The Winterland DPW can purchase road salt from three different mines. Salt from any of these...

Transcribed Image Text:

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.) 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.)

Answer rating: 100% (QA)

Here is a multiperiod linear programming formulation to optimize the inbound supply chain for road s... View the full answer