Can someone help me to model this in Arena? At least map it out

CONTEST PROBLEM 10 IE/RA Contest Problems Tenth Annual Contest: SM Paints SM Paints produces a line of house paints at manufacturing facilities in four North American locations. The finished products are shipped to various distribution centers that carry the company's inventory. This inventory is then used to replenish depleted stock at the company's retail stores. We recently embarked on a lean initiative with a cost-reducing objective of lowering the inventory in the distribution centers while still meeting the requirements of the retail stores. A study revealed that significant cost reductions could be achieved if our manufacturing plants could fill orders for the distribution centers in three working days or less. Currently none of our manufacturing plants are able to meet this three-day delivery requirement consistently. In addition, it is not clear what improvements would be neces- sary in order to remedy this situation. Due to this uncertainty, we are asking you to make some recommendations based on an analysis of a single manufacturing facility. You are asked to evaluate the current system and propose in minimizing operating cost while still achieving the desired performance levels. Al- though it would be desirable to fill all orders in three working days, it is understood that any facility can occasionally be overloaded. With this in mind we would like to achieve a performance level of filling 98% of all orders in the three working days. This document describes the current system and provides data and costs where they are available. modifications that will result The manufacture of paint at this plant is a relatively simple four-step process. It starts by combining the various components and pigments with a base liquid at the mix and grind tanks. The components are first ground together and then mixed in a relatively small tank that looks somewhat like a kitchen mixer. Once this step of the process is complete, the resulting mixture is pumped to a thinning tank where the remaining liquid is added. The thin tanks also have mixers that assure that the resulting paint is homog. enous. After thinning., the mixture is transferred to a hold tank where the paint remains until a fill line becomes available. Once the filling process is complete, the resulting fin ished product is sent to shipping. A high-level view of this flow is shown below. Mbx and Grind Thin Hold Fill The manufacturing facility under study runs 24 hours a day, seven days a week, with new orders being released once each day. The number of new orders averages about 23 per day and appears to follow a Poisson distribution. New orders are classified according to the order batch size as small, medium, or large (in gallons). The small batches make up 10% of the orders. The medium batches make up 35%, and the large batches make up the remaining 55% of the orders. The composition of each of these batches is given in the table below (e.g., 40% of the medium batches are orders for 6,000 gallons). Small Batches Percent Size (gal.) Medium Batches Percent Size (gal.) 4,000 15 The product for each order can be packaged as quarts, gallons, or five-gallon buckets. A single order may require one package type (all gallons), two, or all three types. All orders include a percentage of gallon-size fill. Of the total orders, 75% require quarts and 40% require buckets. If quarts are required for an order, that portion of the order varies from 10% to 40% by volume. If buckets are required, that portion of the order varies from 5% to 20% by volume. The remainder of the order is packaged as gallons. There are seven identical mix and grind machines available. The time required to complete this operation follows a triangular distribution with parameters 1.5, 2.4, and 3.5 (hours). Note that the facility currently only operates the mix and grind system for 16 hours per day. Upon completion of this first operation, the resulting liquid is transferred to an available thin tank, but this transfer can only occur if a thin tank of the proper size is available. There are nine thin tanks of differing sizes in the facility. The number and ca- pacity (in gallons) of the nine thin tanks are shown in the following table Number of Thin Tanks Capacity (gallons) 6,000 0,000 14,000 20,000 Allocation of product to the thin tanks is controlled by batch size, with the larger tanks being reserved for larger batch sizes. For example, orders for batches of 6,000 gallons or fewer can only be transferred to the two 6,000-gallon or the two 10,000-gallon tanks. The table below shows the allowable allocation by batch size to the various thin tanks. Note that the 12,000- to 14,000-gallon batch sizes can only use two of the three large 20,000-gallon thin tanks. Batch Size (gallons) 1,000 to 6,000 8,000 to 10,000 12,000 to 14,000 16,000 to 20,000 