Inventory management

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Inventory Management

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Inventory management

  1. 1. DBH11 Chapter 11 Inventory ManagementInventory: An inventory is a stock or store of goods. Firms stock hundreds or even thousands of itemsin inventory ranging from small things (eg. pencil, paper clips etc) to large items (eg. machines, trucksetc).Major reasons for holding inventory:To understand why firms hold inventories, we need to understand the following functions of inventory. (i) To meet anticipated customer demand: A customer can be a person who walks in off the street to buy a new stereo system, a mechanic who requests a tool at a tool crib, or a manufacturing operation. These inventories are called anticipated stocks because they are held to satisfy expected demand. (ii) To smooth production requirements: Firms that experience seasonal patterns in demand often build up inventories during pre-season periods to meet overly high requirements during seasonal periods. Companies that process fruits and vegetables deal with this inventory. (iii) To decouple operations: Manufacturing firms often use inventories as buffer between successive operations to maintain continuity of production that would otherwise be disrupted by events such as breakdown of equipments, and accidents that cause a portion of the operation to shut down temporarily. (iv) To protect against stock outs: Delayed deliveries and unexpected increases in demand increase the risk of shortages. This risk of shortages can be reduced by holding safety stocks. (v) To take advantage of order cycles: To minimize purchasing costs, a firm often buys in quantities that exceed immediate requirements. This necessitates storing some or the entire purchased amount for later use. (vi) To hedge against price increase: (vii) To permit operations: The production operations take a certain amount of time means that there is some work-in-process inventory. (viii) To take advantage of quantity discounts: Suppliers may give discounts on large orders.Objectives of inventory control:Inventory management has two main concerns: (i) Customer service: That is, to have the right goods, in sufficient quantities, in the right place, at the right time. (ii) Cost of ordering and carrying inventories.Managers have a number of measures of performance they can use to judge the effectiveness ofinventory management. A widely used measure is inventory turnover. Another useful measure is daysof inventory on hand.Inventory turnover: It is the ratio of annual cost of goods sold to average inventory investment.Days of inventory on hand: It is a number that indicates the expected number of days of sales that canbe supplied from existing inventory. 1
  2. 2. DBH11Inventory counting system:It can be (i) periodic or (ii) perpetual.Periodic inventory system: A physical count of items in inventory is made at periodic intervals suchas monthly or weekly in order to decide how much to order of each item. Example: a retailerperiodically checks the selves and stock room to determine the quantity on hand. Then he estimateshow much will be demanded prior to the next delivery period.Perpetual or continual inventory system: System that keeps track of removals from inventorycontinuously, thus monitoring current level of each item.Lead time: Time interval between ordering and receiving the order.Point-of-sale: Record items at time of sale.Inventory costs:There are three basic costs associated with inventories. They are as follows: (i) inventory holding or carrying costs (ii) transaction or ordering costs (iii) shortage costs(i) Holding costs: It relates to physically having items in storage. Example: costs include interest,insurance, taxes, breakage, heat, light, rent security etc.(ii) Transaction costs: The cost of ordering and receiving inventory. Example: preparing invoices,shipping costs, inspection costs, moving the goods to temporary storage.(iii) Shortage cost: Shortage costs result when demand exceeds the supply of inventory on hand.Example: loss of customer goodwill, late charges etc.How much to order: (Economic order quantity (EOQ) models)Economic order quantity (EOQ): The order size that minimize total annual costs.EOQ models: These models identify the optimal order quantity by minimizing the sum of certainannual costs that vary with order size.Three important models are: (i) The basic EOQ model. (ii) The economic production quantity (EPQ) model (iii) The quantity discount model(i) The basic EOQ model: It is used to identify the optimal order quantity by minimizing the sum ofcertain annual costs of holding inventory and ordering inventory. This model involves the followingassumptions: 1. Only one product is involved. 2. Annual demands are known 3. Demand rate is reasonably constant 4. Lead time does not vary 5. Each order is received in a single delivery 6. There are no quantity discount 2
