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MGTSC 352

MGTSC 352. Lecture 22: Finish Inventory Management Start Queueing. Announcements. HW 9 is available Due a week from Tuesday (Dec. 7) Quiz 3 a week from Friday (Dec. 3). Pg. 153. More on EOQ: Economies of Scale.

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MGTSC 352

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  1. MGTSC 352 Lecture 22: Finish Inventory Management Start Queueing

  2. Announcements • HW 9 is available • Due a week from Tuesday (Dec. 7) • Quiz 3 a week from Friday (Dec. 3)

  3. Pg. 153 More on EOQ: Economies of Scale The Capital Health Region* (CHR) operates four hospitals. Presently each hospital orders its own supplies and manages its inventory. A common item used is a sterile intravenous (IV) kit, with a weekly demand of 600 per week at each hospital. Each IV kit costs $5 and incurs a holding cost of 30% per year. Each order incurs a fixed cost of $150 regardless of order size. The supplier takes one week to deliver an order. Currently, each hospital orders 6,000 kits at a time. Question 1a: Should each hospital order more often? Question 1b: Should each hospital place smaller orders? Question 2: Should CHR centralize inventories? * Fictional data

  4. Analysis for one Hospital • D = 600 / week or 600  52 = 31,200 / yr • S = $150 / order • H = 0.3  $5.00 = $1.50 / kit year • Q = SQRT(2 * D * S / H) = 2,498round to 2,500 per order • Costs: • Q = 6,000: (Old)(S  D / Q) + (H  Q / 2) = $780 + $4,500 = $5,280/yr • Q = 2,500: (EOQ Solution)(S  D / Q) + (H  Q / 2) = $1,872 + $1,875 = $3,747/yr • 29% savings • System cost: 4  $3,747 = $14,988/yr

  5. Centralized Inventory • Active Learning: • Groups of two, 2 minutes • Discuss: How would the analysis change if inventory were to be centralized for the four hospitals?

  6. Analysis for four hospitals managed together • D = • S = • H = • Q =

  7. Four hospitals managed together: The Benefits • Costs: • Each hospital operated independently: 4  $3,747 = $14,988 / year • All four together: S  D / Q + H  Q / 2 = $3,744 + $3,750 = $7,494 / year • 50% savings • Quadrupling demand doubles the optimal order quantity and doubles the total relevant cost

  8. Four hospitals managed together: The Costs • How does the system need to be changed to centralize inventory? • What will it cost?

  9. pg. 151 Simulation versus EOQ

  10. Pg. 162 Back to the Distribution Game: Can we use EOQ there? Retailer A “multi-echelon” system Retailer Supplier Warehouse Retailer

  11. Upper echelon: Upper echelon Retailer Retailer Supplier Warehouse Retailer

  12. Lower echelon: Lower echelon Retailer Retailer Supplier Warehouse Retailer

  13. Holding Cost for a two-echelon system • Upper echelon: • Use warehouse holding cost rate • Ignore higher cost of holding inventory at retailers • Lower echelon: • Use incremental retailer holding cost rate

  14. Lead Timefor a two-echelon system • Upper echelon: • Supplier  warehouse, then warehouse  retailer Lead time = 15 days + 5 days = 20 days • Lower echelon: • Assume supply available at warehouse • Lead time = 5 days

  15. Coordination • Suppose each retailer uses QLower = 20 • Would it make sense for the warehouse to use QUpper = 50? • Coordination: Warehouse order size a multiple of sum of retailer order sizes:QUpper = n  SUM(QLower)

  16. Using EOQ for a 2-echelon system: The details • Upper echelon: • DUpper = 3  DRetailer • SUpper = SWarehouse • HUpper = HWarehouse • LTUpper = LTSupplier  Warehouse + LTWarehouse  Retailer • ROPUpper = DUpper  LTUpper • Lower echelon • DLower = DRetailer • SLower = SRetailer • HLower = HRetailer - HWarehouse • LTLower = LTWarehouse  Retailer • ROPLower = DLower  LTLower • Coordination: QUpper = n  SUM(QLower) • Choose n (an integer) and QLower to minimize total cost for the whole system

  17. Congestion

  18. Oh Henry! Sale • 1 Salesperson • 10 customers • Purchase price: $0.02 each (No change available) • I label the customers, Artem records: • when customer gets in line • when customer starts service • when customer finishes service

  19. Oh Henry! Sale • Did a line form? • Why? • What are the parts of a queueing system? • How could we have prevented the line? • What will I do with the money?

  20. Parts of a Queueing System Population Arrival Rate? Interarrival Time? Effectively infinite? Service Process # of servers? Service time? Queue Max size?

  21. pg. 172 Asgard Bank • Automatic bank machine • Investigate long lines at lunch time • Timed entry of customers • Timed service time (card in to card out)

  22. Asgard Bank – Collecting Data • Record: • arrival time • service start • service end • Compute: • inter-arrival time • service time • waiting time • time in system

  23. Asgard Bank: Times Between Arrivals(pg. 173)

  24. Asgard Bank: Arrival Rate • Given: avg. time between arrivals = 1.00 minute • average arrival rate per hour=  = ?

  25. Asgard Bank: Service Times

  26. Asgard Bank: Service Rate • Given: avg. service time = 0.95 minutes • average service rate per hour(if working continuously)=  = ? • Note: • the service rate is not the rate at which customers are served • it’s the rate at which customers could be served, if there were enough customers • service rate = capacity of ONE server

  27. Given:Average inter-arrival time = 1.00 min.Average service time = 0.95 min. Next customer arrives and begins service Customer leaves Customer arrives and begins service Why Do Customers Wait? 0.95 time What’s missing from this picture?

  28. What’s missing from this Picture? VARIABILITY!

  29. Asgard Bank – Collecting Data • Real system: • Record arrival time, service start, service end • Compute inter-arrival times service time, waiting time, time in system • Simulating the system: • Simulate inter-arrival time, service time • Compute arrival time, service start, service end, time in system, waiting time

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