high service level application requires 500 tons of salt per inch of snow, which would require...

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high service level application requires 500 tons of salt per inch of snow, which would require 11,000 tons of salt, if 2 inches of snow fell. These numbers are consolidated at Exhibit 3. Sarah discovered that the surrounding counties established their service level by determining cost calculations and risk tolerance for vehicular accidents. The number of vehicular accidents during the winter season and safety of roadways is directly correlated with road salt application. There are approximately 2,500 vehicular accidents per month from December 1st to March 31st in Winterland with a mild snowfall and no salt applied. From December 1st to March 31st when no salt is applied, 5,000 vehicular accidents occur with an average snowfall and 7,500 vehicular accidents occur with a severe snowfall. If a low service level of salt is applied to the roads, the vehicular accident numbers decrease to 1,800 accidents per month with mild snowfall, 2,500 accidents per month with average snowfall, and 7,500 accidents per month with severe snowfall from December 1st to March 31st. If a standard service level of salt is applied to the roads, the vehicular accident numbers decrease even more to 1,200 accidents per month with mild snowfall, 1,500 accidents per month with average snowfall, and 3,000 accidents per month with severe snowfall from December 1st to March 31st. If a high service level of salt is applied to the roads, the vehicular accident numbers decrease even further to 500 accidents per month with mild snowfall, 1,000 accidents per month with average snowfall, and 1,200 accidents per month with severe snowfall from December 1st to March 31st. The average cost of an accident to the county of Winterland is $800 and 1% percent of accidents result in a death. These numbers are also consolidated at Exhibit 3. Sarah also determined the average cost to the private sector is $1,000 per accident, which includes costs to both the citizen and insurance company. Even though this does not impact her budget, Sarah wanted to keep this figure in mind as it represents the private sector impact to the citizens of Winterland for decisions that she makes. Winterland's Inbound Supply Chain The Winterland DPW currently has 1 storage shed as indicated by the red star on the map at Exhibit 2. The storage shed is located at an optimal point, where a rail head, port, and highway converge; thus, having access to deliveries made by rail, truck, and boat. The initial inventory in October is 50,000 tons of salt. The cost of salt storage is $100 per month per 1,000 tons, which includes costs of storage shed maintenance; this cost is constant throughout the year. The total storage capacity is 180,000 tons and the maximum amount of salt that can be received each month is 85,000 tons. These inventory parameters are displayed at Exhibit 4. Sarah has received the advice of reassessing the road salt inventory at the end of each month and comparing that with the snowfall for the season thus far. This technique will allow Sarah to determine if the snowfall is trending toward an average, mild, or severe amount. She can then adjust the order quantities accordingly. Sarah also does not want to carry enormous amounts of road salt inventory over the spring and summer. Road Salt Winterization 4 of 10 HKS Case 2185.0 The Winterland DPW can purchase road salt from three different mines. Salt from any of these mines must be ordered in 100 ton quantities. Nearby DPW directors that Sarah spoke with stated lead times from the International Mine were inconsistent due to its distance from the Northeast United States, where as lead times from the New York Mine were incredibly reliable due to its close proximity. The mine source data is consolidated at Exhibit 5. International Mine The International Mine salt costs $15,000 per 100 tons delivered to Winterland. The salt travels by boat to Winterland. The lead time for the international Mine is 2 months. The order transaction cost is $2,000. The DPW is able to order unlimited quantities of salt from the International Mine during a winter season. Louisiana Mine The Louisiana Mine salt cost is $10,000 per 100 tons. The salt travels by rail to Winterland. The lead time for the Louisiana Mine is 1 month. The order transaction cost is $1,000. The DPW is only able to order 75,000 tons of salt from the Louisiana Mine per winter season due to its limited quantities. New York Mine The New