das,esd71-final application portfolioardent.mit.edu/real_options/real_opts_portfolio...

Lita Das

ESD. 71 Engineering System Analysis for Design

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Flexibility Analysis: Inventory Management of Ocean Freight System Abstract: Managing inventory in an ocean freight transportation network can be a very challenging task. In the case discussed in this report the decision maker is observing an uncertain demand, which is to be satisfied, by shipping units through ocean freight mode. Another major uncertainty that drives decisions in this system is lead time which is a sum of lead times across 4 different segments of the ocean freight system, namely port to port, destination port dwell, destination port to destination and unloading time at the destination port. The variability in the demand and lead-time force the decision maker to incur inventory carrying costs and high transits cost or switch to airfreight mode to avoid lost sales or invest in options contracts. The objective of this report is to conduct a evaluation for two different flexible cases against a base case scenario and compare the value in terms of annual inventory cost and annual transit cost. The base case and the flexible cases are analyzed using Monte Carlo simulation method by running the simulations in each case for a 1000 times. Finally a comparative analysis of the base case and flexible cases 1 & 2 is done on basis of a Value at Risk & Gain (VARG) curve and multidimensional criteria (expected, maximum and minimum costs), which are a result of the simulation model. The results conclude that the flexible cases prove to be a more favorable decision as compared to the base case in terms of annual inventory and transit cost. Results are tabulated below: (the values marked in yellow are the favorable outcomes) Value in million $ Base Case Flexible Case1 Expected Annual Inventory Cost 28.14 14.64 Minimum Annual Inventory Cost 23.65 12.17 Maximum Annual Inventory Cost 32.68 17.38 Standard Deviation of annual inventory cost 1.40 0.84

P10 26.40 13.55 P90 29.94 15.75 Value in million $ Base Case Flexible Case2 Value in

million $ Base Case Flexible Case2

Expected Annual Inventory Cost

28.14 18.01 Expected Annual Transit Cost

286.22 210.80

Minimum Annual Inventory Cost

23.65 15.74 Minimum Annual Transit Cost

266.03 195.64

Maximum Annual Inventory Cost

32.68 19.90 Maximum Annual Transit Cost

301.93 227.85

Standard Deviation of annual inventory cost

1.40 0.61 Standard Deviation of annual Transit cost

5.02 4.79

P10 26.40 17.25 P10 253.84 195.64 P90 29.94 18.79 P90 301.93 227.85


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Table of Contents

Introduction .............................................................................................................................. 4

System Background ................................................................................................................ 4 The System .......................................................................................................................................... 4 Base Case & Flexible Cases ............................................................................................................. 6 Structure of Analysis ........................................................................................................................ 6

Uncertain Factors Determination ...................................................................................... 7 Fixed Factors Determination ............................................................................................ 11

Sensitivity Analysis .............................................................................................................. 12

Simulation ............................................................................................................................... 15 Calculations ...................................................................................................................................... 17 Simulation Method ......................................................................................................................... 18 Simulation Model for base case .............................................................................................................. 18

Inventory Cost as a Performance Measure .................................................................. 21 Base Case ........................................................................................................................................... 21 Flexible Case .................................................................................................................................... 23 Flexible Case1 ................................................................................................................................................. 24

Base Case vs Flexible Case1 * ..................................................................................................... 28 Flexible Case2 ................................................................................................................................................. 30 Sensitivity Analysis to determine maximum order quantity allowable ............................... 31

Base Case vs Flexible Case2 ........................................................................................................ 36 Transit Cost as a Performance Measure ....................................................................... 38 Base Case ........................................................................................................................................... 38 Results of Simulation for Base Case ...................................................................................................... 38 Flexible Case 2 ............................................................................................................................................... 39

Base Case vs Flexible Case2 ........................................................................................................ 41 Conclusion ............................................................................................................................... 42 Course Reflections and Lessons Learned ..................................................................... 45

References .............................................................................................................................. 45


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Introduction With the ever-increasing growth of international trade, it is very important to recognize uncertainties affecting the ocean freight system. Trends in ocean freight show that US ports handled 17% more cargo (in metric tons) in 2010 as compared to 2009. In the current market, decision makers, who can look out for opportunities in the risks and create flexible designs, which add value to the system, can survive in this global competitive ocean freight network. This application portfolio will discuss an ocean freight network that is affected by demand, lead-time and fuel cost uncertainties that encourage the decision maker to build flexibility into the system in order to gauge the benefits of the latter over the conventional base case. The performance metrics used are annual inventory cost and annual transit cost. Hence the cases with lower costs are more favorable over the other.

System Background

The System The System of interest is global ocean transportation network of leading manufacturing and logistics firms. Specifically it includes freight transportation of from China to Port of Los Angeles. The final destination of the freight is the distribution center in San Francisco. One of the major aspects of their operation is the global transportation of containers of product between suppliers, assembly plants, and customer locations. This network consists of the entire chain from the origin to the destination. A diagrammatic representation of the network is shown below:

Fig. 1: Diagrammatic representation of the System

The system includes the following:

1. Origin, Origin Port, Ocean Transit, Destination Port, Destination 2. Delivery Time Schedule up to the final destination 3. Ground Transportation between the origin/origin port & destination

port/destination 4. Demand of the product being shipped and the urgency to ship the same

Origin Origin Port

Ocean Transit

Destination Port

Destination


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The system excludes:

1. Type of product being shipped 2. Volume of shipments 3. Extent of involvement of the third party logistics firm that is responsible for

handling operations from the origin to origin port before the shipment leaves the port

The decision maker in this system is the party at the destination (San Francisco). They see a daily demand, which is uncertain, and are in contract with the supplier in China. The destination port is LA, USA. The shipment leaves a port in China and reaches the LA port after which it is transferred to San Francisco warehouse via a truck. There is no specific port in China that the shipment can originate from. It can start from Shanghai or Hong Kong or Shenzhen. The lead-time from the origin port to the destination is a sum of the following independent lead-times (LT):

• LT from Origin Port to destination Port • LT from dwell (waiting time) at the destination port • LT due to unloading at the destination port • LT from inland transit from destination port to destination

The party at the destination chooses to order a quantity, the current limit of which is set in the contract with the supplier. It is assumed that the contract allows for any number of orders during the time period of the contract (that is 1 year). The decision maker follows a (R, Q) order policy, where R is the reorder point and Q is the order quantity. According to this policy the decision maker orders Q units every time its inventory position goes below R units. It is also assumed that the inventory is monitored continuously that is every day of the year because demand is observed at the same frequency. The demand that is not met is all converted into lost sales (loss of customers for forever) which have a large penalty cost attached. The costs that the decision maker will incur are

• Annual Inventory Cost 1. Holding Cost – This is the cost incurred because of excess inventory held.

