CDAE Class 27 Dec. 7 Last class: Problem set 5 5. Inventory analysis and applications Quiz 7 Class evaluation Today: 5. Inventory analysis and applications Review for the final exam Reading: Inventory decisions with certain factors

CDAE Class 27 Dec. 7 Important dates: Problem set 5, due today Final exam: 8:00-11:00am, Thursday, Dec. 14

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

Take-home exercise For the liquor store example (pp ), what will be the optimal inventory policy (Q* and R) and what will be the TC if the interest rate is reduced from 10% to 6%, the net cost of each case to the store increased from $2 to $3, and the lead time increased from 1 day to 3 days? Additional question: what is the TC if the store keeps a safety stock (SS) of 20 units?

Take home exercise For the liquor store example we have just analyzed, what will be the optimal inventory policy and what will be the TC if the interest rate is reduced from 10% to 6%, the net cost of each case to the store increased from $2 to $3, and the lead time increased from 1 day to 3 days? Additional question: what will be the profit per year if the price $4? Available information: A = 5200 cases/yrk = $10/order c = $3 per caseh = $0.16 per $ per yr. Optimal policy: Order quantity = Reorder point R = 3 * (5200/365) = 43 units T = Q*/A = 466 / 5200 = yr = days TC = (5200 / 466) * 10 + (466 / 2) * 0.16 * 3 = = If the store keeps a safety stock of 20 units, TC = h*c*20 = $233.03

5.4. Inventory policy with backordering A graphical presentation (page 214) A = Annual demand Q = Order quantity S = Maximum on-hand inventory Q - S = Maximum backorders T = Q/A = time for each inventory cycle T1 = S/A = the time with on-hand inventory T2 = (Q-S)/A = T - T1 T1/T = Proportion of time with on-hand inventory T2/T = Proportion of time without on-hand inventory Lead time and reorder point

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 =T = T1 = T2 =

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 =

5.5. Production lot size model A graphical presentation Production phase (T1) Inventory-only phase (T2) 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

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

Summary of Chapter 5 -- We have discussed three different inventory models: (1) Economic order quantity (EOQ) model -- Graph -- No backordering -- No production -- Lead time is zero or more than zero -- Safety stock (SS) (does not affect Q* but does affect R and TC) (2) Backordering model -- Graph -- Backordering -- Goodwill (shortage) cost (3) Production and inventory model -- Graph -- Production rate -- General procedures of solving an inventory problem -- Which of the three models? -- List the available info. (e.g., A= …, K= …) and pay attention to the units -- Use the CORRECT formula or formulas for each question

Summary and comparison of the three models EOQ model Backordering model Production model Graph Given info A, c, h, K, L, SS A, c, h, K, L, P A, c, h, K, B Solutions Q*, R, TC, T Q*, S*, R, TC, T, T1, T2 Q*, TC, T, T1, T2 Key words backorder, shortage, Production rate goodwill cost 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 production run T1/T = T2/T =

Final exam 1. What will be covered in the exam? 2. What will be the format? 3. What are the study materials and practice problems? 4. What do you need to bring to the exam? 5. Suggestions

Final exam 1. What will be covered in the exam? Chapter 4 (includes project 3)50-60% Chapter %

Final exam 2. What will be the format? -- Short-answer questions (e.g., for an queuing system like a bank, what is the probability to have more than 2 customer in the bank?) -- Problems [e.g, for an inventory problem, what is the optimal order quantity (Q*) and reorder point (R)?] -- Graphical analysis (e.g., graphically present all the available information about an inventory situation).

Final exam 3. What are the study materials and practice problems? Quiz 6 and Quiz 7 Class examples Class exercises Take-home exercises Project 3* Lecture notes (class 19 - class 27) Problem sets 4 and 5 Readings

Final exam 4. What do you need to bring to the exam? -- Formula sheet: one 8.5x11 page (one side), formulas and variable definitions, and graphs without numbers ONLY(the formula sheet will be collected with the exam) -- A calculator (not a cell phone) -- A ruler will be helpful

Final exam 5. Suggestions a. Study and understand the logic of each method (e.g., which formula to use for a particular problem) b. Go over each quiz and make sure you understand each question c. Go over your notes and each class example and exercise, especially for the classes you missed d. Go over your project 3 and problem sets and get help for the problems you are not sure. e. Study hard and feel confident!

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