York Mine salt costs $7,000 per 100 tons. The salt travels by truck to Winterland. The lead time for the New York Mine is 1 month. The order transaction cost is $1,000. The DPW is only able to order 100,000 tons of salt per winter season from the New York Mine due to its limited quantities. Winterland's Outbound Supply Chain The application costs are $1,000 per 1,000 tons of salt applied to roads in the South Quadrant and East Quadrant. The application costs are $2,000 per 1,000 tons of salt applied to roads in the North Quadrant and West Quadrant. These costs are on a per month basis up to 5 inches of snowfall. The cost increases by $500 per 1,000 tons of salt applied per month for every additional 5 inches of snow that fall in a given month for the South and East Quadrants; the cost increases by $750 for the North and West Quadrants. For example, snowfall between 5.1 to 10 inches would cost $2,750 per 1,000 tons of salt applied to roads in the North and West Quadrants; the cost for roads in the South and East Quadrants would be $1,500 per 1,000 tons of salt applied. The costs would be $3,500 and $2,000 respectively for snowfall between 10.1 to 15 inches. These costs incorporate personnel wages, fuel, and vehicle maintenance costs. Sarah has the option to construct three additional storage sheds for $100,000 each, so that one exists in each quadrant on the map. If this occurs, the current shed would remain in the East Quadrant and new storage sheds would be built in the North, South, and West Quadrants. The research that Sarah conducted from neighboring counties indicates that one shed streamlines personnel efforts and costs, but she would like to make a fully informed and analytical decision. The three new sheds would only be located by Road Salt Winterization 5 of 10 HKS Case 2185.0 highways and would not have access to the port or a rail head. As a result, orders from the International Mine or Louisiana Mine would increase by $1,000 per 100 tons of salt for additional handling and transportation costs. For example, orders from the International Mine would have a total cost of $16,000 per 100 tons of salt, if delivered to a shed in the North Quadrant, South Quadrant, or West Quadrant. Orders from the Louisiana Mine would have a total cost of $11,000 per 100 tons of salt for delivery to these quadrants. If these additional sheds in the North, South, and West Quadrants are constructed the application costs are also impacted. The application costs are $1,000 per 1,000 tons of salt applied per month for roads in the same quadrant as a storage shed. The application costs are $1,500 per 1,000 tons of salt applied per month for roads in a different quadrant. These costs are on a per month basis up to 5 inches of snowfall. The cost increases by $500 per 1,000 tons of salt that is applied to the same quadrant as the storage shed and $750 per 1,000 tons of salt that is applied to a different quadrant then where the storage shed is located for every 5 inches of snow per month. These costs incorporate personnel wages, fuel, and vehicle maintenance costs. The outbound supply chain costs have been consolidated at Exhibit 6. Supply Chain Network Design Optimization Sarah's objective is for the DPW to meet the demand for road salt depending upon the snowfall, while minimizing costs and ensuring road safety for the citizens of Winterland. This requires optimization of multiple factors in the supply chain. Sarah needs to determine accurate and defensible costs in preparation for her budget meeting. Additionally, the people of Winterland are relying on the DPW's efforts to keep their roadways safe during the winter season...and winter is coming. Task 1: Draw the supply chain options Map nodes and links Incorporate the lead time and snowfall variability, cost, and capacity of the options to develop a strategy Task 2: Determine the optimal inbound supply chain From suppliers to Winterland's storage shed Build an Excel-based model to assess the options that incorporates service level, supplier selection, road salt order quantity, and timing of road salt orders Task 3: Determine the optimal outbound supply chain From Winterland's one storage shed to its roads From Winterland's four storage sheds to its roads Extend the Excel model Road Salt Winterization 6 of 10 HKS Case 2185.0 Month Exhibit 1 - Winterland Snowfall Average Snowfall in inches 0 October November 1.6 December 10 January 14.2 February 11.5 March 8.7 April May June NOO 2.2 0 Mild Snowfall in inches 0 1 3.2 4.1 3.6 2.1 HOO 1 0 Severe Snowfall in inches 0 0 8.2 30 34.5 