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Periodic inventory models – single level  The objective is to minimize holding and backlog costs.  Unsatisfied demand is backlogged  Holding and backlog.

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Presentation on theme: "Periodic inventory models – single level  The objective is to minimize holding and backlog costs.  Unsatisfied demand is backlogged  Holding and backlog."— Presentation transcript:

1 Periodic inventory models – single level  The objective is to minimize holding and backlog costs.  Unsatisfied demand is backlogged  Holding and backlog costs are convex  Stationary demand  If there is no setup cost for ordering  Base stock (S) policy is optimal  If the inventory position P t <S; order S-P t  If there is a positive setup cost for ordering  Re-order point, order-up-to-level (s, S) policy is optimal  If the inventory position P t <s; order S-P t

2 Multi-echelon systems n n-1 2 1  Ordering cost is for level i is the transportation cost from level i+1 to i  Ordering cost for level n is the purchasing cost  All ordering costs are linear, except at level n  Backlog costs for level 1 is the backlog costs for external demand  Backlog cost for level i is the cost of not being able to support level i-1 when level i-1 requested material

3 Multi-echelon systems n n-1 2 1  Echelon stock for level 2 =  on hand at level 2 +  on hand at level 1 +  on order from level 2 to level 1  Echelon inventory position for level 2 =  echelon stock for level 2 +  on order from level 3 to level 2  Similarly for level j  If there is no setup cost for ordering  Base stock (S j ) policy is optimal for each level j  If the echelon inventory position P j t <S j ; order S j -P j t  If there is a positive setup cost for ordering  Re-order point, order-up-to-level (s j, S j ) policy is optimal for each level j  If the inventory position P j t <s j ; order S j -P j t

4 Tree like supply chains Warehouse Retailer 1 Supplier Retailer 2  Echelon stock for warehouse =  on hand at retailer 1 +  on hand at retailer 2 +  on hand at warehouse +  on hand at warehouse to retailers 1 & 2  Echelon inventory position for warehouse =  echelon stock for warehouse  on order from supplier to warehouse  Assumption: no transshipments  Assumption: retailer 1 and retailer 2 stocks are not seriously out of balance  Base stock policy (S) for no setup case and (s, S) policy for setup case are optimal for the warehouse and retailers (using the echelon stock for warehouse)

5 Minimizing inventory subject to backorders  No repairs  Poisson demands at bases  Demand at depot = 1 + 2  Re-order point at depot = S 0  Re-order point at bases S 1, S 2  Expected number of units being delayed at the depot Depot Base 1 Supplier Base 2   D 22 11  Percentage delayed

6 Minimizing inventory subject to backorders  Backorders at Base j Depot Base 1 Supplier Base 2   D 22 11  Problem

7 Example  If the fill rate at the depot is 50%  Effective lead time at base 1 = 1+0.5*2=2 months  Effective lead time at base 2 = 2+0.5*2=3 months  If the fill rate at the depot is 75%  Effective lead time at base 1 = 1+0.25*2=1.5 months  Effective lead time at base 2 = 2+0.25*2=2.5 months  Effective lead time at the bases is a function of the depot fill rate, which is a function of stock level at the depot.  So fill rate at the base is a function of stock level at the base as well as stock level at the depot Depot Base 1 Supplier Base 2   D=2 months  2 =2 months  1 =1 month

8 Managing inventory  ABC approach: Classify items into A, B, C classes. Tighter management of inventory for A items  Lead time reductions have major impact on inventories.  Inventory turnover ratio = (annual sales)/(average inventory level)  There is “economies of scale” in managing inventory. Fast moving items usually lead to larger inventory turns

9 Inventory turns for different industries IndustryUpper Quartile MedianLower Quartile Electronic components and accessories9.85.73.7 Electronic computers9.45.33.5 Household audio and video equipment6.23.42.3 Household electrical appliances8.05.03.8 Industrial chemicals10.36.64.4 Dairy products34.419.39.2 Publishing and printing9.82.41.3


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