David is an UPS package packer. There are three types of packages: basic package

Question

David is an UPS package packer. There are three types of packages: basic packages, business packages, and oversized packages. Business packages take priority over basic packages and oversized packages because those customers paid a premium to have a two?day delivery.   David has a 9?hour shift. On average, every three hours he receives on one container of packages. Each container has a variety of basic, business, and oversized packages. As soon as David processes a package, he passes it to the next employee, who loads it onto a truck. The times it takes him to process the three different types of packages and the average number of packages per container are shown in the table below. Basic Business Oversized Time to label and package each unit 5 min 4 min 6 min Avg # of units per container 10 10 5 David currently processes packages from each container as follows. First, he processes all business packages in the container. Then he randomly selects either basic packages or oversized packages for processing until the container is empty. However, his manager suggested a different sequencing: business packages first, basic packages second, and the oversized packages last. UPS1. What is the utilization of David? If David follows his supervisor’s advice, what will happen to his utilization?   UPS2. If David follows his supervisor’s advice, what will happen to the average time that a package spends in the container?

David is an UPS package packer. There are three types of packages: basic packages, business packages, and oversized packages. Business packages take priority over basic packages and oversized packages because those customers paid a premium to have a two-day delivery David has a 9-hour shift. On average, every three hours he receives on one container of packages. Each container has a variety of basic, business, and oversized packages. As soon as David processes a package, he passes it to the next employee, who loads it onto a truck. The times it takes him to process the three different types of packages and the average number of packages per container are shown in the table below Basic Business Oversized Time to label and 5 min 4 min 6 min package each unit Avg # of units per container 10 10 David currently processes packages from each container as follows. First, he processes all business packages in the container. Then he randomly selects either basic packages or oversized packages for processing until the container is empty. However, his manager suggested a different sequencing: business packages first, basic packages second, and the oversized packages last. UPS1. What is the utilization of David? If David follows his supervisor's advice, what will happen to his utilization? UPS2. If David follows his supervisor's advice, what will happen to the average time that a package spends in the container?

Explanation / Answer

a) One container of packages is received every three hours. Therefore, available time = 3 hours

Work load = 10 units * 5 minute + 10 units * 4 minutes + 5 units * 6 minutes = 120 minutes or 2 hours

David's utilization = Work load / Available time = 2 hours / 3 hours = 0.67

Following his supervisor's advice, the utilization remains same.

b) Following his supervisor's advice, it takes 40 minutes (=10*4) to pack business packages first. the first unit being packed, spends 4 minutes, second minute 8 minutes and the time in system increases linearly, 10th unit spends 10*4 = 40 minutes in system. So average time spent by business packages is average of Minimum time spent by a unit and Maximum time spent by a unit = 40+4)/2 = 22 minutes

All this while, Basic and Oversized packages are waiting to be packed. So first unit of basic package spends 40+5 = 45 minutes in the system and so on the 10th unit spends 40+10*5 = 90 minutes in the system, so average time spent by a unit in system = (45+90)/2 = 67.5 minutes

All this while, Oversized packages are waiting to be packed. So first unit of oversize package spends 90+6 = 96 minutes in the system and so on the 5th unit spends 90+5*6 = 120 minutes in the system, so average time spent by a unit in system = (96+120)/2 = 108 minutes

Overall average time spent by a unit in system = (22*10 + 67.5*10 + 108*5)/(10+10+5) = 57.4 minutes

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