The decision maker is forced to hold excess inventory or safety stock because of uncertain demand and lead-time.

2. Shortage Cost- This is the cost incurred when customer demand is not met (lost sales). Again shortage cost is a result of demand and lead-time uncertainty.

3. Order Cost- This is a fixed cost incurred every time the decision maker orders from its supplier in China.

• Annual Transit Cost 1. Port to port transit cost –This cost is the cost of travelling the oceanic

distance between China and port of LA. This is affected by the frequency of orders and per ton bunker fuel (ship fuel) cost uncertainty.


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2. Inland transit on truck to the destination- This is the cost of inland transit from port of LA to San Francisco, which is again affected by the frequency of orders and per gallon cost of truck fuel.

3. Storage Cost -A cost incurred to dwell at the destination port for more than the maximum allowable free dwelling days. Dwell time is often unplanned and seen due to “congestion” at the LA port on any day because of other shipments. Congestion can cause delays in customs clearance or unloading and loading operations from the ship to the truck before it is transferred to the destination.

Base Case & Flexible Cases The system analysis will compare 2 flexible cases against a base case. The base case performance is evaluated using uncertainty in demand and lead-time. The flexible cases (1 & 2) are evaluated after building in decision rules into the base case simulation model. They are compared on the basis of calculation of the above-mentioned costs Adding to the base case strategy the:

• 1st flexible case- Since the penalty cost incurred due to lost sales is very large as compared to the order cost, I choose to use the option of shipping the freight through air for the next time period with the penalty of an increased order cost (10 times more than that of base case!) if the lost sales in any time period is beyond a maximum lost sales allowable. Air transportation has a fixed lead-time facing the same demand uncertainty as the base case. Demand stays the same because it is not under the control of the decision maker. Details of this case are described in sections to follow.

• 2nd flexible case- I could choose my contract with the supplier, to allow me to ship out a maximum of 155 units at any time which again comes with an increased order cost (set at $100 more than the base case). I choose to “expand” if I see lost sales >0 in the previous 2 time periods and increase my order quantity by 15 more units as compared to the last time period as long as it is less than 155 units. Details of this case are described in sections to follow.

Structure of Analysis In the following sections the uncertainties that affect the system as mentioned above are defined and reasoned why they are modeled using specific distributions. The base case and the two flexible cases are then modeled in excel Monte Carlo simulation method to arrive at the annual inventory and transit costs which are used to compare the two scenarios. Finally the results are summarized with explanations on the observed trend seen in the VARG graph obtained from the simulation model.


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At this point I would like to justify the use of Monte Carlo simulation method for the purpose of evaluating the base case and the flexible cases in terms of the performance measures indicated above. Monte Carlo allows me to support a wide range of stochastic processes. Also, it does not restrict me to model only particular distributions of uncertainties into my system. Monte Carlo simulation also allows me to effectively incorporate decision rules along the simulated paths.

Uncertain Factors Determination

1. Demand distribution: The distribution of customer demand is a major uncertainty factor that influences the decision to choose between the flexible and the base cases. In this case customer demand is observed everyday of the year. Approximation of the demand distribution can be a pretty difficult task when there is a lack of data. The data available with me does not give me information about the customer demand and for purposes of non-disclosure, information about the type of product is not available, hence eliminating any possibility of researching for realistic data, however the distribution of lead-time is found out to be normal. In this case the demand distribution is assumed to be normal, mainly because the calculations used below are derivable only with normal demand distributions. The demand has a mean of 110 units and a standard deviation of 20. The minimum limit is set at 0 units because demand cannot be negative at any time and is set for a maximum limit of 210, which is 5 standard deviations above the mean. The maximum limit on demand is set at very high limit from the mean to be highly conservative with my results by accounting for seasonality of the products if any. The units being sold are seasonal and 210 units of demand is probably seen during certain times of the year also called the peak seasons.


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Fig. 2: Demand distribution in a year

2. Lead Time Distribution Uncertain lead-time forces companies to make decisions before realization of demand and hence accounts for safety stock inventory levels that account for annual holding cost. More uncertain the lead-time more is the safety stock held in the warehouse. The data available with me for shipments from China to port of LA show a distribution as indicated in the graph in Fig.3 below. Although, the real data shows that the lead times beyond 19 days are outliers, the case study assumes it to be normal between 8 and 34 days (considers the outliers too) as indicated in Fig.4. This would give us a more conservative result, since research on other data set sources indicate pretty high lead times (nearly 44 days) for LA shipments from China. In this case the minimum is set to 5 days instead of 8 days to account for -3 standard deviations from the mean and is also a plausible data set point ascertained from real life cases of shipments from China to LA. The lead-time components of port to port (OP-DP), destination port (DP) to destination and dwell times are extracted from the data set available for shipments between China and LA port. However, unloading time at the destination port is assumed data and is made normal to match with the distributions of the above components of lead times and make calculations easier (it is easier to add 4 normal distributions instead of adding 3 normal and say may be one uniform distribution.) The total lead-time mean and standard deviation calculations are sum of the individual components standard deviation and mean because they are independent and are all normally distributed. The dwell time at the destination ports is affected by factors like loading onto the truck after unloading from the ship, custom clearance at the LA ports, congestion rate at the ports, service level of the freight forwarder trucking responsibilities from the destination port to the destination, number of service booths to help in custom clearance at the destination port and the unforeseen circumstances like natural calamities. The total transit time, which is the sum of the above 4, components is therefore uncertain and is the total lead-time of the ocean transportation from China to LA.


