEastern region Central region Western region Trimmer Edger Snowblower More Data Annual Demand

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

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 = Z Z Z Z Z Z Z X X X X X X X32 -5 Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y323 The Formulation

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 = ) Y313 + Y323 = 362 Plant capacities: 11) 12 X X X X312 <= ) 12 X X X32 <= ) 2 X X X X312 <= ) 2 X X X32 <= Eastern Central Western

Fixed costs: 15) Z11 + X11 <= 0 16) Z21 + X21 <= 0 17) Z311 + X311 <= 0 18) Z312 + X312 <= 0 19) Z12 + X12 <= 0 20) Z22 + X22 <= 0 21) 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

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 Distribution Eastern region Central region Western region The Solution – Max Profit = $309,064

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

Another Example? Could you share with us another example?

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.

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 Stamping Drilling Assembly Finishing Packaging

TABLE 2 Product Data NET SELLINGVARIABLE SALESPOTENTIAL ProductPRICE/UNITCOST/UNIT MINIMUMMAXIMUM Plant 1 Plant $ $ $ $

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

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 X X X X X X X X Y Y Y Y411 - Y112 - Y212 - Y312 - Y Y Y Y Y Y Y Y Y422

Constraints Department processing constraints 2) 0.03 X X X X41 <= 150 3) 0.06 X X X41 <= 200 4) 0.05 X X X X41 <= 300 5) 0.04 X X X X41 <= 175 6) 0.02 X X X X41 <= 300 7) 0.03 X X X X42 <= 250 8) 0.06 X X X42 <= 200 9) 0.05 X X X X42 <= ) 0.04 X X X X42 <= ) 0.02 X X X X42 <= 100 Plant 1 Plant 2

warehouse upper/lower bounds 12) Y111 + Y121 >= ) Y111 + Y121 <= ) Y211 + Y221 <= ) Y311 + Y321 >= ) Y311 + Y321 <= ) Y411 + Y421 >= 40 18) Y411 + Y421 <= ) Y112 + Y122 >= ) Y112 + Y122 <= ) Y212 + Y222 <= ) Y312 + Y322 >= ) Y312 + Y322 <= ) Y412 + Y422 >= 60 25) Y412 + Y422 <= 600 Warehouse 1 Warehouse 2

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 X X41 <= )2 X X42 <= 1000

Solution Prod 1Prod 2 Prod 3 Prod 4 Plant Warehouse max profit = $25,120

Alternate Solution Prod 1Prod 2 Prod 3Prod 4 Plant Warehouse max profit = $25,120

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

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

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

Resource constraints Inventory balance constraints Smoothing constraints Upper / lower bounds

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