GSC Final Assignment Resit
1a
to find the best production plan, a fitting mathematical model is required. This model should
take into account that all plants are for at least for 50% active. To find the cheapest solution,
the first step is to make sure that all the values are given in the same context. This is not the
case with original data presented: the production costs to open the plant were given in the
country’s appurtenant currencies. With the ‘Anticipated Exchange Rates Table’ could the
currencies be transformed into its dollar equivalent. The dollar was chosen over its currency
counterparts since the transportation costs were already given in dollars.
The mathematical model
The mathematical model can be derived from the ‘capacitated plant model with single
sourcing’ described in Chopra, J. ,Meindl, P (2016) Supply Chain Management (6th ed.)
Pearson, shown in figure 1. this model is subdivided into two sperate pieces: the fixed costs
part, and the production/shipping-costs part. For the current case were no fixed costs given.
This means that part of the equation before the plus does not apply. Since the model
combines the shipping and production costs, and the data showed them sperate, they need to
be combined as one value called Cij. The remaining part of the equation is quite simple. Cij is
multiplied by Xij, were Cij the cost of producing and shipping one unit from plant i to market j
is, and xij the quantity shipped from plant i to market j is. This working model is shown in
figure 2. To make this model work, constrains need to be added. These constraints make sure
that impossible things cannot happen such as shipping more than the potential capacity of a
plant or shipping negative amounts of units. The first constraint is the demand constraint
given by figure 3. This constraint makes sure that the exact demand for every market is met.
The second constraint is the capacity constraint (figure 4). this constraint takes the total items
produced by the plant, xij, and checks if it is equal or smaller than the sum of the possibility
that is open, yi, times the total potential capacity of said plant, Ki. This constraint works in
making sure that a plant does not produce more than its capacity, but the extra requirement
regarding the 50%-open-rule is not taken into account. This can be done by adding an extra
capacity constraint in the form of figure 5. this constraint will check if the total amount of
items produced by i is bigger or equal than ½ the potential capacity of plant i. The final
constraint is the binary constraint shown in figure 6. This will ensure that a plant can only be
open, 1, or closed, 0. Directly below is a legend given so that it is easier to read the model
and its constraints.
yi = 1 if factory i is opened, 0 if not
xij = the quantity shipped from plant i to market j
n = number of total plant location
m = number of markets
Cij = cost for producing and shipping from plant i to market j.
Dj = monthly demand for market j.
Ki = potential capacity of plant i
Figure 1
Figure 2
Figure 3
Figure 4
figure 5
Figure 6
The Excel implementation
Before the calculations can start, it needs to be transformed in an excel solver model. This
model will find the lowest number, cheapest solution in this case, while satisfying the
restrictions and rules from the mathematical model.
Preparation
As stated in the into for 1a, some preparatory work is required: the production costs need to
be given in dollars and the shipping costs and production costs need to be combined. The
transformation into dollars is done by importing the given exchange rates from local currency
to dollars and then multiplying the local currencies by those exchange rates as shown in
figure 7.
Figure 7
Figure 8 shows how Cij is obtained.
Figure 8
The Model
Figure 9 shows the model put into excel. the yellow cells are the changing cells and represent
the number of tons shipped from plant i t market j. ‘excess cap constraint’ is the potential
capacity, Ki, minus actual supply from plant i, xij. This is shown in figure 10.
Figure 10
figure 11 shows the demand constraint. The unmet
demand is calculated by deducting the total amount
supplied to market j, from the demand of said
market.
Figure 11
The final costs are calculated by multiplying the
production and shipping costs per ton by the total
supply from plant i to market j. This is shown in
figure 12.
Figure 12
Constrains
As stated previously in the ‘Mathematical Model’ part, are constrains necessary in order to
make the model work. In excel are these rules called the solver parameters. The first
constraint makes sure that negative shipment values cannot exist. In other words: every value
of Xij must be 0 or bigger. This is exactly what the first rule states. The second constraint is
the 50% rule. This is done by requiring the model to keep the excess capacity smaller than
half the potential capacity. The third is the max capacity constraint. This constraint will make
sure that the excess capacity is never negative, thus preventing the capacity used to be bigger
than the potential capacity. The final is constraint is the demand constraint described in the
mathematical model checking if all demand is met.