31.2 5.1 oo 0 0 Service Level High Standard Low None Service Level High Standard Low None Tons of salt per 1,000 miles of road treated per inch of snow 500 400 300 0 5 12 18 25 Road Salt Winterization Exhibit 3-Road Salt Service Levels Vehicle Accident Cost to Winterland - $800 per accident Vehicle Accident Cost to Private Sector - $1000 per accident Deaths per month with mild snow (December to March) Vehicle Accidents per month with mild snow (December to March) 500 1,200 1,800 2,500 Vehicle Accidents per month with average snow (December to March) 10 15 25 50 1,000 1,500 2,500 5,000 Deaths per month with average snow (December to March) Deaths per month with severe snow (December to March) 12 30 40 75 9 of 10 Vehicle Accidents per month with severe snow (December to March) 1,200 3,000 4,000 7,500 HKS Case 2185.0 Initial Inventory in tons of Salt 50,000 Mine International Louisiana New York Storage Sheds 1 in East Quadrant Road Salt Winterization 75,000 100,000 4-1 in North, 1 in East, 1 in West, and 1 in South Quadrant Exhibit 4 - Inventory Parameters Storage Capacity in tons of Salt Maximum Salt Received per month in tons 85,000 Order Capacity per Winter Season Unlimited Exhibit 5 - Road Salt Mine Sources Cost per 100 tons of Salt with 1 Storage Shed $15,000 $10,000 $7,000 180,000 Costs per 1,000 tons of Salt per month up to 5 inches of Snow Exhibit 6 - Road Salt Application Costs Costs per 1,000 tons of Salt per month for 5.1-10 inches of Snow $500 in South and East Quadrants $750 in North and West Quadrants $500 in same Quadrant $750 in different Quadrant $1,000 in South and East Quadrants $2,000 in North and West Quadrants $1,000 in same Quadrant $1,500 in different Quadrant Cost per 100 tons of Salt with 4 Storage Sheds $16,000 $11,000 $7,000 10 of 10 Storage Cost per month per 1,000 tons of Salt $100 Order Transaction Cost $2,000 $1,000 $1,000 Costs per 1,000 tons of Salt per month for 10.1-15 inches of Snow $500 in South and East Quadrants $750 in North and West Quadrants $500 in same Quadrant $750 in different Quadrant Lead Time 2 months 1 month 1 month Construction Costs $0 $300,000 HKS Case 2185.0 #3) (27 marks) Using the information and the data provided in the case and on the supplementary Excel spreadsheet that is available, develop a multi period linear programming (LP) formulation to deal with an optimization problem of your choice relevant to the case. (The scope of the chosen problem does not have to incorporate the entire set of data provided in the text and / or in the Excel supplement. However, the scope should be coherent, using part, not all, of the information and data provided in the case and / or in the Excel supplement.) Do not solve the formulated problem. a) Provide the assumptions involved in the LP formulation. b) Define (in mathematical notation and in words) the decision variables. c) Define (in mathematical notation and in words) the parameters involved in the objective function and the constraints. d) Write the LP formulation in its entirety using the relevant parameter values provided in the case. (i.e., Do not write CX. Instead, provide the value for C from the case.) HARVARD Kennedy School JOHN F. KENNEDY SCHOOL OF GOVERNMENT Designing and Optimizing a Supply Chain: Keeping Drivers Safe in the Winter ROAD SALT HTT DS "No Bob, praying for climate change cannot be our only strategy!" HKS Case KS1325 June 30, 2020 Ome_me_cartoon Road Salt Overview On average in the United States 17 million tons of salt is applied to roads during the winter. The salt used on roads is often called rock salt, because its grains are much coarser than table salt, but it is still the same molecule-sodium chloride. Salt is applied to roadways to lower the freezing point by 10 to 15 degrees, inhibiting ice from forming on roads until the temperature is well below freezing.3 Most rock salt for roads is mined "dry" from underground seams of crystal salt, which formed from the evaporation of ancient seas.4 Miners follow shafts underground and break out slabs of salt with dynamite and powered shoveling machines. Trucks or conveyors haul the salt to crushing machines. Supply Chain Challenges Salt itself is a very abundant resource, but, in 2015, much of the United States was not able to acquire the quantity it needed to properly winterize roads. The "perfect storm" was the culmination of issues including worker strikes, salt mine closures, and transportation issues. One of the major salt mines suffered major shortages from a 12-week worker strike, while another mine struggled with replenishing its stock