Thin Tanks (capacity in gallons) 6,000 or 10,000 10,000 or 14,000 14,000 and two of the three 20,000 20,000 Once a thin tank is available, the transfer time follows a triangular distribution with parameters of 20, 35, and 45 minutes. This transfer time is independent of the batch size. After the transfer is complete, the now-empty mix and grind machine requires a cleaning cycle before the next batch can be started. This follows a uniform distribution with parameters of 18, 24 minutes. The thinning operation consists of adding additional liquid to the product from the mix and grind operation. The time to complete this operation is dependent upon the batch size of the order since the liquid is added at a rate of 175 gallons per minute. The opera- tion is complete, the batch is transferred to an available hold tank. The transfer rate is 195 gallons per minute. There are 10 hold tanks in this facility, with capacities shown below. batch is mixed at the same time that the liquid is being added. Once the thinning Number of Hold Tanks Capacity (gallons) 8,000 12,000 20,000 As was the case with the thin tanks, it is not desirable to use the larger tanks for the smaller batches. The table below shows what batch sizes can use the various hold tanks Batch Size (gallons) 1,000 to 8,000 8,000 to 12,000 12,000 to 20,000 Hold Tanks (capacity in gallons) 8,000 or two of the four 12,000 12,000 or one of the four 20,000 20,000 The batches are held in the hold tanks until the required fill lines become available. There are four quart lines, four gallon lines, and two bucket lines. The fill rates and clean times for these lines are shown below Line Fill Rate (gallons per minute) Quart Gallon Bucket Clean Time (minutes) 20 18 40 38 The fi a hold tank. Once that transfer is complete, the filling operation can start. If a batch requires all three filler types, the fillers do not all have to be available at the same time. For example, if only a gallon line is available, that part of the operation can be started. Once the other lines become available, those remaining portions of the operation can be started. The hold tank is only made available to the next batch when all of the filling operations for an order are complete. lling process is not allowed to start until the entire batch has been transferred to The facility has been configured so that any mix and grind tank can be connected to any thin tank, any thin tank can be connected to any hold tank, and any hold tank can be connected to any filler. A quick examination of the production for the current system indicates that we are unable to meet the three-day performance target. Thus, the first question we would like you to address is: What changes would be required in order for the current system to meet the three-day performance level? Since several configurations are possible that might meet this level, we would like your recommendation to include the minimum investment required. Approximate upgrade costs are given below .Mix and grind tank $600,000 per tank Thin tank . Fixed cost of $1,200,000 per tank Variable cost of $40,000 per 1,000 gallons of tank capacity Hold tank - Fixed cost of $900,000 per tank . Variable cost of $30,000 per 1,000 gallons of tank capacity Quart line $1,200,000 per line $1,400,000 per line $400,000 per line Gallon line Bucket line These costs include both equipment and installation costs. In addition, a third shift could be added to the existing mix and grind area at a cost of $800 per day Furthermore, we are considering accepting a request by a nationwide chain of home improvement stores to produce paint that would be marketed under their private label. This paint would be produced in same the facility, and we expect that this would require the production of an average of three additional orders or batches per day. The estimated mix of batch sizes is shown below Private Label Batches Percent 25 45 30 Size 10,000 15,000 20,000 We estimate that this would yield an additional income of S50,000 per day. If we agree to a contract to produce these private-label orders, we would need to be In summary, your analysis and recommendations should address the following . Scenario 1: What changes in the current system would be required to meet the sure that we could ship 95% of them within five working days. questions three-day performance level? What is the cost? Scenario 2: If we invest in the changes to meet the three-day performance level, what additional changes would be necessary to meet the additional production requirements of the private-label contract? Does this scenario make economic sense? Scenario 3: If we decide NOT to invest in changes to meet the three-day perfor- mance level, what changes in the current system would be required to meet the existing and private-label production requirements? Does this scenario make eco- nomic sense? . . Please provide all cost