operational planning & control CHAPTER 7

6.1. Introduction Production Planning & Control All activities related to purchasing, storing, and manufacturing materials, products, & components. Involve different functions Forecasting: predicting future customer demands Planning: planning for future. Long range: capacity (aggregate) planning, Short range: materials requirements planning (MRP) Inventory Control: raw material, components, finished products Production scheduling: time, machine, workers, for each job

7.3. Demand Forecasting 7.3.1. Moving Average (MA) method: Forecast = Average of actual demand in last (n) time periods Weighted MA (WMA): higher weight to more recent data or

7.3.1. Moving Average (MA) Choice of (n) and weights (wi) Arbitrary, Based on experience Can be determined by experimentation The last forecast (Ft) is forecast for all the future. It will be updated when a new time period brings a new actual demand value

7.3.1. Moving Average (MA) Example Given the data below, forecast using the moving average method with(n = 4) Given weights (0.4, 0.8, 1.2, 1.6), calculate the forecast using the weighted moving average method t 1 2 3 4 5 6 7 8 9 10 Xt

7.3.1. Moving Average (MA) Example t 1 2 3 4 5 6 7 8 9 10 11 Xt Ft (4 +6 +3 +6) /4 = 4.75 (6 +3 +6 +5) /4 = (3 +5 +4) 4.5 5.25 4.25 +4 +5)

7.3.1. Moving Average (MA) Example WMA(4): Normalized weights ( 4) = 0.1, 0.2, 0.3, 0.4 t 1 2 3 4 5 6 7 8 9 10 11 Xt Ft (1*4 +2*6 +3*3 +4*6) /10 = 4.9 (1*6 +2*3 +3*6 +4*5) /10 (1*3 +3*5 +4*4) 4.6 5.2 4.3 4.1 +3*4 +4*5) 4.4

7.3.2. Exponential Smoothing (ES) Weights decrease exponentially with the age of data Similar to WMA but more efficient, especially for computer Need 3 pieces of data: last period demand (Xt-1), last period forecast (Ft-1), smoothing constant ().

7.3.2. Exponential Smoothing (ES) Choice of () Arbitrary, based on experience Can be determined by experimentation Initial Value (F1). Set F1 = X1. or F1 = average of first few actual demands

7.3.2. Exponential Smoothing (ES) Example For the data below, calculate the forecast using the exponential smoothing method with  = 0.2 F1 = X1 t 1 2 3 4 5 6 7 8 9 10 Xt

7.3.2. Exponential Smoothing (ES) Example WMA(4): Normalized weights ( 4) = 0.1, 0.2, 0.3, 0.4 t 1 2 3 4 5 6 7 8 9 10 11 Xt Ft .2*4 + .8*4 = .2*6 4.4 2*3 + .8*4.4 4.12 2*6 + .8*4.12 4.496 4.597 4.477 4.782 4.426 4.34 4.472

7.3.3. Regression Analysis Regression models assume the same pattern (curve) of demand will continue in the future Least-Squares Regression Minimize the sum of squared errors Linear Regression Ft = a + bt a = intercept, b = slope

7.3.3. Regression Analysis Linear Regression Forecasted demand: Ft = a + bt Actual demand: Xt Error: a + bt - Xt Sum of Squared Errors:  (a + bt – Xt)2 Minimizing gives

7.3.3. Linear Regression Example For the data below, calculate the forecast using linear regression t 1 2 3 4 5 Xt 7 8 10

7.3.3. Linear Regression Example  t 1 2 3 4 5 15 Xt 7 8 10 33 t*Xt 21 32 50 116 t2 9 16 25 55

7.3.3. Linear Regression Example Ft = 1.5 + 1.7t F6 = 1.5 + 1.7(6) = 11.7 F7 = 1.5 + 1.7(7) = 13.4 . . .

7.5. Inventory Planning & Control Objective: Determine proper inventory levels to satisfy customer demands & minimize total cost Decisions: What to order How much to order When to order

7.5. Inventory Planning & Control Types of inventory costs Procurement cost (PC): order processing, paper work, supplier fees, receiving, & inspection (per order) Carrying cost (CC): investment opportunity, storage, obsolescence, spoilage, insurance, taxes (per unit/per time unit) Total cost (TC) = PC + CC

7.5. Inventory Planning & Control Basic inventory (EOQ) model Assumptions Demand rate is constant & known A complete order arrives when inventory level drops to 0 Definitions: T = cycle time (time between successive orders) D= demand rate (unit/time unit) Q = quantity of each order (lot size)

7.5. Inventory Planning & Control Basic inventory (EOQ) model

7.5. Inventory Planning & Control Basic inventory (EOQ) model Number of orders/yr =D/Q Ordering cost/yr = PC*D/Q Average inventory level = Q/2 Holding cost/yr = CC*Q/2 Total cost/yr: TC(Q) = PC*D/Q + CC*Q/2

7.5. Inventory Planning & Control Basic inventory (EOQ) model To minimize TC, set: TC’ = 0 - PC*D/Q2 + CC/2 = 0 Solving gives the Economic Order Quantity (EOQ)

7.5. Inventory Planning & Control EOQ Example: Given D = 50 units/month PC = $72/order CC = $6/unit/year Find Q, T, TC CC = 6/12 = $0.5/unit/month = 120 units T = Q/D = 120/50 = 2.4 months TC = 72(50/120) + 0.5(120/2) = $60/month

End of Chapter 7 Questions?