Figure 13
Results
With all the constrains satisfied, the model spat out the results shown in figure 14. The total
costs are 7974950$ to meet all the demand in the cheapest way. The results were quite easy to
understand. Every land supplied their own continent. This is because the shipping costs are
smaller for shorter distances, and all plants had to operate for at least 50%. Germany supplied
not only its own continent but also North America, Japan, and Asia. North America and
Japan are supplied by Germany since it was cheaper than inhouse manufacturing. Japan is
only supplying itself because of the 50% rule. This is the case since Japan has by far the
highest production costs. All the other options, including shipping, are cheaper than inhouse
manufacturing with a considerable margin for Japan. USA has also considerably high
manufacturing costs. The total cost of production and shipping from Brazil or Germany to
North America are cheaper than producing it local. The only reason that USA produces more
than 50% of its potential capacity, is because of the lack of capacity regarding Brazil and
Germany. India is also ‘helped’ by filling up the demand in the Asian market by Germany.
This is because the capacity of India was not sufficient for supplying the whole Asian market.
Figure 14
1b
The assignment for 1b remains fairly much the same. The main difference is the possibility to
close a plant. This maybe seems like a minor change, but this can have great consequences in
total cost reductions since the expensive plants are not obliged to be open.
The Model
To suffice the new requirements, a small modification to the model must be made: The 50%
constraint must be deleted from the model. The excel implementation is nearly the same: the
50% constraint in the solver is deleted and the option to open or close a plant is added. The
option to open or close a plant can be done by adding a ‘decision constraint’. In the previous
model was Yi always 1 because all plants had to be open. The decision constraint is a binary
constraint: 1 for open, 0 for closed. To enforce this, a small change to the demand constraint
was required. The new constraint multiplies the supply from plant a to market b by the
decision variable Ya, if the plant is opened this result in multiplying the xab with 1, this value
is than subtracted from the demand of market b. If the plant is closed, and xab thus multiplied
by 0, stays the demand the same. Figure 15 is the old solver, used for 1a, 16 is the new solver
with the added binary constraint and deleted 50% constraint, figure 17 is the old demand
constraint and figure 18 the new demand constraint.
Figure 15
Figure 17
Figure 16
Figure 18
Results
The results look quite a bit different compared to the 1a run. The costs reduction however is
smaller than anticipated. The total costs dropped from 7974950$ to $7816450. In absolute
values seems it like quite a big decrease, 158500$, but in reality is this decrease of a mere
2%. The plant allocation changes were less subtle, as shown in figure 19. The japan plant
closed all the way and is now fully supplied by Germany. To make room for the extra
demand in japan, was Germany forced to cut back on the supply of North America. This gap
in supply is filled in by the USA since the cheaper Brazil is also capped out.
1c
for 1c some new requirements are given: 1 plant can have a 10 ton increase in capacity. The
increased capacity can go to a cheap plant. This increased capacity will have as result that a
more expensive plant can supply less than in previous iteration of the model, therefore is a
decrease in total costs expected.
The model
The model is the previous model with a small addition: a second decision variable is added
with the extra 10 tons in capacity. This will have an effect in the capacity constraint, since the
model must be able to consider that some plants have an increased capacity. On the left side,
figure 19, is the model used for 1b, figure 20 is the model for the current case. This decision
variable ‘plants Extra’ is multiplied with the 10 tons extra capacity and added to the previous
capacity constraint calculations. To make sure that 1 extra facility is opened, is an extra
constraint added. The ‘sum bin’ is the sum of the ‘plant extra’ decision variable. To make
sure that 1 plant has the extra capacity, is the ‘sum bin’ capped to 1 as shown in the last row
of figure 21.