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Fig. 3: Port-‐to-‐Port real lead-‐time distribution

Fig. 4(a): Port-‐to-‐Port modeled lead-‐time distribution


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Fig. 4(b): Total lead-‐time modeled distribution

Distribution Mean (days) Standard deviation

(in days) OP-DP Normal 14 3 DP-Destination Normal 1.9 0.3 Unloading Normal 0.4 0.1 Dwell time @ destination

Normal 5.4 1.8

3. Fuel cost This case study is concerned with two types of fuel for the two legs of freight transportation. During the oceanic transportation segment, the ships use bunker fuel. The second segment, which is the inland transfer from the destination port to destination by truck, is the fuel used in cargo trucks. The fuel cost data for bunker fuel is obtained from historical data (for the first quarter of 2011). The maximum and minimum limits are the limits for the first quarter year 2011 and bunker fuel cost for any day is modeled as a random number between the set limits. The cost for truck fuel is equal to the average price of fuel in the state of California for the months Jan to Nov 2011. The price for December is assumed to be the same as that of November.


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Fixed Factors Determination The performance evaluation of the oceanic freight transportation base and flexible cases also involves a number of fixed factors as follows:

4. Holding cost factor: It is the carrying charge, the cost of having one dollar of the item tied up in inventory for a unit time interval. ($/$/time). This is expressed as a percentage of per unit cost of an item.

5. Per Unit cost: This is the cost of a unit item, which is variable in the sense that it the total cost depends on the number of units bought. It is fixed on a per unit basis.

6. Order Cost: This cost is a fixed cost per order irrespective of the number of units being shipped. This includes the cost of labor and miscellaneous factors that are involved in shipping. In my case I have set the order cost for air to be 10 times more than that of ocean freight, which is used while evaluating the first flexible case. In case of the second flexible case where the contract allows setting a maximum limit on the number of items that the shipper can ship, the ordering cost is set at $100 more than that of the base case wherein the option is not available.

7. Average fuel consumption: This is the fixed average fuel consumption in terms of tons of bunker fuel a day for the ship and miles per gallon in case of the truck.

Fig. 5: Bunker Fuel consumption vs. speed (knots)

It is known that the size of containers used for ocean freight in this case is 8000 TEU and it is assumed that the ships go on the normal speed of 22 knots. Hence the graph suggests that the bunker fuel consumption in 160 tons/day.

8. Storage cost and maximum allowable free storage days at the destination port:


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When the cargo reaches the destination port, it is allowed to dwell at the port for a maximum allowable of 4 days for free after which is charged a storage cost of $500 every day beyond 4 days. The cost of storage is obtained by research on the storage cost in port of LA. This is used to calculate the storage cost, which is a part of the total transit cost.

9. Maximum lost sales allowable: The maximum number of lost sales allowable is fixed at 110 units for the company (or the decision maker). This is a constraint used to evaluate the flexible case of shipping more units when the lost sales (or customers) are above 110 units. It is set at 110 units because it is equal to the mean of demand and thus the logic is such that lost sales beyond average of the demand observed can prove a loss for the company.

10. Lost Sales Cost: This is the penalty cost incurred by the decision maker when he loses the sale of a unit. This is set at $1000/unit, which is usually calculated by the marketing and finance department of the organization. Calculating the cost of lost sales can be a pretty difficult task. Different companies follow different calculation procedures and depend on factors like estimating the type of customer lost and the effect on company profits on losing them forever.

11. Lead Time for air freight transportation: Freight transportation through air is usually not variable and is an expedited shipping option. This lead-time is assumed to be equal to 3 days in this case for China to LA shipments. It is set at 3 days after a little research on airfreight lead times between China and US shipments. This lead-time includes the total number of days until the final destination (San Francisco in this case).

12. Destination Port to Destination Distance: This is the road distance between Port of Los Angeles to the distribution center in San Francisco, which is the final destination of the shipments from China.

13. Safety Stock Factor: This is the normal distribution service factor based on desired service level. In this case the safety cost factor is 1.64, which is based on a desired customer service level of 95% as set by the decision maker.

14. Maximum Order Quantity is the maximum number of units allowable as per the contract between the shipper (the decision maker) and the supplier. In other words the shipper can ship in any number of units less than or equal to the maximum order quantity. This limit is used to exercise the decision rule of the second flexible case.

Sensitivity Analysis Since the input variables are uncertain, sensitivity analysis was conducted to find out if the performance measures are affected on changing the numerical values assigned to the factors were changed to other plausible values. Tornado diagram was used to understand


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the importance of the effect of the uncertain factors. The minimum and the maximum values of a particular factor are plugged into the base model to find the changes in the annual inventory and transit cost. While doing so, all other factors, besides the one whose effect is being estimated, are kept constant. For instance while finding the effect of demand on the annual inventory cost, total lead-time was set at a constant, (at the mean of the total lead time), while finding the cost for a minimum of 0 demand and 210 units. The tornado diagram is as below. Parameter Unit Low parameter

value High parameter value

Sensitivity

Demand Units 0 210 21768.57% Lead Time Days 6.2 49 380.79% Lost sales cost per unit

$/unit 1000 1500 49.96%

Order Cost $ 100 700 0.2% Holding cost factor

% 8 16 0.15%

Fig. 6(a): Tornado Diagram for the uncertain factor determination for

annual inventory cost The above diagram suggests that demand, lead-time and lost sales cost per unit have a pretty significant impact on the annual inventory cost. Clearly, demand and lead-time are important uncertainties to be kept in mind while modeling the simulation model for inventory cost. At the same time order cost and holding cost factors have small affects on the inventory cost as compared to demand and lead-time changes. Hence they can be fixed at certain values with no distribution in the simulation model. Historical data is

$-‐ $10 $20 $30 $40 $50 $60 $70 $80

holding cost factor

Order Cost

lost sales cost per unit

Lead Time

Demand

Annual inventory Cost in millions


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used to set the holding cost factor to 16%, which is generally used by logistics firms that handle large supply chains. However, for the lost sales parameter, it is unlikely that a firm will choose a distribution for the same. It is because this factor is based on setting at a reasonable limit based on past experience of losing customers due to unavailability of stock at hand. But the main take away from the graph with respect to the lost sales parameter is that flexible decision rules should be modeled around lost sales per unit because it has a considerable impact on the performance measure. Similarly, the tornado diagram for annual transit cost gives us an idea of the parameters that have considerable effect on the performance measure. Parameter Unit Low parameter

value High parameter value

Sensitivity

Demand Units 0 210 704.55% Lead Time Days 6.2 49 255.53% Bunker Fuel Cost $/tons 200 500 73.18% Trucking fuel cost

