Further Business Applications Lesson 6.3

Economic Lot Size A manufacturer can produce its product in varying batch sizes 120 once a year 60 twice a year 10 each month … etc. Elements to be considered k = Costs for storage one unit for a year f = Fixed setup cost per batch g = Mfg. cost per item M = Total number of items per year q = Number of items per batch 2

Economic Lot Size Manufacturing cost per batch Number of batches per year Total annual manufacturing cost Inventory goes down linearly q to 0 Average inventory q/2 units per year Storage costs 3

Economic Lot Size Total production cost is sum of Manufacturing costs Storage costs To minimize T(q) we solve T '(q) = 0 for q Find this solution before proceeding Check your answer with text book solution 4

Try It Out LeTourneau Lamps makes 100,000 lamps annually Costs $1 to store a lamp for a year Costs $500 to set up factory to produce a batch What is the optimum number of lamps to produce in each batch? 5

Economic Order Quantity Suppose we purchase an item for sale How often should we order How many do we buy for each order Elements to be considered k = Costs for storage one unit for a year f = Fixed costs to place an order M = Total number of items per year q = Number of items per batch Goal: minimize Total Cost = Storage Cost + Reorder Cost 6

Economic Order Quantity Assume average inventory of q/2 Yearly storage cost Number of orders placed annually Reorder cost Total cost 7 Determine T '(q) Solve T '(q) = 0 for q

Sample Problem The LeTourneau Bookstore has an annual demand for 100,000 copies of that best seller, Calculus with Applications It costs $.50 to store the copy for one year It costs $60 to place an order What is the optimum number of copies per order? 8

Assignment Lesson 6.3 Page 333 Exercises 5 – 13 odd 9