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Lot Sizing

Lot Sizing. Inventory. Types of inventory Raw materials/purchase parts Work-in-process Finished goods Holding of inventory is expensive Ties up funds Requires space People/system needed to track What happens when the product changes?. Inventory control.

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Lot Sizing

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  1. Lot Sizing

  2. Inventory • Types of inventory • Raw materials/purchase parts • Work-in-process • Finished goods • Holding of inventory is expensive • Ties up funds • Requires space • People/system needed to track • What happens when the product changes?

  3. Inventory control • Inventory control aimed at providing items at the time of need • Need to determine re-order point (inventory level at which a new supply should be ordered to bring inventory to its desired level) • Attempt to provide some safety stock to compensate for fluctuations in demand, however, difficult to predict reasonable safety stock due to: • False assumptions about observed demand (quantity) • Lack of ability to determine specific timing of future demand (timing) • Leads to: • Inventory imbalance • Stockouts (shortages) • High overall inventory

  4. Approaches to inventory control • Work without inventory or reduce to minimum (JIT) • Utilize an inventory management system, MRP System (Materials Requirements Planning System) • Economic order quantity

  5. MRP

  6. Example of MRP logic • It takes 1 unit of B and 2 units of C to assemble product A • The gross requirements for A: 200 due in week 4 and 250 due in week 5 • At the beginning of week 1 • Determine the production schedules for A, B and C

  7. EOQ model • Simplest and most fundamental of all inventory models • Describes the important trade-off between fixed order cost and holding costs

  8. EOQ model assumptions • Demand rate is known and is a constant λ units per unit time • Unit of time may be days, weeks, months, …, as long as all relevant variables are expressed in the same units • Default unit of time is a year • Shortages are not permitted • There is no order lead time • The costs include • Setup costs at K per order placed • Proportional order cost at c per unit ordered • Holding cost at h per unit held per unit time

  9. Changes in stock levels over time

  10. EOQ model development • Objective is to choose Q to minimize the average cost per unit of time (typically assumed to be a year) • Components of the average annual cost • In each cycle, the total fixed order cost (K) plus the proportional order cost (c∙Q) is K + c∙Q • To obtain the order cost per unit time, divide by the cycle length T → (K + c∙Q)/T • The average inventory level during one cycle is Q/2 → because all cycles are identical, the average inventory level over a time horizon composed of many cycles is also Q/2 • Holding cost (carrying cost) per unit time is h∙Q/2

  11. Average annual cost • Average annual cost, G(Q) • As Q units are consumed each cycle at a rate of λ, it follows that T = Q/λ • Three terms above represent setup cost, purchase cost, and holding cost

  12. Determine the minimum of the average annual cost

  13. Determine EOQ • Find Q to minimize G(Q) • Set the derivative equal to zero • Proportional order cost incurred per unit time (λ∙c) is independent of Q and is generally ignored when computing average costs • c does affect the value of EOQ indirectly, as h appears in the formula and h = I∙c, I = interest rate (I is typically an annual interest rate)

  14. EOQ example • Number 2 pencils at the bookstore are sold at a fairly steady rate of 60 per week. The pencils cost the bookstore 2 cents each and sell for 15 cents each. It costs the bookstore $12 to initiate an order, and holding costs are based on an annual interest rate of 25 percent. Determine the optimal number of pencils for the bookstore to purchase and the time between placement of orders. On average, what are the yearly holding and setup costs for this item?

  15. Another EOQ example • The Ohio State University location of McDonald’s uses 120 six-ounce paper cups per day. McDonald’s plans to be open 360 days per year. The cups cost $.10 per dozen; ordering costs are $5 per order; and carrying costs are 50 percent of the item cost (since space is at a premium). (a) Find the economic order quantity if delivery is instantaneous (work the problem in units of dozens of cups). (b) Currently, cups are ordered every thirty days. Relate current order quantity, optimal order quantity, current total costs, and optimal total costs. What do you recommend?

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