$/gallon 3.36 40 0.92%

Storage Cost @ destination port

$ 100 500 2.16%

Fig. 6(b): Tornado Diagram for the uncertain factor determination for

annual transit cost

Again, the considerable effects of demand and lead-time are evident from the sensitivity analysis shown above. As in the case of annual inventory cost, transit cost is also affected


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by uncertain lead-time and demand. Bunker fuel cost has a significant impact too and hence is given a distribution such that it generated random numbers between a set limit, which are obtained from historical data as indicated before. It is important to note the effect of trucking fuel on the transit cost, the maximum limit that I have used for sensitivity analysis is highly unrealistic (40 $/gallon) but it is meant to show the fact that the effects of trucking fuel cost are not drastic, although the inland transportation cost constitutes a significant part of the annual transit cost. In order to be as close to real life as possible I have set the trucking fuel cost to be the average of the trucking fuel for the month for the state of California (the destination state) for the year 2011, as described before. Change in storage cost per day beyond the allowable number of free days again does not have a significant impact on the transit cost but historical data suggests that storage cost is set at $500 in port of LA.

Simulation Simulation is used to evaluate the performance of the base case and the two flexible cases. The first flexible case and the base case are compared on the basis of the annual inventory costs. The case with the lower annual inventory costs and lower annual transit costs is better than the other. The simulation model will include the uncertain and the fixed factors explained above to arrive at the annual inventory and transit costs. The input/entries for the simulation model are described below: Factor Fixed/

Variable

Distribution

Mean Std Dev.

Minimum

Maximum

Unit Value (if fixed)

Demand Variable

Normal 110 20 0 210 Units

Origin –Destination Port Lead Time

Variable

Normal 14 3 5 34 Days

Destination port to destination lead time

Variable

Normal 1.9 0.3 1 3 Days

Destination port dwell time

Variable

Normal 5.4 1.8 0.1 11 Days

Unloading time

Variable

Normal 0.4 0.1 0.1 1.0 Days

Lost Sales Cost

Fixed $/unit

1000

Holding cost factor

Fixed $/unit/day

16%


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Per unit cost Fixed $ 50 Order cost for ocean freight

Fixed $ 500

Order cost for air freight

Fixed $ 5000

Average bunker fuel consumption

Fixed Tons/day

160

Average fuel consumption by truck

Fixed mpg 25

Bunker fuel cost

Variable

Random 200 500 $/ton

Storage cost at the destination port

Fixed $/day

500

Number of days allowed to store free of cost

Fixed Days 4

Maximum lost sales allowable

Fixed Units

110

Total lead time through air transportation

Fixed Days 3

Maximum Order Qty

Fixed Units

155

Destination port to Destination distance

Fixed Miles

350

Notes

• There can be other factors like exploring the possibility of transferring shipping responsibility to the freight forwarders (party responsible for shipping) that can be


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included in the evaluation of the annual inventory cost and annual transit cost. However, this analysis will be a stepping stone for more detailed levels in the future long term project.

• Since contractual terms for the maximum allowable order quantity and maximum allowable lost sales vary according to different organizations (or decision makers), I have assumed their values for the current decision maker and also assumed that they serve the demand 365 days a year.

Calculations Before explaining the calculation of the annual inventory and the transit costs, I will include the calculations for the factors used to calculate the former. They are listed below.

1. Order Quantity (Q) - Starting order quantity is the Economic order quantity (EOQ). EOQ is often the starting point of order quantity in case of uncertain demand and lead-time scenarios because it is proven to minimize the inventory cost.

𝑄 = 2 ∗ 𝐴 ∗ 𝐸(𝐷)

𝑣 ∗ 𝑟

Where:

• A = Order Cost • E(D) = Expectation of the Demand (Mean) • v = per unit cost • r = holding cost as % of per unit cost 2. Reorder point (R)- is the point when an order is placed by the shipper (in this

case the decision maker), if the inventory position is below this point. The formula below is again proven to be an optimized reorder point in terms of inventory cost.

𝑅 = 𝐸 𝐿 𝐸 𝐷 + 𝑘 ∗ ( 𝐸(𝐿) ∗ 𝜎!! + 𝐸 𝐷 ! ∗ 𝜎!!) In case of uncertain demand and fixed lead time, as in the case of airfreight mode

for the first flexible case

𝑅 = 𝑙 ∗ 𝐸 𝐷 + 𝑘 ∗ 𝜎! ∗ 𝑙


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Where:

• E(L) = expected lead time =sum of mean of individual lead times because they are independent of each other

• E(D) = Expected Demand • 𝜎!! = Variance of Demand • 𝜎!! = Variance of Lead time = sum of variance of individual paths because they

are independent of each other • 𝑘 = Safety stock factor • l = fixed lead time

3. Per Unit Holding Cost (HC)- is the per unit cost of holding an unit in inventory

which accounts for the holding cost for the annual inventory cost.

𝐻𝐶 = 𝑟 ∗ 𝑣 Where: r = holding cost per unit item per unit time as a percentage of the cost of one item (v) v = cost of per unit item

4. Short Cost (SC)- is the per unit cost of losing the sale of the items, which accounts for the shortage costs for the annual inventory costs.

𝑆𝐶 = 𝑙 ∗ 𝑒𝑛𝑑 𝑖𝑛𝑣 where: l = cost per unit lost sale (here it is $1000) end inv = ending inventory evaluated at the end of every day

Simulation Method The following will describe the steps used to set up the base and flexible cases along with the evaluation of the performance metrics-Annual Inventory Cost and Annual Transit Cost. The two cases are compared on basis of VARG curves, which are a result of simulation.

Simulation Model for base case

1. The order quantity (Q) and reorder point(R) is calculated using the formula mentioned above in calculation section.

2. The initial inventory is set to be equal to the order quantity. It is assumed that an initial inventory equal to the order quantity is passed on to the beginning of the


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current time period. The values for the base case are as follows:

No. of units Order Qty 117 Reorder point 3337 Initial inventory 117

For Day 1:

3. Generate lead-time for the 4 segments of lead time, namely Origin port to destination port (OP-DP LT), destination port dwell (DPD), destination port to destination (DP-D LT) and unloading at destination port (UDP) lead times using the mean and standard deviation as stated in the entries / input section using the following excel command: MIN(MAX((NORMINV(RAND(),Mean,Std.Dev)),Minimum limit),Maximum limit) Total Lead time = (OP-DP LT) + DPD + (DP-D LT) + (UDP)

It is important to note here that the lead-time segments are independent of each other and can be added for the mean and standard deviation of the total lead-time because they are all normally distributed and independent.