Figure 19
Figure 21
Figure 20
Results
The results are very similar to the results in the previous question. The total costs dropped
from $7816450 to $7795510, this reduction is almost neglectable since this is a change of less
than 0,27%. This change is smaller than normal fluctuation of currencies over the course of a
year. The extra capacity is given to Brazil and used to supply North America. This is to be
expected since previous models showed that North America is the market that had room to be
optimized and Brazil is the cheapest supplier for North America. The plants table shows that
japan is opened but when we look closer it is very clear that japan does not supply any
market. The reason for this seems to be the lack of a fixed cost: Because there is no fixed cost
penalty, Cij is multiplied with Xij, and Xjapanj is an empty row, is zero added to the total cost
thus not effecting the model.
Figure 22
1d
The devaluation or revaluation of a currency is not the main problem, it is the
unpredictability. If a ProdInter knew that the dollar would lose value compared to the yen
with exactly 1% per year is this not that big of a deal since it is predictable. With this
predictability is ProdInter able to create smaller margins and undersell its competition who
need to factor in the possible currency fluctuation. Luckily are there multiple strategies to
minimize the fluctuation risks. Most of the strategies are taken from: Deloitte Research,
Vikram Mahidhar: ‘Managing in the Face of Exchange-Rate Uncertainty: A Case for
Operational Hedging’, Chris Becker and Daniel Fabbro, RDP 2006-09: ‘Limiting Foreign
Exchange Exposure through Hedging: The Australian Experience’, and: ASCE, Prashant
Kapila and Chris Hendrickson: ‘EXCHANGE RATE RISK MANAGEMENT IN
INTERNATIONAL CONSTRUCTION VENTURES’.
hedging strategies
the most traditional way to eliminate exchange rate-risk is by the implementation of financial
hedging strategies. Financial hedging is a method to cover a company or person’s financial
risk of movements in a market with a derivative. This derivative will grow in value if the
underlying variable, exchange rates in this case, go down. This will ensure that the total value
of the hedged variable stays more or less the same. The strategies are very well known and
used by almost every global company. The simplest form is by the acquisition of future
contracts. Future contracts are basically obligations for a buyer to buy or sell a predetermined
amount of currency in this case for a predetermined price at a predetermined time. This will
mean that the buyer has a fixed exchange rate for the duration of the contract, therefore
eliminating the risk of currency depreciation. another well-known hedging strategy is ‘natural
hedging’. In this case will it mean that ProdInter takes on foreign assets and currency to
match the local assets and currency. If the dollar goes down in value compared to the foreign
currency, will the foreign part of their assets grow in value while the local assets decrease,
evening each other out.
Question 2
To give a good insight on how the lot size policies could change for the better, the MRP runs
with the current policies need to be calculated. ProdInter provided all the necessary data like
the Bill Of Materials, the gross requirements for item A and B, the lot size policies, the safety
stocks, the on-hand inventories, the lead times and the scheduled receipts.
The MRP runs
The MRP runs can be calculated from top to bottom: starting with the
first level, item A and B, then using the planned release as the gross
materials for the items K and O multiplied by the required items
specified in the BOM. The bill of material specifies how many items
from 1 item are required to make the next. Take for example item B, in
figure 23 is it clear that for 1 item B, 2 item Ks and 3 item Os are
required. Therefore, are the gross requirements for O, 3 times the
planned release of item B + 2 times the planned release of item K.
Figure 23
Item A
The MRP run for item A is shown below in figure 24. The lot size policy for item A was FOP
2. This means that every 2 periods an order is placed. The size of this order is calculated as
the sum of the net requirements of the 2 upcoming periods. Item a has also a fixed Leadtime
of 2.
Figure 24
Item B
Item B has also a FOP lot size policy with 2 periods as period, and a lead time of 2. The gross
requirements for item B were also given thus making it fairly straightforward to calculate.