due to a water leak.5 This caused cities across the United States to resort to importing salt supplies from other countries. Imported salt also faced challenges. First, there was a shortage of shipping vessels. Second, when the imported product arrived in port, it was often delayed at customs and wasn't able to get to its final destination in time. Furthermore, transportation costs on the imported salt were 10-15 percent higher than domestic product. Moving domestic salt was also problematic. Much of the country experienced a deep freeze which meant frozen waterways. The Illinois Waterway was closed for repairs, causing shipping delays and increased costs. This in turn meant barges were unable to move excess supplies from one region to another that desperately needed it. The Mississippi River also faced major issues because of this extreme deep freeze and heavier than normal snowfall, which caused two-month delays in shipping, plus barge and diesel shortages. To top that off, many areas of the Midwest and Northeast saw record snow and ice levels-they simply needed more salt than normal or expected. Any one of these issues would impact the availability of salt but to have all of these issues happening at once caused major disruptions, chaos, and higher prices. Winterland's Road Salt Dilemma Winterland is a county that encompasses a major metropolitan city located in the Northeast United States. Sarah has lived in Winterland most of her life and was recently hired into her dream job of overseeing Operations and Maintenance for Winterland's Department of Public Works (DPW). Sarah is replacing Don, who held the position of Operations and Maintenance Chief in the DPW for over 20 years. Don was incredibly knowledgeable of all Operations and Maintenance activities, but passed little records onto Sarah. Not only is Sarah an incredibly hard worker, but she realizes that the services provided to the residents of Winterland are vital. Sarah would like her transition to be seamless, especially when it comes to road safety during the winter season. Additionally, Sarah is entering her position under great financial strain due to the COVID-19 pandemic. The county of Winterland is reexamining its budget to minimize costs, while optimizing the services it provides to its residents. Sarah would like to propose a budget for road salt during the next budget meeting that incorporates both the inbound supply chain and outbound supply chain costs. The budget should also examine service levels provided to Winterland's citizens as the safety of citizens is critical to their wellbeing. Sarah has conducted a fair amount of benchmarking research to determine best practices for neighboring counties in the Northeast United States. Sarah also understands that there are some environmental concerns with road salt and has conducted research on various alternatives. She is planning on proposing more environmentally friendly options in two to five years, but has decided to use road salt during this winter until a fully formalized plan for alternatives is established. Winterland's Snowfall Sarah is trying to determine a road salt strategy for Winterland's DPW to winterize roads for the upcoming winter season. The average snowfall for Winterland is outlined in the chart at Exhibit 1. There is variability to account for in snowfall as the 2015 season was incredibly severe with almost 109 inches that year, but only 15 inches of snow fell during the 2020 season. As a result, some winters have been mild with considerably less snowfall than average and other winters have been severe with considerably more snowfall than average. There is a 25% chance of a mild snowfall, 50% chance of an average snowfall, and 25% chance of a severe snowfall this upcoming winter. Winterland's Roads Winterland consists of 11,000 miles of road that need to be treated with road salt. A map of Winterland's quadrants can be found at Exhibit 2. The North Quadrant of Winterland has 2,000 miles of road, the West Quadrant has 1,000 miles of road, the South Quadrant has 3,500 miles of road, and the East Quadrant has 4,500 miles of road. All of Winterland must be treated to the same service level for the duration of the winter season. A standard service level requires 400 tons of salt per 1,000 miles of road treated per inch of snow. For example, if 2 inches of snow fell in Winterland, 8,800 tons of salt would comprise a standard application. A low service level application requires 300 tons of salt per 1,000 miles of road treated per inch of snow. For Winterland, a low service level