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					                 Inventory Cost
   Captures time-value of holding product
   Perishability, theft, opportunity cost of cash,
    insurance, shrinkage, obsolescence
   Usually 10-15% for electronics

   Value of good*interest rate*time
                                            Fuel economy: 10 mpg
                                            Driver wages: $15/hour
                                            Ignore depreciation of vehicle, insurance
                                            Speed of vehicle: 25 mph
                                            Price of fuel: $2.50 per gallon

                                   60       Value of goods in a truck: $100,000
                                   miles    Interest rate: 6% per year

                                            Time spent at DC: 3 days
                                            Handling cost at DC: $50 per truck
100             100                DC       Ignore rent, operating cost of DC
miles           miles
                                            Calculate one way transportation
                                            cost and one way inventory cost.

                        50      40         50
                        miles   miles      miles
                  Cost Comparison
         Transportation   Inventory    Handling   Total
Direct   3($60+$25)       3($2.74)     $0         $263.22
         =$255            =$8.22

DC (3    ($36+$15)+       $4.93+       $150       $476.73
days)    2($30+$12.50)    2($1.37)+
         +($24+$10)       $1.10+
         =$170            3*($49.32)
DC (1    ($36+$15)+       $4.93+       $150       $378.09
days)    2($30+$12.50)    2($1.37)+
         +($24+$10)       $1.10+
         =$170            $49.32
                 Hypothetical curves
                                            Minim cost shipment frequency





                            Shipment frequency

We will identify the optimal when we talk about distribution systems
                 Cumulative Number of Items
                          Diagram     Production (rate D’)


number of

An item is a
fixed quantity
of infinitely                 H
quantity (e.g.
parcel, case                 tm
of beer)                                            Consumption (D’)

                             time                Consider units on area
    Cumulative Number Diagram
   Good for one origin/one destination problems
   Identify production and consumption rates
   Items waiting to be shipped
   Shipment times
   Shipment sizes
   Items waiting to be consumed
   Total wait time from production to consumption (if FIFO)
   Headway (H)
   Travel time
   Units
   Storage space proportional to max accumulation is D’H
            Network Structures
   Trade-off inventory cost and transportation cost
   Milk-run
   Hub and spoke (distribution center)
   Direct Shipping
                                      warehouse                crossdocks

•No DC cost              •Store goods to pool       •Not stored for a
•Reduce lead times       inventory risk             significant length of time
•Higher transportation   •Trade-offs in size as     •Sorted, consolidated,
expense                  more demand can be         shipped out directly
•Good if fully loaded    pooled, but then farther   •Use different containers
trucks or timely goods   from destination           •Requires high volume

                                                   Inventory Pooling

                                                   What is the inventory held
                                                   in the system without
                                   60              the distribution center?
                                                   What is the inventory held
                                                   in the system with the
                                                   distribution center?
100             100                DC
miles           miles

                        50      40         50
                        miles   miles      miles
            Inventory Aggregation
                   Store 1              Store 2             Store 3
Average            10 units/day 20 units/day 30 units/day
Standard           2 units/day          4 units/day         6 units/day
deviation of

 Calculate number required on hand if held at 3 stores, central facility.
 Online retailers as well as traditional retailers
 Typically increases transportation cost (think outbound, but who pays?)
         Inventory Management
   Improve service level
   Reduce logistics cost
   Cope with randomness and seasonality
   Speculate on price
   Overcoming inefficiencies in managing the
    logistics system
Distribution Systems
    Prof. Anne Goodchild
         Spring 2009
          Distribution systems
   One to one
   One to many
   Many to one
   Many to many
        1-1 Distribution Examples
   Port to rail head drayage
   Small in scale and/or scope

   Decisions:
     Shipment frequency
     Route (this is typically a function of the network and
      travel times)
     Shipment times
               1-1 Distribution
   Constant demand
   Trade-off inventory and transportation cost:
         z=minv{(ch/D’)v+cf/v}, s.t. v<vmax
   cf: fixed transportation cost
   ch: holding cost
   v*=sqrt{cfD’/ch}
    EOQ (economic order quantity)
   z=minv{Av+B/v+C}
   v*=sqrt{B/A}
   z*=2sqrt{AB}
   If v*>vmax use v=vmax

   v* makes both of the terms in the objective
    function equal (motion cost = holding cost)
   Why should these be equal?
      Lot Size problem with Variable
   D(t) gives cumulative number of items demanded
    between 0 and t
   D’(t) is variable demand rate
   Seek the set of times when shipments are to be received
    and the shipment sizes that will minimize sum of
    motion plus holding costs over some time period
   With an infinite time horizon and constant demand this
    is the EOQ problem just discussed
    When holding cost close to rent
   Variable demand
   Inventory cost negligible (big, cheap items)
   Increases with maximum inventory accumulation
   Recall motion cost independent of shipment sizes and
    times (only dependent on total amount moved or
   Thus we want to choose times and sizes to minimize
    holding cost
   V*= D(tmax)/n, all equal minimizes cost
   cost/time=crD(tmax)/n+cfn/tmax, find n by minimizing
         When rent is negligible
   Small, expensive items
   Simple expression cannot be obtained unless
    D(t) varies slowly with t (CA method)
   Use numerical solution (e.g. dynamic
         One to Many Distribution
   Movement of containers from the port to landside
   Delivery systems

   Decisions:
       Network structure
       Fleet size (VRP and TSP)
       Shipment frequency
       Use of an intermediate facility (minimizing logistics cost)
           Many to one distribution
   Export containers being delivered to a marine port
   Collection systems
   The same analytical methods can be used as with one to
    many distribution

   Decisions:
       Network structure
       Fleet size
       Shipment frequency
       Use of an intermediate facility
        Many to Many Distribution
   Global distribution of marine containers
   Collection and distribution systems

   Decisions:
     Network structure
     Coordination of inbound
      and outbound shipments
        Many to many distribution
   The problem can often, and should often, be
    broken down into pieces
     Inbound logistics (many to one)
     Outbound logistics (one to many)
     Be mindful of who is responsible for cost within the
      supply chain
     Most supply chains are not operated by the same
     Use terminals to consolidate some of the flow


Reduce line-haul cost through consolidation

                                                         Influence area




Introduce levels of transshipment terminals
These can be used on the collection side or the distribution side
Consider the use of tiered airports in a hub and spoke system
                               Influence Areas

Cost per item delivered



                          Size of influence area
   Scale
     What part of the logistics system will you consider?
     Typically determined by ownership and operating
      units but it depends on your goals
   Consistency
       Logistics systems are more manageable