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MGTSC 352

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					MGTSC 352

QUIZ 3 NOTES
         Distribution Planning
• What should overall distribution system be?
• Where should inventories of products or raw
  materials be stored?
• How much inventory of each product and raw
  material should be stored at each location
• How should the flow of products and raw
  materials through the distribution be coordinated
• What models of transportation should be used?
        Distribution Planning
• All distribution problems are really special
  case of minimum cost problem, even the
  shortest distance problem, which replaces
  distances with cost
• Remember to freeze cells when using the
  sumif function
• Hit ctrl + ~ to get into formula mode, will
  make it much easier to debug
        Distribution Planning
if demand is greater than supply, solver will
   try to solve to satisfy the demand but there
   wont be enough supply, so it will cause an
   error (infeasible solution)

if you have a node with no demand or
   supply, flow will come in and won't stay
   cause there is nothing required and will
   immediately flow out, like intersection
              Distribution Planning

• Shortest path problem
  – If we are required to go to a certain path, best way is
    to solve it in two parts
     • 1st part is when we go from supply city to intermediate path
     • 2nd part is when we go from intermediate city to final demand
       path
  – Set demand = 1 at destination city and set supply = 1
    at city of origin
  – Make sure that supply + flowin = demand + flow out
     • This will allow us to make a path with no jumps
          Distribution Planning
• Shortest Path problem cont.
  – If we have to traverse a specific arc, but not to a
    specific city to within that arc, before going to a
    specific city, make sure you allow for two-way travel
     • In three cells, have:
         – city 1 -> city 2
         – City 2 -> city 1
         – sum
     • Each path will reference truckload along that path
     • Sum is the sum of the two arcs
     • Constrain solver so that the sum>=1, that way it must
       traverse the path but also allows for back travel
         Distribution Planning
• New locations
• If wondering whether or not to open a new
  facility, use a binary variable
• To ensure that we don’t produce if we don’t
  open:
  – Set an upper bound = max prod * binary
  – Constrain solver so that production can not be greater
    than the upper bound
• Must constrain solver so that supply + flow in +
  production >= demand + flow out
       Inventory Management
• Goods that have not yet been sold
• Keep inventory when
  – Demand unpredictable
  – Delivery takes time
  – Fixed cost for delivery
• Relevant question
  – When to order (ROP = Reorder point)
  – How much to order (Q = reorder quantity)
• MAKE SURE TIME UNITS ARE CONSISTENT,
  DON’T MIX YEARS WITH MONTHS
                   Relevant Costs

• Acquisition cost          • Carrying costs = Holding costs
  ($/unit purchased)          ($/unit/time unit)
                               –   cost of capital
                               –   insurance
• Ordering costs               –   shrinkage, spoilage, obsolescence
  ($/order)                    –   material handling (fork lifts, space)
   – clerical expenses
   – delivery, inspection   • Shortage costs
   – setup (prod.)            ($/unit short)
                               – lost goodwill, discounts, penalties
                               – lost sales
                               – shut down of assembly line (prod.)
  Inventory
                                   Maximum inventory