application would require 6,600 tons of salt, if 2 inches of snow fell. A high service level application requires 500 tons of salt per inch of snow, which would require 11,000 tons of salt, if 2 inches of snow fell. These numbers are consolidated at Exhibit 3. Sarah discovered that the surrounding counties established their service level by determining cost calculations and risk tolerance for vehicular accidents. The number of vehicular accidents during the winter season and safety of roadways is directly correlated with road salt application. There are approximately 2,500 vehicular accidents per month from December 1st to March 31st in Winterland with a mild snowfall and no salt applied. From December 1st to March 31st when no salt is applied, 5,000 vehicular accidents occur with an average snowfall and 7,500 vehicular accidents occur with a severe snowfall. If a low service level of salt is applied to the roads, the vehicular accident numbers decrease to 1,800 accidents per month with mild snowfall, 2,500 accidents per month with average snowfall, and 7,500 accidents per month with severe snowfall from December 1st to March 31st. If a standard service level of salt is applied to the roads, the vehicular accident numbers decrease even more to 1,200 accidents per month with mild snowfall, 1,500 accidents per month with average snowfall, and 3,000 accidents per month with severe snowfall from December 1st to March 31st. If a high service level of salt is applied to the roads, the vehicular accident numbers decrease even further to 500 accidents per month with mild snowfall, 1,000 accidents per month with average snowfall, and 1,200 accidents per month with severe snowfall from December 1st to March 31st. The average cost of an accident to the county of Winterland is $800 and 1% percent of accidents result in a death. These numbers are also consolidated at Exhibit 3. Sarah also determined the average cost to the private sector is $1,000 per accident, which includes costs to both the citizen and insurance company. Even though this does not impact her budget, Sarah wanted to keep this figure in mind as it represents the private sector impact to the citizens of Winterland for decisions that she makes. Winterland's Inbound Supply Chain The Winterland DPW currently has 1 storage shed as indicated by the red star on the map at Exhibit 2. The storage shed is located at an optimal point, where a rail head, port, and highway converge; thus, having access to deliveries made by rail, truck, and boat. The initial inventory in October is 50,000 tons of salt. The cost of salt storage is $100 per month per 1,000 tons, which includes costs of storage shed maintenance; this cost is constant throughout the year. The total storage capacity is 180,000 tons and the maximum amount of salt that can be received each month is 85,000 tons. These inventory parameters are displayed at Exhibit 4. Sarah has received the advice of reassessing the road salt inventory at the end of each month and comparing that with the snowfall for the season thus far. This technique will allow Sarah to determine if the snowfall is trending toward an average, mild, or severe amount. She can then adjust the order quantities accordingly. Sarah also does not want to carry enormous amounts of road salt inventory over the spring and summer. Road Salt Winterization 4 of 10 HKS Case 2185.0 The Winterland DPW can purchase road salt from three different mines. Salt from any of these mines must be ordered in 100 ton quantities. Nearby DPW directors that Sarah spoke with stated lead times from the International Mine were inconsistent due to its distance from the Northeast United States, where as lead times from the New York Mine were incredibly reliable due to its close proximity. The mine source data is consolidated at Exhibit 5. International Mine The International Mine salt costs $15,000 per 100 tons delivered to Winterland. The salt travels by boat to Winterland. The lead time for the international Mine is 2 months. The order transaction cost is $2,000. The DPW is able to order unlimited quantities of salt from the International Mine during a winter season. Louisiana Mine The Louisiana Mine salt cost is $10,000 per 100 tons. The salt travels by rail to Winterland. The lead time for the Louisiana Mine is 1 month. The order transaction cost is $1,000. The DPW is only able to order 75,000 tons of salt from the Louisiana Mine per winter season due to its limited quantities. New York Mine The New York Mine salt costs $7,000 per 100 tons. The salt travels by truck to