  3. 3. DBH11 QAnnual carrying cost = × H ............................(i) 2where Q = order quantity in units and H = carrying cost per unit. It is proportional to Q. Q Annual ×H cost 2 Q DAnnual ordering cost = Q ×S ..............................(ii)where D = demand in units per year and S = ordering cost. D ×S QTotal annual cost = Annual carrying cost + Annual ordering cost Q D TC = ×H + ×S .......................................(iii) 2 QDifferentiating (iii) w. r. to Q, setting the results equal to zero and solving for Q, we find 2 DSthe minimum order quantity Q0 = ...............................(iv) H Q D Annual TC = ×H + ×S cost 2 Q Q Q0Length of order cycle = .............................................(v) D DNumber of orders per year = .....................................(vi) Q0Example: A local distributor for a national tire company expects to sell approximately 9,600 steel-belted radial tires of a size and tread design next year. Annual carrying cost is $16 per tire and orderingcost is $75. The distributor operates 288 days a year. 3
  4. 4. DBH11 (a) What is the EOQ? (b) How many tires per year does the store order? (c) What is the length of an order cycle? (d) What is the total annual cost if the EOQ is ordered?Solution:Given, D = 9,600 tires per year H = $16 per unit per year S = $75 2 DS 2 × 9,600 × 75a. Q0 = = = 300 tires. H 16 D 9,600b. Number of orders per year = = = 32 . Q0 300 Q0 300 1 1c. Length of order cycle = = = = × 288 = 9 workdays. D 9,600 32 32 Q D 300 9,600d. TC = ×H + ×S = ×16 + × 75 = 2,400 + 2,400 = $4,800 . 2 Q 2 300Example 2: Piddling manufacturing assembles security monitors. It purchases 3600 black-and-whitecathode ray tubes a year at $65 each. Ordering costs are $31, and annual carrying costs are 20% of thepurchasing price. Compute the optimal quantity and the total annual cost of ordering and carrying theinventory.Economic production quantity (EPQ): This model involves the following assumptions: 1. Only one item is involved. 2. Annual demands are known 3. The usage rate is constant 4. Usage occurs continually but production occurs periodically 5. The production rate is constant 6. Lead time does not vary 7. There are no quantity discount I max DTCmin = Carrying cost + Setup cost = ×H + × S where Imax =Maximum inventory. 2 Q0 2 DS pThe optimal run quantity is Q0 = × where p = production or delivery rate and u = usage H p −urate. Q0Cycle time (the time between orders or between the beginning of the runs) = u Q0Run time (The production phase of the circle) = p Q0The maximum inventory level = I max = ( p − u) . p I maxThe average inventory level = I average = 2Example: A toy manufacturer uses 48,000 rubber wheels per year for its popular dump truck series.The firm makes its own wheels, which it can purchase at a rate of 800 per day. The toy trucks are 4
  5. 5. DBH11assembled uniformly over the entire year. Carrying cost is $1 per wheel a year. Setup cost for aproduction run of wheels is $45. The firm operates 240 days per year. Determine the (a) Optimal run size (b) Minimum total annual cost for carrying and setup (c) Cycle time for the optimal run size (d) Run timeSolution: Given, D = 48,000 wheels per year H = $1 per wheel per year S = $45 p = 800 wheels per day u = 48,000 wheels per 240 days or 200 wheels per day. 2 DS p 2 × 48,000 × 45 800a. Q0 = × = = 2,400 wheels. H p −u 1 800 − 200 Q0b. The maximum inventory level = I max = ( p − u ) = 2400 ( 800 − 200) = 1800 wheels. p 800 I max The average inventory level = I average = = 900 2 I max D 1800 48000 TCmin = Carrying cost + Setup cost = ×H + ×S = ×1 + × 45 = $1,800 2 Q0 2 2400 Q0 2400c. Cycle time = = = 12 workdays. i.e., a run of wheels will be made every 12 days u 200 Q0 2400d. Run time = = = 3 workdays. i.e., each run will take 3 days to complete. p 800Quantity discount Model:Quantity discounts are prices reductions for large orders offered to customers to induce them to buy inlarge quantities. Q DTC = Carrying cost + Ordering cost + Purchasing cost = 2 × H + Q × S + P × D where P = Unit price.Example: The maintenance department of a large hospital uses about 816 cases of liquid cleanserannually. Ordering costs are $12, carrying costs are $4 per case a year, and the new price scheduleindicates that orders of less than 50 cases will cost $20 per case, 50 to 79 cases will cost $18 per case,80 to 99 cases will cost $17 per case, and large orders will cost $16 per case. Determine the optimalorder quantity and the total cost.Solution:Given D = 816 cases per year S = $12 H = $4 per case per yearand Range Price 1 - 49 $20 5