4. Beginning inventory is equal to ending inventory of the previous day

5. Generate Demand for the day using the following excel statement: MIN(MAX((NORMINV(RAND(),Mean,Std.Dev)),Minimum limit),Maximum limit) Where the mean, standard deviation and the limits are 110, 20, 0 and 210 respectively.

6. Orders Received is a binary variable, which can either be true or false. Orders received are True if there are any orders to be received this current day. We know that orders are to be received if the orders are placed on any day before the current day and the time when the order is due of any of the previous days matches the day number of the current day, using the following statement: NOT(ISERROR(MATCH(Current day, Time due on day 1:Time due (current day-1),1))) For instance, Orders received for Day 1 is set to False. Orders received for day 2 is True if Orders were placed on Day 1 and the total


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lead-time for day 1 is equal to 1 day.

7. Units Received is equal to the order quantity if there are any orders received this current day. (Or Orders received is True)

8. Ending Inventory is equal to MAX(0,Beginning Inventory –Demand for the day + Units Received)

9. Lost Sales is equal to IF(Demand>BeginningInv + UnitsRecd, IF(Beginning Inv+units Recd>=0,Demand-Beg. Inv- Units Recd,Demand),0)

10. Orders Placed is again a binary variable, which can be either True or False. Orders Placed is true if : Ending Inventory < = Reorder Point

11. Time the order is Due is IF(Orders are placed,Current Day+Total lead time of the current day+1,)

12. Holding Cost is equal to MAX(0,Ending Inventory*holding cost per unit item)

13. Order Cost is equal to If (Orders are placed, Ordering Cost, 0)

14. Short Cost is equal to : Lost Sales * per unit cost of lost sales

15. Total Inventory Cost for the day is equal to Holding Cost for the day + Short Cost for the day + Lost Sales Cost

16. Generate Bunker fuel cost for the day RANDBETWEEN (minimum fuel cost, maximum fuel cost)

17. Trucking fuel cost is known from historical data for 2011. The average cost per

Month is used as tabulated below: Ja

n Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec

Cost( $/gallon)

3.356

3.491

3.963 4.2 4.213 3.953

3.824

3.785 3.946 3.865

3.834 3.834


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18. Port to Port Transit Cost If(Orders are placed, (OP-DP LT * number of tons of bunker fuel consumed/day * fuel cost for the day),0)

19. Destination Port to Destination Transit Cost is If(Orders are placed, (Destination port to destination distance (in miles)/fuel consumption by truck(milespergallon) * cost of fuel per gallon),0)

20. Storage Cost at the destination port

If (dwell time > maximum number of allowable free days, cost of storage per day* (dwell time- maximum number of allowable free days),0)

21. Total transit cost is equal to Port to port transit cost + Destination port to destination transit cost + Storage Cost

22. The above steps are repeated 365 times for annual inventory and transit costs, which is the sum of inventory and transit cost per day for the entire year.

Inventory Cost as a Performance Measure Base Case The base case considers that the decision maker is observing an uncertain demand each day and is also forced to deal with uncertain lead time factors leading to lost sales and safety stock inventory levels. It has no option of increasing the order quantity or choosing an expedited shipping method like airfreight transportation to avoid lost sales for the day. The decision maker incurs the total inventory and total transit cost as per the contractual terms. The calculations for the annual inventory and transit costs are done as described in the “Calculations” section above. The annual inventory cost is affected by uncertainty in demand and lead-time. Monte Carlo Simulation is run for 1000 times, results of which are summarized below.


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Fig. 7 : Sample Base Case spreadsheet with the annual inventory cost Results of Simulation for Base Case Value in million $ Expected Annual Inventory Cost 28.14 Minimum Annual Inventory Cost 23.65 Maximum Annual Inventory Cost 32.68 Standard Deviation of annual inventory cost

1.40


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Fig. 8: VARG curve for Base Case

Fig. 9: Histogram for Base Case

Flexible Case I will be analyzing two flexible cases with different decision rules. The ocean freight transportation has potential for a number of flexible cases; the two mentioned below are the cases, which I think are suitable to be implemented if I were the decision maker in


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real life. The two flexible cases are called flexible Case1 and flexible Case 2. It is important to note there that the two flexible cases are compared against the base case but not compared with each other.

Flexible Case1 Transit time, demand variability and the associated unreliability impose the highest penalty in form of service failures leading to short sales. In real life, as companies keep increasing their sourcing from countries like China, length of supply chains keep increasing and problems associated with them keep getting worse. One coping mechanism is to use airfreight, which usually comes at an added ordering cost, in this case it is 10 times more than the base case ordering cost. Since it comes with an added cost, if lost sales keep recurring the decision maker opts for airfreight. The specification of the circumstances in which airfreight is chosen is under the decision maker’s control. The advantage of using airfreight is certain (or in some real life cases a very low variability) lead-time. It is assumed to be a constant of 3 days as obtained from research. However, since it comes with an added cost, the purpose of the simulation is used to decide if a trade off is advantageous to the decision maker economically. The simulation model is designed to take maximum benefit of the flexible design by reducing the risk of uncertain lead-time. Demand uncertainty is not under the control of the decision maker and hence he chooses to concentrate on uncertain lead-time. In my case the decision maker choses to use air freight transportation if the lost sales in any time period is greater than maximum allowable lost sales in the particular time period. It is important to set a maximum limit on the lost sales allowable because it comes with a large penalty cost and also affects the image of the company in the present and future time periods. In this case the decision maker choses to set the maximum allowable lost sales in any time period to be 110 units. This decision for shifting to air mode once made, is, not a one time decision, implying that the decision maker can choose to go back to ocean freight transportation when lost sales are observed to be less than the maximum allowable lost sales in the following time periods after the decision is made to use air mode. Similarly, it is assumed that the decision maker can choose airfreight mode any number of times in the time period in question (1 year). For the purposes of simplistic simulation model, I have assumed that the decision maker decides to ship in all the units using airfreight in the anticipation of lost sales in day x to be more than the maximum allowable lost sales if the lost sales in day (x-1) is greater than maximum allowable lost sales. In other words, since the decision maker is seeing an uncertain demand, he will anticipate that the demand observed the following day would lead to lost sales more than maximum allowable if a similar pattern is seen the day before. The inventory cost for the flexible case on any day is the inventory cost due to airfreight transportation mode if airfreight is chosen for the current day or is equal to the inventory cost due to ocean freight if the freight is shipped via ocean. A binary variable is used to indicate if implementing the decision rule as stated above uses airfreight. The annual