Winterland. The lead time for the New York Mine is 1 month. The order transaction cost is $1,000. The DPW is only able to order 100,000 tons of salt per winter season from the New York Mine due to its limited quantities. Winterland's Outbound Supply Chain The application costs are $1,000 per 1,000 tons of salt applied to roads in the South Quadrant and East Quadrant. The application costs are $2,000 per 1,000 tons of salt applied to roads in the North Quadrant and West Quadrant. These costs are on a per month basis up to 5 inches of snowfall. The cost increases by $500 per 1,000 tons of salt applied per month for every additional 5 inches of snow that fall in a given month for the South and East Quadrants; the cost increases by $750 for the North and West Quadrants. For example, snowfall between 5.1 to 10 inches would cost $2,750 per 1,000 tons of salt applied to roads in the North and West Quadrants; the cost for roads in the South and East Quadrants would be $1,500 per 1,000 tons of salt applied. The costs would be $3,500 and $2,000 respectively for snowfall between 10.1 to 15 inches. These costs incorporate personnel wages, fuel, and vehicle maintenance costs. Sarah has the option to construct three additional storage sheds for $100,000 each, so that one exists in each quadrant on the map. If this occurs, the current shed would remain in the East Quadrant and new storage sheds would be built in the North, South, and West Quadrants. The research that Sarah conducted from neighboring counties indicates that one shed streamlines personnel efforts and costs, but she would like to make a fully informed and analytical decision. The three new sheds would only be located by Road Salt Winterization 5 of 10 HKS Case 2185.0 highways and would not have access to the port or a rail head. As a result, orders from the International Mine or Louisiana Mine would increase by $1,000 per 100 tons of salt for additional handling and transportation costs. For example, orders from the International Mine would have a total cost of $16,000 per 100 tons of salt, if delivered to a shed in the North Quadrant, South Quadrant, or West Quadrant. Orders from the Louisiana Mine would have a total cost of $11,000 per 100 tons of salt for delivery to these quadrants. If these additional sheds in the North, South, and West Quadrants are constructed the application costs are also impacted. The application costs are $1,000 per 1,000 tons of salt applied per month for roads in the same quadrant as a storage shed. The application costs are $1,500 per 1,000 tons of salt applied per month for roads in a different quadrant. These costs are on a per month basis up to 5 inches of snowfall. The cost increases by $500 per 1,000 tons of salt that is applied to the same quadrant as the storage shed and $750 per 1,000 tons of salt that is applied to a different quadrant then where the storage shed is located for every 5 inches of snow per month. These costs incorporate personnel wages, fuel, and vehicle maintenance costs. The outbound supply chain costs have been consolidated at Exhibit 6. Supply Chain Network Design Optimization Sarah's objective is for the DPW to meet the demand for road salt depending upon the snowfall, while minimizing costs and ensuring road safety for the citizens of Winterland. This requires optimization of multiple factors in the supply chain. Sarah needs to determine accurate and defensible costs in preparation for her budget meeting. Additionally, the people of Winterland are relying on the DPW's efforts to keep their roadways safe during the winter season...and winter is coming. Task 1: Draw the supply chain options Map nodes and links Incorporate the lead time and snowfall variability, cost, and capacity of the options to develop a strategy Task 2: Determine the optimal inbound supply chain From suppliers to Winterland's storage shed Build an Excel-based model to assess the options that incorporates service level, supplier selection, road salt order quantity, and timing of road salt orders Task 3: Determine the optimal outbound supply chain From Winterland's one storage shed to its roads From Winterland's four storage sheds to its roads Extend the Excel model Road Salt Winterization 6 of 10 HKS Case 2185.0 Month Exhibit 1 - Winterland Snowfall Average Snowfall in inches 0 October November 1.6 December 10 January 14.2 February 11.5 March 8.7 April May June NOO 2.2 0 Mild Snowfall in inches 0 1 3.2 4.1 3.6 2.1 HOO 1 0 Severe Snowfall in inches 0 0 8.2 30 34.5 31.2 5.1 oo 0 0 Service Level High Standard Low None Service Level High