Disappearing Ice
I'm reviewing the last topic for my Management Science Final for tomorrow...which I don't quite understand since we only spent two lectures on it and no lab. Anyway, it's called congestion management (how interesting, eh?!)
It's ermmm, as dry as the ice we're studying.
Here's a problem I'm thinking on how to solve:
Aqua Fria Ltd. (AFI) is a manufacturer and wholesaler of packaged party ice. A special machine freezes ice in AFI's Nanton, Alberta plant and crushes it into small chunks. As the ice emerges from the machine a human bagger measures and bags the ice into ten-pound bags. Cole Waters, the company's production manager was going over some figures one frosty Alberta morning when he noticed that the weight of ice shipments the previous month was only 90% of the weight of the purified water used in the machine. Some loss was to be expected but a 10% loss was alarming. He hurried down to the production floor. The machine was operating at its usual setting of 1200 pounds per hour. Ice sporadically spilled out of the machine onto a bagging platform, which could hold 40 pounds of ice. There it was scooped up into bags by the bagger. Both the machine and the bagger varied in the time it took to do their tasks. It appeared that the bagging platform was filling up with ice according to a memoryless arrival process. The time it took the bagger seemed to follow an exponential distribution. On average the bagger could fill 160 ten-pound bags per hour. Cole went back to his office and opened up the waiting line analysis template he had remembered using in his B.Comm. program and set about to model his problem as a waiting line with each ten-pound bag of ice being a customer and the bagger as the server. Using an arrival rate (out of the machine) of 120 bags per hour (or 2 per minute) and a service rate 160 per hour (2.67 per minute), he ran an M/M/s model with 1 server. He got the result that on average, ice was on the bagging platform for only 1.5 min. (W=1.5) so this ruled out melting as a source of the loss. Was someone stealing the ice? Can you help Cole find the disappearing ice?
(Taken from Management Science 352 Course at the University of Alberta)
Anyone any guesses how to solve it? Thiefs or what??
It's ermmm, as dry as the ice we're studying.
Here's a problem I'm thinking on how to solve:
Aqua Fria Ltd. (AFI) is a manufacturer and wholesaler of packaged party ice. A special machine freezes ice in AFI's Nanton, Alberta plant and crushes it into small chunks. As the ice emerges from the machine a human bagger measures and bags the ice into ten-pound bags. Cole Waters, the company's production manager was going over some figures one frosty Alberta morning when he noticed that the weight of ice shipments the previous month was only 90% of the weight of the purified water used in the machine. Some loss was to be expected but a 10% loss was alarming. He hurried down to the production floor. The machine was operating at its usual setting of 1200 pounds per hour. Ice sporadically spilled out of the machine onto a bagging platform, which could hold 40 pounds of ice. There it was scooped up into bags by the bagger. Both the machine and the bagger varied in the time it took to do their tasks. It appeared that the bagging platform was filling up with ice according to a memoryless arrival process. The time it took the bagger seemed to follow an exponential distribution. On average the bagger could fill 160 ten-pound bags per hour. Cole went back to his office and opened up the waiting line analysis template he had remembered using in his B.Comm. program and set about to model his problem as a waiting line with each ten-pound bag of ice being a customer and the bagger as the server. Using an arrival rate (out of the machine) of 120 bags per hour (or 2 per minute) and a service rate 160 per hour (2.67 per minute), he ran an M/M/s model with 1 server. He got the result that on average, ice was on the bagging platform for only 1.5 min. (W=1.5) so this ruled out melting as a source of the loss. Was someone stealing the ice? Can you help Cole find the disappearing ice?
(Taken from Management Science 352 Course at the University of Alberta)
Anyone any guesses how to solve it? Thiefs or what??
posted by Grace at 12/12/2005 10:36:00 PM
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