# 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
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)
• 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 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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 views: 2 posted: 5/7/2012 language: English pages: 24