3. A production system consists of two workstations operating in series, with Station 1 feeding Station 2 as shown in the figure below. Each station consists of an incoming queue of work, the machine itself, and an outgoing inventory point where completed parts are stored while waiting for transfer to the next station. The two stations are linked by a kanban system where each production kanban corresponds to twenty parts. The line faces a demand that is Normally distributed with a mean of 200 parts per hour and a standard deviation of 50 units. Any missed demands can be backlogged. Station 1 Lead Time = 2 hours Station 2 Lead Time = 2 hours Machine 1 Machine 2 2.64 Incoming queue Incoming queue Outgoing inventory a. Compute the mean and standard deviation of the lead time demand faced by Station 2. b. Compute the number of kanban at each station using the deterministic (average-based) approach with a safety factor of a=0.1. Estimate the stockout probability at each station if this number of kanbans is used, treating each station independently of the other. c. Compute the number of kanban required at each station to ensure a stockout probability of less that 10% at each of the outgoing inventory points. d. Now suppose we operate the entire line as a CONWIP system, where all material in the line including the outgoing inventory at Station 2 are counted as part of the WIP. In other words, a new part can enter the line only when a demand occurs and a part is removed from the outgoing inventory point of Station 2. Compute the WIP level that will ensure a stockout probability no greater than 10%. e. Compare the total material in the line (queue for Station 1 through outgoing inventory for Station 2) you obtained in parts b and c and explain the difference. 3. A production system consists of two workstations operating in series, with Station 1 feeding Station 2 as shown in the figure below. Each station consists of an incoming queue of work, the machine itself, and an outgoing inventory point where completed parts are stored while waiting for transfer to the next station. The two stations are linked by a kanban system where each production kanban corresponds to twenty parts. The line faces a demand that is Normally distributed with a mean of 200 parts per hour and a standard deviation of 50 units. Any missed demands can be backlogged. Station 1 Lead Time = 2 hours Station 2 Lead Time = 2 hours Machine 1 Machine 2 2.64 Incoming queue Incoming queue Outgoing inventory a. Compute the mean and standard deviation of the lead time demand faced by Station 2. b. Compute the number of kanban at each station using the deterministic (average-based) approach with a safety factor of a=0.1. Estimate the stockout probability at each station if this number of kanbans is used, treating each station independently of the other. c. Compute the number of kanban required at each station to ensure a stockout probability of less that 10% at each of the outgoing inventory points. d. Now suppose we operate the entire line as a CONWIP system, where all material in the line including the outgoing inventory at Station 2 are counted as part of the WIP. In other words, a new part can enter the line only when a demand occurs and a part is removed from the outgoing inventory point of Station 2. Compute the WIP level that will ensure a stockout probability no greater than 10%. e. Compare the total material in the line (queue for Station 1 through outgoing inventory for Station 2) you obtained in parts b and c and explain the difference