THIS SOLUTION MAY ONLY BE USED FOR IE 1055/2025 SPRING 2017 IE 1055/2025 Homework 1 Due January 11, 2017 Read Chapters 1 and 2 1. Email your picture. 2. Superior testing is a company that manufactures testing equipment used to test asphalt and metal specimens. Superior has a 30,000 square foot facility and does fabrication work such as shearing, welding and machining in addition to assembly of their test devices. Thus, they receive some raw materials such as bar stock and sheet steel that they process in addition to electrical components and other parts that they assemble. They ship approximately 40 units per month, have a work force of about 75, and annual revenues of approximately $18 million. Given this brief background, list and discuss possible layout objectives for Superior. (13 pts) Answer (13 pts) Superior facility objectives: - Given that it is a manufacturing facility the facility objectives are largely dominated by flow and material movement issues. So it will be important to understand the processes required and how they impact material flow. - Facilitate the flow of material. Consider the movement of the raw material, WIP and finished products. Design a streamlined production line, such as a U shaped or S shaped line. - Optimize storage of material - consider the size and amount of raw material, WIP and finished products in order to design the storage and inventory space. - Consider the machine size and the possibility of multiplying machines to balance the workload of the line. - To promote effective space utilization consider combining the receiving and shipping docks together, especially considering the shipping amount per month is not large. - Regarding the workforce of 75, they need to have sufficient restrooms, lockers, lunch areas, etc.THIS SOLUTION MAY ONLY BE USED FOR IE 1055/2025 SPRING 2017 3. If you were in charge of redesigning Benedum Hall what personnel would you want to have as members of your redesign team? Why? What personnel would you want to solicit information from concerning how Benedum Hall is used? (13 pts) Answer (13 pts) Representatives from the following groups: - Undergraduate and graduate students: since they are the ones who will be affected most by the redesign. Their needs represent the primary purposes of the redesign. They also may give some new ideas. They may also point out the possible problems with the current layout. - Faculty: the same reasons as the students. - Staff including custodians and librarians: custodians and the libraries are the third group using the building so the same points with the first two groups. - Dean’s office and financial departments: without the consent of the finance department, none of the proposed changes can be achieved so they should participate in the decisions. - Industrial engineer or facilities planner: the efficiency of the layout should be evaluated by a professional and experience is helpful in designing new layouts. - Facilities management: they would be involved in actually making changes to the layout. They may also have useful input on design issues. 3. Suppose you work at the Wesco distribution center in Cranberry and you are the Industrial Engineer in charge of operations. You need to decide how many shelving unit storage locations to allocate to an electronic switchbox. The switchbox comes in a cardboard carton and you can fit 10 of these cartons onto one shelving unit. Currently shipments arrive following a Normal distribution with a mean of 80 cartons per month and a standard deviation of 7 cartons per month. Assume that the switchboxes arrive during the first week of the month and then are shipped out during the last three weeks of the month. a. How many shelving units do you need to allocate to switchboxes to be 98% certain that you can store all the switchboxes that arrive during one month? Comment on your answer. (6 pts) b. What is the probability that more than 88 cartons arrive during the first month? (6pts) c. What is the probability that more than 88 cartons arrive in at least 5 of the next 6 months? (6 pts) d. What is the likelihood that more than 510 switchboxes arrive over a six month period? (6 pts)THIS SOLUTION MAY ONLY BE USED FOR IE 1055/2025 SPRING 2017 Answer (24 pts) a) (6 pts) You need to find the 98th percentile of the distribution. Z.02 = 2.054, thus the value is 80 + 2.054*7 = 94.4. This means you need 10 shelving units. But 10 shelving units will actually give you enough shelving to cover much more than the 98th percentile. In fact, it will cover the 99.7th percentile 0017099830192862178051005100 ..).().().( XPXP Note that we used 100.5 because we needed a continuity correction since the number of cartons is discrete and the Normal distribution is continuous. b) (6 pts) The probability that more than 88 cartons arrive in one day is 112088801214311780588588 ..).().().( XPXP Or use Excel function a. NORMDIST(88.5,88,7,TRUE) =1- 0.888 = 0.112 Note that we used 88.5 because we needed a continuity correction since the number of cartons is discrete and the Normal distribution is continuous. c) (6 pts) What is the probability that more than 88 cartons arrive in at least 5 of the next 6 months? The probability that more than 88 cartons arrive in at least 5 of the next 6 months is 0000959.00000197.000094.)5(00000197.0)112.0(*1)1(66000094.0888.0*)112.0(*6)1(56606515atleastPppPppP Or use Excel function 1-BINOMDIST(4, 6 , 0.112,TRUE) = .0000959 d) (6 pts) Calculate the probability of 510 cartons arriving over 6 months Let Y denote the number of cartons arriving over 6 months. Then, 654321XXXXXXY assuming theiXare iid random variables Therefore )*,*(~276806NY, i.e. ).,(~214617480NY 0380962017788111461748055105510510 ..).()..().()( YPYPYP 1- NORMDIST(510.5,480, 17.146,TRUE) =1-0.962 =