comparisons in dollars per week. CONTEST PROBLEM 10 IE/RA Contest Problems Tenth Annual Contest: SM Paints SM Paints produces a line of house paints at manufacturing facilities in four North American locations. The finished products are shipped to various distribution centers that carry the company's inventory. This inventory is then used to replenish depleted stock at the company's retail stores. We recently embarked on a lean initiative with a cost-reducing objective of lowering the inventory in the distribution centers while still meeting the requirements of the retail stores. A study revealed that significant cost reductions could be achieved if our manufacturing plants could fill orders for the distribution centers in three working days or less. Currently none of our manufacturing plants are able to meet this three-day delivery requirement consistently. In addition, it is not clear what improvements would be neces- sary in order to remedy this situation. Due to this uncertainty, we are asking you to make some recommendations based on an analysis of a single manufacturing facility. You are asked to evaluate the current system and propose in minimizing operating cost while still achieving the desired performance levels. Al- though it would be desirable to fill all orders in three working days, it is understood that any facility can occasionally be overloaded. With this in mind we would like to achieve a performance level of filling 98% of all orders in the three working days. This document describes the current system and provides data and costs where they are available. modifications that will result The manufacture of paint at this plant is a relatively simple four-step process. It starts by combining the various components and pigments with a base liquid at the mix and grind tanks. The components are first ground together and then mixed in a relatively small tank that looks somewhat like a kitchen mixer. Once this step of the process is complete, the resulting mixture is pumped to a thinning tank where the remaining liquid is added. The thin tanks also have mixers that assure that the resulting paint is homog. enous. After thinning., the mixture is transferred to a hold tank where the paint remains until a fill line becomes available. Once the filling process is complete, the resulting fin ished product is sent to shipping. A high-level view of this flow is shown below. Mbx and Grind Thin Hold Fill The manufacturing facility under study runs 24 hours a day, seven days a week, with new orders being released once each day. The number of new orders averages about 23 per day and appears to follow a Poisson distribution. New orders are classified according to the order batch size as small, medium, or large (in gallons). The small batches make up 10% of the orders. The medium batches make up 35%, and the large batches make up the remaining 55% of the orders. The composition of each of these batches is given in the table below (e.g., 40% of the medium batches are orders for 6,000 gallons). Small Batches Percent Size (gal.) Medium Batches Percent Size (gal.) 4,000 15 The product for each order can be packaged as quarts, gallons, or five-gallon buckets. A single order may require one package type (all gallons), two, or all three types. All orders include a percentage of gallon-size fill. Of the total orders, 75% require quarts and 40% require buckets. If quarts are required for an order, that portion of the order varies from 10% to 40% by volume. If buckets are required, that portion of the order varies from 5% to 20% by volume. The remainder of the order is packaged as gallons. There are seven identical mix and grind machines available. The time required to complete this operation follows a triangular distribution with parameters 1.5, 2.4, and 3.5 (hours). Note that the facility currently only operates the mix and grind system for 16 hours per day. Upon completion of this first operation, the resulting liquid is transferred to an available thin tank, but this transfer can only occur if a thin tank of the proper size is available. There are nine thin tanks of differing sizes in the facility. The number and ca- pacity (in gallons) of the nine thin tanks are shown in the following table Number of Thin Tanks Capacity (gallons) 6,000 0,000 14,000 20,000 Allocation of product to the thin tanks is controlled by batch size, with the larger tanks being reserved for larger batch sizes. For example, orders for batches of 6,000 gallons or fewer can only be transferred to the two 6,000-gallon or the two 10,000-gallon tanks. The table below shows the allowable allocation by batch size to the various thin tanks. Note that the 12,000- to 14,000-gallon batch sizes can only use two of the three large 20,000-gallon thin tanks. Batch Size (gallons) 1,000 to 6,000 8,000 to 10,000 12,000 to 14,000 16,000 to 20,000 Thin Tanks (capacity in gallons) 