                                              Avg. inventory

ROP
           LTD =
         Demand                Q
           during   Leadtime
         leadtime
                                   Minimum inventory
                                       Time
                  Histogram
Need 3 columns
  – # sold, bins, and frequency as headers
  – # sold will be a range (0-2, 3-4, etc..)
  – Bins refers to values at or below that value
     • 2 means 0-2, 4 means 3-4, etc..
  – Frequency means how often value
    corresponding to a bin shows up in the
    dataset
                 Histogram
• Highlight the empty frequency cells
• Type in frequency (data, bins)
• While they are all highlighted, hit
  ctrl + shift + enter, this will cause the
  frequency to appear in the cells
              Histogram
• in the graph template, hit column graph
• Highlight # sales and frequency to be
  graphed
• Once graph is made, double click the
  graph and under options you can change
  the distance between the columns to be 0
• Histogram complete
               Simulation
• Orders take time to come into your place
  of business, this time will affect how your
  business is run because it will effect your
  reorder points and order quantities
• Beginning inventory is equal to ending
  inventory of the previous day + the order
  that came in that day
              Simulation
• Inventory position is beginning inventory
  plus inventory that is in transit. If we
  ordered two day ago, and we know we will
  get the inventory in 5 days, then we
  wouldn’t order more stock because we
  know that we have an order on the way
• If a new order just arrives and it is too
  short, then we would put a new order
  through
               Simulation
• Order if demand is greater than the
  inventory position
  – We can use if statements to ensure this
  – If(demand>=inventory position, order amount
    Q, else don’t place order)
• Sales will be the minimum of demand or
  beginning inventory, not inventory position
  because that inventory is not in the store
  – Min(demand, beginning inventory)
               Simulation
• Shortage is demand less sales
• Ending inventory is beginning inventory
  less sales. If your order will come in at the
  end of the business day, then ending
  inventory will include this as well
• Holding cost is the average of beginning
  and ending inventory, multiplied by the
  holding cost per unit
               Simulation
• Fill rate is the amount of demand that is
  satisfied by the inventory
• =total sales/total demand
                Tables in Excel
• Say we want to see how net profit varies with differing
  ROP and Q
• Put values for ROP and Q along row and column, except
  leave the top left corner of the table blank
• In the top left corner, reference net profit
• Highlight entire area, then go data->table
• For row, reference original value for row, and for
  column, reference original value for column
• Can use conditional formatting to highlight the max
  amount or to highlight minimum amounts, if you require
  that we must reach a certain profit, or fill rate or whatever
 EOQ = Economic Order Quantity
• Assumptions
  – Demand is constant
  – Inventory drops to zero just before an order arrives
  – Variables:
     •   S = order cost ( per order)
     •   H = carrying cost (per item per order)
     •   D = annual demand
     •   Order cost = (D/Q)/S; Carrying Cost = (Q/2)*H

                           Q* = sqrt(2DS/H)

     • Q* = quantity to order that will minimize cost under the EOQ
       model
  EOQ = Economic Order Quantity
• Simulation modeling is a flexible modeling approach that is capable
  of replicating the real world intricacies of an inventory system but it
  is also generally an expensive (time and money) approach. In the
  previous worksheet we used a historical simulation to find a good
  policy (values for Q and ROP). We found the policy by trial and
  error, facilitated by a two-way data table.
• We will use a simpler approximate two-step analytical method to first
  find Q and then find ROP. We use the well-known EOQ model
  (which trades off ordering costs with holding costs) to find Q. Then
  we use this Q and an estimate of the probability distribution of
  demand during the lead time to determine ROP, either by meeting a
  pre-specified level of service or fill rate or by minimizing the costs of
  incurring a shortage plus the cost of carrying extra safety stock).
  This two-step method involves many approximations, but in practice
  it usually gives a near-optimal policy
• Find Q*, then use LTD (lead time demand model) to find ROP using
  Q from previous step.
                                                             pg. 151

            Simulation versus EOQ
     Dimension               Simulation              EOQ + LTD
Ease of evaluating a   Need to build model –    Simple formula for RC
policy                 time consuming           – back of an envelope
Finding the optimum    Trial and error / data   Plug into formula for
                       table                    Q*
Random demand          Taken into account       Ignored in EOQ
fluctuations
Seasonal demand        Can be taken into        Ignored
fluctuations           account
Shortages              Taken into account       Ignored in EOQ
Likely errors          Errors in formulas       Inconsistent units
(common mistakes)
    LTD – Lead time demand
• Lead time = how long we wait while
  receiving an order
• Lead time demand = how much demand
  would occur while we are waiting for our
  order to arrive
• Goal is to reduce the probability of
  shortages
     LTD – Lead time demand
• Set the lead time
• LTD will be the sum of the demand for the lead
  time
• Shortage will occur if LTD>=ROP
  – If(LTD>=ROP,LTD-ROP,0)
• For shortage per cycle
  – cycle= demand/Q
  – Shortage = cycle*average shortages/year
  – Fill rate
     • = sales/demand
     • = (demand-shortages)/demand

				
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posted:5/7/2012
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