IE 1055 2025 Homework 12 Not to be turned in 1 Problem 7 2 from the text Let denote the arrival rate of trucks and denote the service rate at the docks Since arrivals occur at a Poisson rate and service times are exponentially distributed the problem is of the class M M c GD The problem reduces to determining the smallest value of c number of docks such that the average time trucks spend in the system W is less than 50 minutes The relationship between W and the expected number of trucks in the system L is given by L W Hence since it is desired that W 50 60 hr then it is desired that L 50 60 Since 20 8 or 2 5 trucks per hour then the problem reduces to determining the smallest value of c such that L 2 0833 From figure 10 63 we can determine the value of c The utilization factor is given by c With 60 40 1 5 trucks per hour we find that for c equal to 3 2 5 3 1 5 0 5556 from Figure 10 63 L 2 0833 For c 2 0 8333 and from Figure 10 63 L 2 0833 Therefore 3 docks are required to ensure that the average amount of time spent waiting and being loaded or unloaded is less than 50 minutes 2 Problem 7 7 from the text Increases in the length of trucks imply that more space will be needed to maneuver trucks around shipping and receiving docks Furthermore certain access roads about the plant warehouse may need to be modified to better accommodate longer trucks trailers Increases in both width and height of trucks and trailers imply that docks may have to be modified to accept taller and in many cases wider trucks and trailers Some of the changes can be handled by using permanent adjustable dock leveling equipment whose dynamic ranges can accept taller or wider trucks Redesigning the dock area as well as the inside of the shipping and receiving areas may nevertheless be required should the width and height of the new vehicles fall outside of the current equipment s dynamic ranges Thus one would want to provide additional space at the docks in anticipation of future changes in truck sizes 3 Problem 7 11 from the text By stock assignment planning I mean how do you decide which items to store in which locations in the warehouse a Simple ranking of SKUs based on the ratio of pick frequency the number of times a SKU is requested to shipped cube the product of unit demand and unit cube establishes a baseline for intelligent stock assignment planning SKUs with high rankings should be assigned to the most accessible locations b A distribution illustrating SKUs ranked by popularity and the portion of total picking activity they represent in the ABC or Pareto plot used in intelligent stock THIS SOLUTION MAY ONLY BE USED FOR IE 1055 2025 SPRING 2017 assignment planning More popular SKUs with the highest picking activity ought to be distributed closer to the input output point c Correlated stock assignment planning ranks SKUs by popularity as well as considering the correlations between various items in storage Correlations mean items that are often picked together such as salt and pepper A small picking zone dedicated to high density high throughput order picking is used for SKUs with high correlations THIS SOLUTION MAY ONLY BE USED FOR IE 1055 2025 SPRING 2017