6,000 or 10,000 10,000 or 14,000 14,000 and two of the three 20,000 20,000 Once a thin tank is available, the transfer time follows a triangular distribution with parameters of 20, 35, and 45 minutes. This transfer time is independent of the batch size. After the transfer is complete, the now-empty mix and grind machine requires a cleaning cycle before the next batch can be started. This follows a uniform distribution with parameters of 18, 24 minutes. The thinning operation consists of adding additional liquid to the product from the mix and grind operation. The time to complete this operation is dependent upon the batch size of the order since the liquid is added at a rate of 175 gallons per minute. The opera- tion is complete, the batch is transferred to an available hold tank. The transfer rate is 195 gallons per minute. There are 10 hold tanks in this facility, with capacities shown below. batch is mixed at the same time that the liquid is being added. Once the thinning Number of Hold Tanks Capacity (gallons) 8,000 12,000 20,000 As was the case with the thin tanks, it is not desirable to use the larger tanks for the smaller batches. The table below shows what batch sizes can use the various hold tanks Batch Size (gallons) 1,000 to 8,000 8,000 to 12,000 12,000 to 20,000 Hold Tanks (capacity in gallons) 8,000 or two of the four 12,000 12,000 or one of the four 20,000 20,000 The batches are held in the hold tanks until the required fill lines become available. There are four quart lines, four gallon lines, and two bucket lines. The fill rates and clean times for these lines are shown below Line Fill Rate (gallons per minute) Quart Gallon Bucket Clean Time (minutes) 20 18 40 38 The fi a hold tank. Once that transfer is complete, the filling operation can start. If a batch requires all three filler types, the fillers do not all have to be available at the same time. For example, if only a gallon line is available, that part of the operation can be started. Once the other lines become available, those remaining portions of the operation can be started. The hold tank is only made available to the next batch when all of the filling operations for an order are complete. lling process is not allowed to start until the entire batch has been transferred to The facility has been configured so that any mix and grind tank can be connected to any thin tank, any thin tank can be connected to any hold tank, and any hold tank can be connected to any filler. A quick examination of the production for the current system indicates that we are unable to meet the three-day performance target. Thus, the first question we would like you to address is: What changes would be required in order for the current system to meet the three-day performance level? Since several configurations are possible that might meet this level, we would like your recommendation to include the minimum investment required. Approximate upgrade costs are given below .Mix and grind tank $600,000 per tank Thin tank . Fixed cost of $1,200,000 per tank Variable cost of $40,000 per 1,000 gallons of tank capacity Hold tank - Fixed cost of $900,000 per tank . Variable cost of $30,000 per 1,000 gallons of tank capacity Quart line $1,200,000 per line $1,400,000 per line $400,000 per line Gallon line Bucket line These costs include both equipment and installation costs. In addition, a third shift could be added to the existing mix and grind area at a cost of $800 per day Furthermore, we are considering accepting a request by a nationwide chain of home improvement stores to produce paint that would be marketed under their private label. This paint would be produced in same the facility, and we expect that this would require the production of an average of three additional orders or batches per day. The estimated mix of batch sizes is shown below Private Label Batches Percent 25 45 30 Size 10,000 15,000 20,000 We estimate that this would yield an additional income of S50,000 per day. If we agree to a contract to produce these private-label orders, we would need to be In summary, your analysis and recommendations should address the following . Scenario 1: What changes in the current system would be required to meet the sure that we could ship 95% of them within five working days. questions three-day performance level? What is the cost? Scenario 2: If we invest in the changes to meet the three-day performance level, what additional changes would be necessary to meet the additional production requirements of the private-label contract? Does this scenario make economic sense? Scenario 3: If we decide NOT to invest in changes to meet the three-day perfor- mance level, what changes in the current system would be required to meet the existing and private-label production requirements? Does this scenario make eco- nomic sense? . . Please provide all cost comparisons in dollars per week