  6. 6. DBH11 50 - 79 $18 80 - 99 $17 100 or more $16 2 DS 2 × 816 ×121. Q0 = = = 69.97 ≈ 70 cases H 42. Total cost to purchase 816 cases a year at the rate of 70 cases per order is Q D 70 816TC 70 = ×H + ×S + P ×D = ×4 + ×12 +18 × 816 = $14,968 2 Q 2 70Total cost to purchase 816 cases a year at the rate of 80 cases per order is Q D 80 816TC 80 = ×H + ×S + P ×D = ×4 + ×12 +17 × 816 = $14,154 2 Q 2 80Total cost to purchase 816 cases a year at the rate of 100 cases per order is Q D 100 816TC100 = ×H + ×S + P ×D = ×4 + ×12 +16 ×816 = $13,354 2 Q 2 100Since 100 cases per order yields the lowest cost, 100 cases is the overall optimal order quantity.Example 2: Surge electric uses 4000 toggle switches a year. Switches are priced as follows. It costsapproximately $30 to order and receive it and carrying costs are 40% of the purchase price per unit onan annual basis. Determine the optimal order quantity and the total annual cost. Range Price 1 - 499 $0.90 500 - 999 $0.85 1000 or more $0.80Solution: 6
  7. 7. DBH11 50 - 79 $18 80 - 99 $17 100 or more $16 2 DS 2 × 816 ×121. Q0 = = = 69.97 ≈ 70 cases H 42. Total cost to purchase 816 cases a year at the rate of 70 cases per order is Q D 70 816TC 70 = ×H + ×S + P ×D = ×4 + ×12 +18 × 816 = $14,968 2 Q 2 70Total cost to purchase 816 cases a year at the rate of 80 cases per order is Q D 80 816TC 80 = ×H + ×S + P ×D = ×4 + ×12 +17 × 816 = $14,154 2 Q 2 80Total cost to purchase 816 cases a year at the rate of 100 cases per order is Q D 100 816TC100 = ×H + ×S + P ×D = ×4 + ×12 +16 ×816 = $13,354 2 Q 2 100Since 100 cases per order yields the lowest cost, 100 cases is the overall optimal order quantity.Example 2: Surge electric uses 4000 toggle switches a year. Switches are priced as follows. It costsapproximately $30 to order and receive it and carrying costs are 40% of the purchase price per unit onan annual basis. Determine the optimal order quantity and the total annual cost. Range Price 1 - 499 $0.90 500 - 999 $0.85 1000 or more $0.80Solution: 6
  8. 8. DBH11 50 - 79 $18 80 - 99 $17 100 or more $16 2 DS 2 × 816 ×121. Q0 = = = 69.97 ≈ 70 cases H 42. Total cost to purchase 816 cases a year at the rate of 70 cases per order is Q D 70 816TC 70 = ×H + ×S + P ×D = ×4 + ×12 +18 × 816 = $14,968 2 Q 2 70Total cost to purchase 816 cases a year at the rate of 80 cases per order is Q D 80 816TC 80 = ×H + ×S + P ×D = ×4 + ×12 +17 × 816 = $14,154 2 Q 2 80Total cost to purchase 816 cases a year at the rate of 100 cases per order is Q D 100 816TC100 = ×H + ×S + P ×D = ×4 + ×12 +16 ×816 = $13,354 2 Q 2 100Since 100 cases per order yields the lowest cost, 100 cases is the overall optimal order quantity.Example 2: Surge electric uses 4000 toggle switches a year. Switches are priced as follows. It costsapproximately $30 to order and receive it and carrying costs are 40% of the purchase price per unit onan annual basis. Determine the optimal order quantity and the total annual cost. Range Price 1 - 499 $0.90 500 - 999 $0.85 1000 or more $0.80Solution: 6
  9. 9. DBH11 50 - 79 $18 80 - 99 $17 100 or more $16 2 DS 2 × 816 ×121. Q0 = = = 69.97 ≈ 70 cases H 42. Total cost to purchase 816 cases a year at the rate of 70 cases per order is Q D 70 816TC 70 = ×H + ×S + P ×D = ×4 + ×12 +18 × 816 = $14,968 2 Q 2 70Total cost to purchase 816 cases a year at the rate of 80 cases per order is Q D 80 816TC 80 = ×H + ×S + P ×D = ×4 + ×12 +17 × 816 = $14,154 2 Q 2 80Total cost to purchase 816 cases a year at the rate of 100 cases per order is Q D 100 816TC100 = ×H + ×S + P ×D = ×4 + ×12 +16 ×816 = $13,354 2 Q 2 100Since 100 cases per order yields the lowest cost, 100 cases is the overall optimal order quantity.Example 2: Surge electric uses 4000 toggle switches a year. Switches are priced as follows. It costsapproximately $30 to order and receive it and carrying costs are 40% of the purchase price per unit onan annual basis. Determine the optimal order quantity and the total annual cost. Range Price 1 - 499 $0.90 500 - 999 $0.85 1000 or more $0.80Solution: 6

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