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inventory cost is then added for the 365 days in a year and compared against that of base case, which uses only ocean freight transportation. The Decision rule used in the simulation model is as stated below: For time t and maximum lost sales allowable =110:

If lost sales in t >110

Air = True

Ship order using airfreight

Inventory cost (t) = air freight inventory cost

If Yes

Inventory cost (t) = ocean freight inventory cost

If No


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Fig. 10(a): Sample Flexible Case 1 spreadsheet with the annual inventory cost based on airfreight or ocean mode for every day


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Fig. 10(b): Sample Flexible Case 1 spreadsheet with the annual

inventory cost based on airfreight or ocean mode for every day Fig 10(a) can be used to demonstrate the implementation of the decision rule for flexible case1. The binary variable that we are concerned with is the column named “Air (Y/N)”. For the day 1 (first row), where the value of lost sales with the base case is 0 units, exercising the decision rule results tell the decision maker not to use the air option because the lost sales units is less than maximum allowable lost sales (0<110). However, day 7 (row 7) sets the binary variable to “True”. It is because the number of lost sales units is greater than maximum allowable units (164>110 units).

Results of Simulation for Flexible Case 1 Value in million $ Expected Annual Inventory Cost 14.64 Minimum Annual Inventory Cost 12.17 Maximum Annual Inventory Cost 17.38 Standard Deviation of annual inventory cost

0.84


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Fig. 11 : VARG curve for Flexible Case 1

Fig. 12 : Histogram for Flexible Case 1

Base Case vs Flexible Case1 *


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Value in million $ Base Case Flexible Case1 Expected Annual Inventory Cost

28.14 14.64


23.65 12.17


32.68 17.38


1.40 0.84

P10 26.40 13.55 P90 29.94 15.75

*(the values marked in yellow are the favorable outcomes)

Fig. 13: VARG curve for Flexible case1 and Base case.

The penalty cost that I incur due to lost sales is 1000 per unit whereas the ordering cost for airfreight shipment is $5000(is10 times more than ocean shipping). In the base case cost due to lost sales account for a large percentage of the total inventory cost, which are due to uncertain demand and uncertain lead-time. On getting the air option I make my system flexible and hence the total inventory costs reduce because shortage cost reduces much more as compared to increase in the ordering cost and holding cost. Numbers from one simulation indicates that while the holding and ordering costs increase, the shortage


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cost in the flexible option is 97% less than that of base case, which is about 28 million USD. This improvement in shortage cost outweighs increase in cost due to holding cost and ordering cost. The simulation results show that the flexible case is stochastically dominant and is preferred over the base case always. This flexible design reduces the downside risk by reducing / eliminating the lost sales and also takes advantage of the opportunities (in this case reduced holding cost because of certain lead time factor instances as compared to always procuring units via highly uncertain ocean transportation). The histograms of the flexible case and the base cases show that the base case inventory costs have more tendencies to be towards higher costs as compared to the flexible case. (Base case between 26.81-29.97; flexible case between 14.00-15.56). Since our objective is to minimize the costs flexible case looks better than the base case, on comparing the above histograms.

Flexible Case2 Due to highly uncertain demand and lead time pattern in this case the decision maker can use real options contract for very long supply chain from China to USA like the one being discussed here. It helps the decision maker hedge the risk of lost sales due to uncertainties. The decision maker (the shipper) will have the right but not an obligation to ship in a maximum of 155 units. Sensitivity analysis is used to arrive at the maximum allowable order quantity in terms of its sensitivity to the inventory cost. The results are described in the following section. Exercising the right allows the decision maker to expand based on a certain decision rule. In this case the decision rule is based on observing lost sales over 2 consecutive days before the current day and the current order quantity is less than the maximum order quantity allowable under the contract, the decision maker has the option of increasing the order quantity by 15 units (or “expanding”). The advantage of this option is reducing the lost sales to the maximum extent possible, sometimes even to 0. However, it comes with a cost of having the option, which is $100 more than the base case in terms of the ordering cost. The decision maker has to trade off between the two options to settle on the base or the flexible case. The decision maker is allowed to expand any number of times as long as the condition of maximum allowable order quantity is satisfied, that is the order quantity after expanding is less than or equal to the maximum allowable order quantity under the options contract. If the option is exercised, the order quantity remains the same for the rest of the following days until the option is exercised again. In other words, the simulation model is set such that the order quantity in day x is greater than or equal to the order quantity in day (x-1). The inventory costs are calculated using the same calculations as described before.


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Annual Inventory costs and annual transit costs of the base case and the flexible cases are now compared.

Sensitivity Analysis to determine maximum order quantity allowable Sensitivity analysis was done to determine the maximum order quantity allowable since there is no data available on the same. Assuming 165 units as the maximum allowable order quantity, the flexible and the base cases were analyzed. Although it gave the desired results (flexible case 2 being stochastically dominant), changing the order quantity limit to 155 units gave even better results. Also it was interesting to note that the lost sales with 155 units were less than setting the limit anywhere between 130- 145 units. So 155 units gave a lower cost and lower lost sales on average. In real life, managers like the decision maker in the current case, base their analysis on the inventory cost. Hence the difference between average annual inventory cost obtained from simulation of the base case and the flexible case 2 suggested maximum cost difference (maximum value) for a maximum order quantity of 155 units. In the figure below a positive cost difference implies annual inventory cost of flexible case is better (lower) than the base case.

