CDAE Class 26 Dec. 4 Last class: Result of Quiz 6 5. Inventory decisions Problem set 6 Today: Result of group project 3 5. Inventory decisions Quiz 7 ( quiz for extra credit and due Thursday, Dec. 6 ) Class evaluation Next class: Review for the final exam

CDAE Class 26 Dec. 4 Important dates: Problem set 5: due Thursday, Dec. 6 Problems 6-1, 6-2, 6-3, 6-4, and 6-13 from the reading package Take-home quiz for extra credit: Due Thursday, Dec.6 Final exam, 8:00-11:00am, Monday, Dec. 10 (Chapter 4 and Chapter 5 only) $10 for the reading packages

Result of group project 3 N = 56Range = 70 – 97 Average = 89 Comments: -- Format -- Writing -- Calculation -- Recommendations

Project Labor Construction Goodwill Total  S cost Rent cost cost cost Current Option 1 Option 2 Option 3a Option 3b Options 1+3a Options 1+3b Options 2+3a Options 2+3b

5. Inventory analysis and applications 5.1. Basic concepts 5.2. Inventory cost components 5.3. Economic order quantity (EOQ) model 5.4. Inventory policy with backordering 5.5. Inventory policy and service level 5.6. Production and inventory model

5.4. Inventory policy with backordering A graphical presentation (page 214) A = Annual demand (e.g., 7300 kg per year) Q = order quantity [ e.g., 200 kg per order (delivery) ] S = Maximum on-hand inventory (e.g, 150 kg) Q - S = Maximum backorders (e.g., 50 kg) T = Q/A = time for each inventory cycle (e.g., T = 200/7300 = yr = 10 days) T1 = S/A = the time with on-hand inventory (e.g., T1 = 150/7300 = yr = 7.5 days) T2 = (Q-S)/A = T - T1 (e.g., T2= 50/7300 = yr = 2.5 days) T1/T = Proportion of time with on-hand inventory T2/T = Proportion of time without on-hand inventory Lead time and reorder point (e.g., L = one day)

5.4. Inventory policy with backordering Total relevant (variable) inventory cost TC = annual ordering cost + annual holding cost + annual shortage (goodwill cost) = ……(see page 214) p = per unit goodwill (shortage) cost per year (e.g., p=$2 per unit per year) Optimal inventory policy (page 215) Q* = S* = R =

5.4. Inventory policy with backordering Example (pp ) A = 1000 cases of wine per year K = $100 per order (delivery) C = $20 per case h = $0.20 per dollar value per year p = $3.65 per unit of shortage per year L = 0 Q* = S* = R =

5.6. Production lot size model A graphical presentation (P. 220) Production phase Inventory-only phase Available information: A = annual demand K = fixed cost per production run B = annual production rate C = production cost per unit h = holding cost per dollar value per year

5.6. Production lot size model Annual total variable production cost = start-up cost + holding cost = Optimal solutions (P. 221) Q* = An example (pp ) Other useful results Maximum inventory = T1 =T2 = T1/T =T2/T =

Summary and comparison of the three models EOQ Backordering Production Graph: Given info A, c, h, K, L, SS A, c, h, K, L, P A, c, h, K, B Solutions (formulas) Q*, R, TC, T Q*, S*, R, TC, T, T1, T2 Q*, TC, T, T1, T2 Key words backorder, shortage, Production rate, goodwill cost production run Variable definitions: A = Annual demandQ* = Optimal order (production) quantity L = lead timeS* = maximum on-hand inventory c = Per unit value or priceR = reorder point h = holding cost per $ value per yearTC = total relevant inventory cost hc = holding cost per unit per yearT = Length of each inventory cycle P = goodwill (shortage) cost per unit per yearT1 = B = production rate per yearT2 = K = fixed cost per order or per production run T1/T = T2/T =