Figure 25
Item K
The MRP run for item K was a bit less straight forward than the previous 2. The gross
requirements were calculated as: 2*planned-release-item-A + 2*planned-release-item-B. That
meant that the A and B had to be precisely checked on calculation errors to prevent the MRP
runs down the line to be wrong. Furthermore, a new batch size policy and a new type of lead
time were introduced. The new batch size policy is fixed order quantity, this means that a
fixed amount, or a multiple of it, is ordered each time if the stock drops below the safety
stock. In this case is the quantity 50. The dynamic lead time is also newly introduced for Item
K. The total lead time is the dynamic part per item multiplied by the items ordered + the
planned lead time fixed part. For item K was translates that to: total leadtime period-a=
(0.01*planned receipts-a) + 1. The problem with this solution was the possibility to end up
with a leadtime of 1,5 periods. These values are not possible since the calculations were done
in whole periods, this meant that rounding was necessary. The rounding was done by
rounding up to the nearest integer. the reason for this way of rounding was because starting
production and getting the supplies in the afternoon is not feasible since the machines will
run the whole morning without producing a single item since there is no stock, thus the
supplies are ordered a day earlier. This means that the supplies for production are ready at the
required station half a day before production starts. the MRP run is shown below in figure 26
Figure 26
Item O
Item O is very similar to Item K, they have both FOQ policy, Item O with a quantity of 100
and item K with 50, both have a dynamic lead time, 0.005 periods per order for item O and
0.01 periods for item K and are both depended on previous MRP runs. Item O however does
not have a fixed lead time part, and its lead time is solely dependent on the number of ordered
items. The gross requirements are: 2*planned-release-item-K+3*planned-release-item-B.
Figure 27
MRP runs and BOM combined
In figure 28 are all MRP runs placed in the BOM sequence with the amount of items that are
necessary for each item shown next to the blue arrows.
Figure 28
Optimized Lot size policies
Since the setup times are so small the best fitting policy would be the Lot-For-Lot policy.
This policy entails that every period the required materials are ordered. This means that the
inventory can be kept as small as possible, thus greatly reducing the storing costs. Besides the
reduced inventory costs will this policy also result in a more reactive system, which will be
more easily able to supply fluctuation in the demand without being over- or understocked.
Question 3
ProdInter owns currently one truck to bring raw materials from suppliers to its factory.
ProdInter would like to know if it is beneficial to operate a second truck. To answer this
question an anylogic model is created that will be able to simulate both scenarios and give
useful data so that a conclusion can be reached.
The Model
Figure 29
Figure 29 shows the final layout of the model. Up top is the general layout for this case, with
the source, an order que, the trucks, and the destination: the factory. The left side is the model
with 1 truck and the right side is the model with 2 trucks. The variables for the KPI’s are
placed directly below, together with the statistics for the KPI’s. The graphs are placed at the
bottom.
Source
Figure 30
Figure 30 shows the mechanics and inner workings of the source block. The arrival times are
based on the table in the database. The atrArrivelTime stores the time the agent arrives at the
source and is necessary for future calculations. In the advanced is the custom agent selected
called “Order1”.
Order que
the orderQue queues the orders in first-infirst-out sequence if there are no trucks
available. Every incoming order will add 1
to the work in process variable. Also is the
work in progress updated.
Figure 31: order que interface
Trucks
Figure 32
As shown in figure 32 is the ‘Trucks’ block by far the most used for updating variables and
stats. The delay time is the value of the attribute atrTimeStamp1. This attribute stores the
shipping times for all orders.
The capacity is 1, to simulate the single truck available, but the double truck configuration is
identical besides the variable names.
‘On enter’
On enter are 2 variables updated, these are the varUtilization and the varUperc. The
varUtilization adds 1 to its value if an agent enters the ‘Trucks’ block. This will result in a
variable ranging from 0, no trucks are currently active, to 1, all trucks are used. To transform
this stat into a percentage varUperc is made. varUperc multiplies varUtilization by 100. This
value is than divided by the total amount of trucks, 1 in this case, to end up with a percentage.
The stat statUtilization is also updated on the enter block and saves the utilization percentage
against the time.
The attribute atrTransportStart saves the time an agent enters the block.
statTransportTime saves the transport time variable against the time
‘On exit’
On the exit are many variables and stats updated. The varWIP value is decreased by 1, the
statWIP is updated, the varUtilization value is lessoned by 1 and the varUperc is updated, as
is the statUtilization. The attribute atrTimeDone is also given the time value of when the
agent exits the block.