Fig. 14: Sensitivity Analysis to determine maximum order quantity

The analysis shows that beyond 170 units the flexible case 2 starts performing worse than the base case because at this point the holding cost overcomes the shortage and ordering cost. It is because increasing the order quantity reduces the lost sales, constantly reducing


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shortage cost and thus for every order cycle a lot more units are ordered than required. A point after which the lost sales goes to 0, shortage costs no longer have a bearing on the total annual inventory cost and hence ordering just the optimum amount enough to counter the lost sales is the answer. For day t, order quantity Q and maximum order quantity allowable under the options contract =155:

If lost sales in (t -‐2) AND (t-‐1)>0 AND Q(t-‐1) <155

Expand

Ship current order using new order quantity

Calculate New inventory Cost

If Yes

Inventory cost (t) = base case order quantity inventory cost

If No

If Q(t-‐1) < = 155

If Yes

Q(t) = Q(t-‐1)+ 15

If No Q(t) = Q(t-‐1)


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Fig. 15: Sample Flexible Case spreadsheet with the annual inventory cost

In order to demonstrate how the flexibility rule works, we could take a look at snapshot of the spreadsheet for the flexible case above (Fig.15). Under the column named “expand”, the 4th day suggests that the decision maker should expand. It is because the lost sales column (column to the left) indicates a lost sale of 81 and 75 units for day 2 and 3 (2 time periods before 4) which are greater than 0 units. However, for day 2, the model suggests that there should be no expansion because day 1 fortunately did not see any lost sale and hence only one day between day 1 and 2 saw a positive lost sale unit. Also, after the order quantity (column to the right of expand) reaches 143 units from the starting point of 128 units, the model restricts any more expansion even though the model suggests expansion because 143 +15 =158 units is greater than 155 units, which is the maximum number of units allowable under contract between the decision maker and the shipper.

Results of Simulation for Flexible Case 2 With maximum order quantity = 155 units


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Value in million $ Expected Annual Inventory Cost 18.01 Minimum Annual Inventory Cost 15.74 Maximum Annual Inventory Cost 19.90 Standard Deviation of annual inventory cost

0.61

Fig. 16(a1): VARG curve for Flexible case2 (155 units)

Fig. 16(a2): Histogram for the annual inventory costs in flexible case2 (155 units)


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For the purposes of comparison and to understand the results of the sensitivity analysis the inventory cost corresponding to 165 units are tabulated below: Value in million $ Expected Annual Inventory Cost 25.09 Minimum Annual Inventory Cost 23.25 Maximum Annual Inventory Cost 26.96 Standard Deviation of annual inventory cost

0.62

Fig. 16(b1): VARG curve for Flexible case2


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Fig. 16(b2): Histogram for the annual inventory costs in flexible case2

Base Case vs Flexible Case2 Value in million $ Base Case Flexible Case2 Expected Annual Inventory Cost

28.14 18.01


23.65 15.74


32.68 19.90


1.40 0.61

P10 26.40 17.25 P90 29.94 18.79


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Fig. 17: VARG curve for Flexible case2 and Base case.

Flexibility of having the option of “expanding” or increasing the order quantity based on a decision rule of lost sales comes with a cost premium. However the results above justify the added cost by benefitting in inventory costs (and later as we will see in transit costs too). The cost of lost sales of one unit is much more ($1000) as compared to added costs of $100. Although the costs are not directly comparable, the scale difference speaks a lot about the effect of lost sales on the cost. Hence the flexibility rule can be seen as an insurance against lost sales outcomes. In case of the flexible case, increasing the order quantity in light of uncertain demand and lead-time reduces the shortage cost part of the annual inventory cost. This “benefit” again outweighed the increase in cost of ordering. Also, increasing the order quantity reduces the number of instances of orders placed. On comparing the results, the flexible option is a more favorable decision when compared to the base case. On comparing the expected annual inventory cost, the company reduces the cost by about 10 million USD by exercising the flexibility of increasing the order quantity. VARG curve comparison of the base case and the flexible case analysis of extreme values can reveal interesting results to the decision maker. It also shows that the curve for the base case reaches higher values of cost faster than the flexible case, thus proving that the flexible case is better than the base case. The VARG curve shows that the flexible case is better than the base case under all circumstances and is stochastically dominant (since the X axis is the cost the graph to the left is better performing than the one on the


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right). Also the flexible has a lower annual inventory cost or greater value (lower inventory cost) at the P90 & P10. Other parameters like the maximum cost and the standard deviation reiterates the fact that the flexible case is better than the base case and helps the decision maker to be completely sure when investing in the option.

Transit Cost as a Performance Measure

Base Case Transportation costs, I believe, is an important measure for the performance of the ocean transportation system. This is the responsibility of the shipper if it owns the ships that are used to ship the products. In many other cases the shipper transfers the responsibility to the freight forwarder who owns the ships and the shipper pays a transportation cost which is added to the fixed order cost. In the case being discussed here, the former case is used which implies that the decision maker is responsible for the transit cost. This is turn implies that the decision maker is affected by uncertainties in fuel cost. The transit cost as discussed earlier constitutes three parts, oceanic transit fuel cost, in land transit fuel and the storage cost at the destination port because of the dwell time exceeding 4 days, which is the maximum number of days allowed to be stored for free in the destination port. Fuel used in ships or bunker fuel is modeled to be random numbers between 200 and 500 USD/ton and the cost for truck fuel is set as the average price for each month. Similar to the simulation for annual inventory cost, 1000 simulations are run for the base case and the flexible case to compare the annual transit cost. Calculations for the cost are described in the section above. Again the case with the lower transit cost is valued superior to the other.

Results of Simulation for Base Case Value in million $ Expected Annual Transit Cost 286.22 Minimum Annual Transit Cost 266.03 Maximum Annual Transit Cost 301.93 Standard Deviation of annual Transit cost

5.02


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Fig. 18: VARG curve for Base Case for annual transit cost

Fig. 19: Histogram for Base Case for annual transit cost

Flexible Case 2 Besides affecting the annual inventory cost, the real options flexibility in case of the second flexible case has effects on the transit cost. The change in order quantity changes the number of orders that are placed and hence this frequency is responsible for a change in the annual transit cost as compared to the base case. This is known to indirectly affect the storage costs at the destination port because the lead-time, which is different for different days when the order is placed, leads to a different storage cost. The same logic applies to all the 3 parts of the annual transit cost. The simulation decision rule is the same as that described in the section for decision rule for inventory costs for flexible case 2. The transit costs are updated similar to the inventory costs. The transit costs are independent of the number of units being shipped.


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I have not compared flexible case 1 and base case transit cost because of the unavailability of information on the airfreight fuel costs.