Standard Low None Tons of salt per 1,000 miles of road treated per inch of snow 500 400 300 0 5 12 18 25 Road Salt Winterization Exhibit 3-Road Salt Service Levels Vehicle Accident Cost to Winterland - $800 per accident Vehicle Accident Cost to Private Sector - $1000 per accident Deaths per month with mild snow (December to March) Vehicle Accidents per month with mild snow (December to March) 500 1,200 1,800 2,500 Vehicle Accidents per month with average snow (December to March) 10 15 25 50 1,000 1,500 2,500 5,000 Deaths per month with average snow (December to March) Deaths per month with severe snow (December to March) 12 30 40 75 9 of 10 Vehicle Accidents per month with severe snow (December to March) 1,200 3,000 4,000 7,500 HKS Case 2185.0 Initial Inventory in tons of Salt 50,000 Mine International Louisiana New York Storage Sheds 1 in East Quadrant Road Salt Winterization 75,000 100,000 4-1 in North, 1 in East, 1 in West, and 1 in South Quadrant Exhibit 4 - Inventory Parameters Storage Capacity in tons of Salt Maximum Salt Received per month in tons 85,000 Order Capacity per Winter Season Unlimited Exhibit 5 - Road Salt Mine Sources Cost per 100 tons of Salt with 1 Storage Shed $15,000 $10,000 $7,000 180,000 Costs per 1,000 tons of Salt per month up to 5 inches of Snow Exhibit 6 - Road Salt Application Costs Costs per 1,000 tons of Salt per month for 5.1-10 inches of Snow $500 in South and East Quadrants $750 in North and West Quadrants $500 in same Quadrant $750 in different Quadrant $1,000 in South and East Quadrants $2,000 in North and West Quadrants $1,000 in same Quadrant $1,500 in different Quadrant Cost per 100 tons of Salt with 4 Storage Sheds $16,000 $11,000 $7,000 10 of 10 Storage Cost per month per 1,000 tons of Salt $100 Order Transaction Cost $2,000 $1,000 $1,000 Costs per 1,000 tons of Salt per month for 10.1-15 inches of Snow $500 in South and East Quadrants $750 in North and West Quadrants $500 in same Quadrant $750 in different Quadrant Lead Time 2 months 1 month 1 month Construction Costs $0 $300,000 HKS Case 2185.0 #3) (27 marks) Using the information and the data provided in the case and on the supplementary Excel spreadsheet that is available, develop a multi period linear programming (LP) formulation to deal with an optimization problem of your choice relevant to the case. (The scope of the chosen problem does not have to incorporate the entire set of data provided in the text and / or in the Excel supplement. However, the scope should be coherent, using part, not all, of the information and data provided in the case and / or in the Excel supplement.) Do not solve the formulated problem. a) Provide the assumptions involved in the LP formulation. b) Define (in mathematical notation and in words) the decision variables. c) Define (in mathematical notation and in words) the parameters involved in the objective function and the constraints. d) Write the LP formulation in its entirety using the relevant parameter values provided in the case. (i.e., Do not write CX. Instead, provide the value for C from the case.) HARVARD Kennedy School JOHN F. KENNEDY SCHOOL OF GOVERNMENT Designing and Optimizing a Supply Chain: Keeping Drivers Safe in the Winter ROAD SALT HTT DS "No Bob, praying for climate change cannot be our only strategy!" HKS Case KS1325 June 30, 2020 Ome_me_cartoon Road Salt Overview On average in the United States 17 million tons of salt is applied to roads during the winter. The salt used on roads is often called rock salt, because its grains are much coarser than table salt, but it is still the same molecule-sodium chloride. Salt is applied to roadways to lower the freezing point by 10 to 15 degrees, inhibiting ice from forming on roads until the temperature is well below freezing.3 Most rock salt for roads is mined "dry" from underground seams of crystal salt, which formed from the evaporation of ancient seas.4 Miners follow shafts underground and break out slabs of salt with dynamite and powered shoveling machines. Trucks or conveyors haul the salt to crushing machines. Supply Chain Challenges Salt itself is a very abundant resource, but, in 2015, much of the United States was not able to acquire the quantity it needed to properly winterize roads. The "perfect storm" was the culmination of issues including worker strikes, salt mine closures, and transportation issues. One of the major salt mines suffered major shortages from a 12-week worker strike, while another mine struggled with replenishing its stock due to a water leak.5 This caused cities across the United States to resort