The varTransporttime is calculated by substracting the atrTimeDone by the atrTransportStart
and is saved with the current time in the stat statTransportTime.
Factory
The factory gives the current time value to atrTimeDone, calculates the
varShippingLeadTime and adds the histodata to histoShippingLeadTime.
Figure 33: factory interface
Data table
Figure 34: Data Table
The data for transport times and interarrival times were pulled from the database. The
interarrival times look a bit different because dates are used instead of time periods, but the
interarrival times are still the same as the ones given in the assignment.
Starting date
Figure 35
Starting and stopping dates were used because the program would not run on the interarrival
times as inputs, so they had to be changed to dates, this had as result that the program also
needed to start and end on specific dates.
KPI’s
The KPI’s calculated are the utilization, WIP, lead time, and transportation time. The average
WIP and the max WIP are also calculated and plotted. The same is done for the utilization
and transport time. The lead time is a graph made with the leadtimes against time, and the
average leadtime is calculated.
Results
After the simulation was ran, the model spit out the results. The results are split up in the
KPI’s, the data until period 10, and the data for the whole period.
KPI results
In the table below are the results from the KPI’s shown
The WIP and Utilization are down a considerable amount. This is to be expected since the
capacity is doubled, and the orders are still the same. The leadtime dropped by a significant
amount, this is also due the increased capacity: the orders do not have to wait in que since
more trucks are available.
Data period 10
Figure 37 shows the data the model spat out until period 10. The left side of the screenshot
shows the graphs and KPI’s for 1 truck, the right side for 2. For both scenarios are graphs
made for the average WIP, the current WIP, the Shipping lead time, the Utilization, the
Maximum utilization, the average utilization, the transportation time, the average
transportation time and the max transportation time.
Figure 37
Data period 15
Figure 38 shows the graphs the model generated until period 15. The structure is the same as
the one used for the period 10-part. The table shown in figure 39 shows the average WIP, the
average Lead Time, the average Utilization and the average transport time. The trucks
column shows the scenario with 1 truck and with 2 trucks, were the row with 1 is the row for
1 truck and the row with 2 data for the scenario with 2 trucks.
Figure 38
Figure 39
Analyses
The difference between the 2 scenarios is quite clear: over 15 periods, the leadtime is more
than twice as high for the single truck scenario, however the utilization and WIP are
massively down. Figure 40 is the single truck scenario and figure 41 is the double truck
scenario. If compered, it is quite clear that the extra truck is not used as much, with an
average utilization of 65% and several times a utilization of 0%. The 1 truck configuration is
really at its limits. The que is at multiple times 2 orders; however, the que goes down every
time and is never bigger than 2 backorders. If ProdInter strives for shorter shipping times and
wants to increase their production, an extra truck is a no-brainer, but if the production stays
the same, 1 truck should be sufficient. The problem with the 1 truck scenario is that in the
case of a breakdown, no backup truck is available, but by having 1 truck in the inventory the
shipping costs can be kept a lot cheaper since the extra costs like truck acquisition, extra
drivers, spare parts, and maintenance can be cut in halve. That’s why the single truck
configuration is the best for ProdInter if they have no plans to increase their production and
have a truck rental company close in the case of breakdowns.
Figure 40
Figure 41
Executive Summary ProdInter
The executive summery will be sub-dived into three parts: one part for each question. The
answers are based on the full report. The full report will also host a more elaborate
explanation on how the data is generated, interpreted and used for reaching the conclusions
presented in this summary.