Results of Simulation for Flexible Case 2 Value in million $ Expected Annual Transit Cost 210.80 Minimum Annual Transit Cost 195.64 Maximum Annual Transit Cost 227.85 Standard Deviation of annual Transit cost

4.79

Fig. 20 : VARG curve for Flexible Case 2 for annual transit cost


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Fig. 21 : Histogram for Flexible Case 2 for annual transit cost

Base Case vs Flexible Case2 Value in million $ Base Case Flexible Case2 Expected Annual Transit Cost

286.22 210.80

Minimum Annual Transit Cost

266.03 195.64

Maximum Annual Transit Cost

301.93 227.85

Standard Deviation of annual Transit cost

5.02 4.79

P10 253.84 195.64 P90 301.93 227.85


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Fig. 22: VARG curve for Flexible case2 and Base case. The VARG curve for the annual transit costs again show a clear stochastic dominance of the flexible case over the base case scenario. Although, the magnitude of performance depends on the numbers chosen, flexible case is expected to perform better than the base case because the flexible case 2 reduces the number of orders with increased order quantities until the maximum quantity allowed thus reducing the transit cost, as described above. Also, it is observed that the “benefit” in transit cost is much better in the flexible case as compared to the “benefit” in case of inventory cost

Conclusion Implementing the decision rules to the base case in simulation model prove the value of flexible cases under uncertainty. In both the cases (1 &2) flexible option is stochastically dominant over the base case and is preferred under all circumstances. No matter whether the decision maker is risk averse or risk seeking, he will always go for the flexible case because it invariably performs better than the base case in all the multidimensional criteria discussed above. In this case the average annual inventory cost for flexible case 1 is twice as better (twice as low) as compared to the base case. This amounts to about 14 million USD in savings. Flexible case 2 is about 1.6 times better than the base case amounting to 10 million USD in savings. Similar analysis shows that flexible case 2 performs about 1.4 times (about 76


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million USD in savings) better than the base case in terms of the annual transit cost. Also, comparison of the extreme values of the three alternatives shows that the flexible cases (1 &2) are a better option when compared to the base case in all the criteria discussed (stochastically dominant). The comparison of standard deviations in case of the base case and flexible cases 1 and 2 show that the standard deviation for the latter are much lower than the base case. This is probably particularly attractive for a risk averse person because a greater standard deviation combined with a greater mean of base case suggests higher possibility of a large cost which is incurred due to maximum peak cases of demand and lead time. In case of the flexible cases, the decision maker is given an opportunity to decide with more information whether to switch to air mode or increase the order quantity only when it is required and thus avoiding excess inventory or shortage cost. The flexibilities handle both the extremes by reducing excess inventory and reducing shortage cost. The table below summarizes the comparison of flexible case and base case on basis of multidimensional criteria. The Value (how better the flexible case performs over the base case) of flexible case over base case is the reciprocal of cost of flexible case to base case. FlexibleCase1/Base

Case Value of flexible

case1 Flexible

Case2/Base Case

Value of flexible case2

Expected Annual Inventory Cost

0.52 1.92 0.64 1.57


0.51 1.96 0.67 1.49


0.53 1.89 0.61 1.64


0.60 1.67 0.44 2.27

P10 0.51 1.96 0.65 1.54 P90 0.53 1.89 0.94 1.06 FlexibleCase2/Base Case Value of flexible case2

Expected Annual Transit Cost

0.74 1.35

Minimum Annual Transit Cost

0.74 1.35


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Maximum Annual Transit Cost

0.92 1.09

Standard Deviation of annual Transit cost

0.95 1.05

P10 0.77 1.29 P90 0.72 1.39 Thus, flexibility is clearly worthwhile because it reduces the cost incurred by the decision maker by significant amounts annually. Certain external elements like contractual agreements with the supplier and also trade laws between China-US can affect the decision maker’s choice. The decision is set such that the flexible decisions allow for lower inventory and transit cost even though you pay a certain “insurance” to achieve it. I would also like to note that I did not compare the flexible case 1 and 2 amongst themselves because they are based on incomparable decision criteria (1. Choosing airfreight if lost sales are beyond a certain allowable limit; 2. Opting to ship in more units within a certain contract limit if lost sales are more than 0 units in the previous two time periods). Comparison between them is not reasonable in all situations. For instance, if the decision maker is not able to convince the supplier to reach the required flexible contractual terms, then flexible case 2 cannot be exercised. The use of simulation taught in the class, for the above analysis, helped me model a real life system with many uncertainties (like uncertain demand, lead time and uncertain fuel costs). It proved that we could use tools like simulation to analyze system with uncertain parameters and improve the value of the project by embedding flexibility into the system. Flexibility in the system, though incurred at a cost, has better returns than the base case scenario. Flexibility reduces the downside risk and takes advantage of available opportunities like alternative mode of transportation (e.g. air freight) or growth opportunity (contractual terms). There were a few problems encountered during the modeling of the system. One of the most important questions that took a while for me to answer is to frame an efficient flexible case for the abovementioned system. During the process of trying to comprehend the same, I had to model many different flexible cases but did not always see results that reduced the cost of the inventory held or annual transit cost. Future work of the simulation model is to allow for both back orders and lost sales. The calculations involve setting a service limit or an item fill rate to allow for x% of unmet demand as back orders and (1-x)% as lost sales. Then back orders will have a lower penalty because these will be met in a certain time period as compared to lost sales where in the customers are lost forever. This comes with an added complexity to the simulation model but also creating more opportunities for flexible decisions.


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Course Reflections and Lessons Learned The process of developing the simulation model and the application portfolio has been a rigorous but an extremely valuable process. The learning curve, if drawn, would suggest an improvement in my understanding of the effect of uncertainties and why organizations and decision makers should invest time, money and energy to explore flexible cases. The revelations from the application of simulation model can be pretty interesting, similar to the conclusions seen above. The process of framing decision rules helped me to delve deep into the problem scenario and think as a real life ocean freight manager. I think I can now identify sources of uncertainty and modeling variability in the model to see its effect on the value of a complex system in terms of a performance measure.

References http://www.thepriceoffuel.com/whataffectsfuelpricing/#gasoline http://www.tsacarriers.org/fs_bunker.html http://www.wilhelmsen.com/services/maritime/companies/wpmf/TradingandHedging/Pages/Prices.aspx http://www.bts.gov/publications/americas_container_ports/2011/pdf/entire.pdf Silver, Edward. A., Pyke, David F. and Peterson, Rein. Inventory Management and Production Planning and Scheduling

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