to importing salt supplies from other countries. Imported salt also faced challenges. First, there was a shortage of shipping vessels. Second, when the imported product arrived in port, it was often delayed at customs and wasn't able to get to its final destination in time. Furthermore, transportation costs on the imported salt were 10-15 percent higher than domestic product. Moving domestic salt was also problematic. Much of the country experienced a deep freeze which meant frozen waterways. The Illinois Waterway was closed for repairs, causing shipping delays and increased costs. This in turn meant barges were unable to move excess supplies from one region to another that desperately needed it. The Mississippi River also faced major issues because of this extreme deep freeze and heavier than normal snowfall, which caused two-month delays in shipping, plus barge and diesel shortages. To top that off, many areas of the Midwest and Northeast saw record snow and ice levels-they simply needed more salt than normal or expected. Any one of these issues would impact the availability of salt but to have all of these issues happening at once caused major disruptions, chaos, and higher prices. Winterland's Road Salt Dilemma Winterland is a county that encompasses a major metropolitan city located in the Northeast United States. Sarah has lived in Winterland most of her life and was recently hired into her dream job of overseeing Operations and Maintenance for Winterland's Department of Public Works (DPW). Sarah is replacing Don, who held the position of Operations and Maintenance Chief in the DPW for over 20 years. Don was incredibly knowledgeable of all Operations and Maintenance activities, but passed little records onto Sarah. Not only is Sarah an incredibly hard worker, but she realizes that the services provided to the residents of Winterland are vital. Sarah would like her transition to be seamless, especially when it comes to road safety during the winter season. Additionally, Sarah is entering her position under great financial strain due to the COVID-19 pandemic. The county of Winterland is reexamining its budget to minimize costs, while optimizing the services it provides to its residents. Sarah would like to propose a budget for road salt during the next budget meeting that incorporates both the inbound supply chain and outbound supply chain costs. The budget should also examine service levels provided to Winterland's citizens as the safety of citizens is critical to their wellbeing. Sarah has conducted a fair amount of benchmarking research to determine best practices for neighboring counties in the Northeast United States. Sarah also understands that there are some environmental concerns with road salt and has conducted research on various alternatives. She is planning on proposing more environmentally friendly options in two to five years, but has decided to use road salt during this winter until a fully formalized plan for alternatives is established. Winterland's Snowfall Sarah is trying to determine a road salt strategy for Winterland's DPW to winterize roads for the upcoming winter season. The average snowfall for Winterland is outlined in the chart at Exhibit 1. There is variability to account for in snowfall as the 2015 season was incredibly severe with almost 109 inches that year, but only 15 inches of snow fell during the 2020 season. As a result, some winters have been mild with considerably less snowfall than average and other winters have been severe with considerably more snowfall than average. There is a 25% chance of a mild snowfall, 50% chance of an average snowfall, and 25% chance of a severe snowfall this upcoming winter. Winterland's Roads Winterland consists of 11,000 miles of road that need to be treated with road salt. A map of Winterland's quadrants can be found at Exhibit 2. The North Quadrant of Winterland has 2,000 miles of road, the West Quadrant has 1,000 miles of road, the South Quadrant has 3,500 miles of road, and the East Quadrant has 4,500 miles of road. All of Winterland must be treated to the same service level for the duration of the winter season. A standard service level requires 400 tons of salt per 1,000 miles of road treated per inch of snow. For example, if 2 inches of snow fell in Winterland, 8,800 tons of salt would comprise a standard application. A low service level application requires 300 tons of salt per 1,000 miles of road treated per inch of snow. For Winterland, a low service level application would require 6,600 tons of salt, if 2 inches of snow fell. A