ProdInter is an international organization specialized in the production of chassis of
electronic devices. Being an international firm with globally scattered production plants and
markets to supply, brings a whole lot of complications. One of those complications is figuring
out where to open production plants and which plants should supply which markets. Luckily
is PordInter not the first Organization with this problem. The capacitated plant model is made
for this specific reason and is able, if used well, to calculate the cheapest solution for this
problem. The first task was to find out which plants should supply which market with the
constraint that all plants had to be open for at least 50%. Since the Japan plant was the most
expensive to operate, was that the only plant who was limited by the constraint. Germany and
Brazil were also supplying the North American market, but the capacity constraints on those
plants meant that the fairly expensive USA plant had to supply the majority. For the second
task was the 50% rule omitted. This had as consequence that the Japan plant was not obliged
to stay open anymore and was thus closed. The closing of this plant led to a 2% reduction in
total cost, making it 158500$ cheaper than the previous option. For the third task a capacity
increase of ten tons could be granted to one of the plants. In the previous models was it clear
that the North American market had room for improvement. The new model showed that
exactly that. The Brazil plant increased its capacity to supply the North American market.
This change of 10 tons was however too small to make a significant impact. The total costs
dropped with a mere 0.27%, an almost insignificant change. The last problem that had to be
researched for ProdInter was the exchange rate problem. Since exchange rates fluctuate over
time, is it near impossible for the company wield proper margins. A sudden increase in the
euro price against the dollar could mean that the probability of a plant operated in Europe
would evaporate within the time period of mere days. Therefore, are predictable exchange
rates extremely sought after for international operating companies. The solution presented in
the model was a combination of two widely known hedging methods. A hedging method is a
way for a company to make an asset, in this case currency, stable over time. The first method
presented was by the use of future contracts on currencies. A future contract is an agreement
between two parties to buy or sell an asset at a predetermined price on a specific date in the
future. In the case of ProdInter would it mean that ProdInter agrees with a European
counterpart that in a couple years’ time ProdInter is obliged to buy a specific amount of euros
against a predetermined price in dollars. This would mean that for the time of the contract
ProdInters exchange rates are predetermined and fixed, eliminating the uncertainties of
currency fluctuations. The second proposed hedging method is the use of a natural hedge. A
natural hedge is taking on foreign assets that react opposite to the assets at risk. If one
depreciates, the other will appreciate. In the case of ProdInter would it mean that the profits
made in foreign markets are kept in the local currency. Eventually will the foreign assests
grow until it is matched by the operating currency, the dollar in this case. From this point
onwards: If the dollar goes down in value compared to the foreign currency, the foreign
assets appreciate the exact amount the dollar depreciates making the net total even.
For question 2 the task was to evaluate the current situation of the ERP system, more
specifically: can a change in lot size policy be beneficial for ProdInter? Before this question
could be answered, the current situation had to be calculated. After doing all the MRP runs,
room for improvements were found. The Lot-for-Lot policy was found to be the best match.
The highly reactive nature of the short setup times will work the best with an equally reactive
policy. The LPL policy is just that. The LPL policy entails that every period the minimum
number of required products is ordered, supplying just one period, keeping the inventory
small. Keeping a small inventory is a great way to safe costs since a large stock is really
costly. Besides the reduced inventory costs, will this policy also result in a more reactive
system, which will be more easily able to supply fluctuation in the demand without being
over- or understocked.
ProdInter owns currently one truck to bring raw materials from suppliers to its factory.
ProdInter would like to know if it is beneficial to operate a second truck. To answer this
question, an anylogic model was made. This model can simulate both scenarios
simultaneously while giving insightful data in the form of key performance indicators. The
model showed quite a big difference between the two scenarios. The lead time for example,
was more than twice as high in the single truck scenario compared to the double truck
scenario. This however does not mean that buying the second truck is a no-brainer. The
model also showed that the single truck configuration handled the situation fine. The
backorders did not pile up to unmanageable amounts and decreased swiftly again. A bigger
issue with the one truck configuration is the lack of backup in the case of breakdowns. This
issue can be addressed in the form of a deal with a truck rental service who will be able to
provide trucks in the case of breakdowns. The single truck configuration has also advantages
compared to the dual truck scenario in the form of reduced costs. One truck to operate means
one truck to buy, one truck to have the spare parts for, one truck to provide with staff and one
truck to pay taxes on. The choice comes down to ProdInters plans for the future: If ProdInter
wants to increase their production, an extra truck is a must-have. If not, a single truck is
sufficient.