Name: ______________________ Homework 8 Please write the steps that led you to your answer in detail. Full points will be given to those that provide the correct intermediary steps and the answers. An oversea manufacturer, Taoci King (TK), is scheduling its production of 400 porcelain tea sets for its U.S. retailer, Porcelain Queen (PQ). According to their contract, this batch of tea sets need to be delivered to PQs shipping dock located at Qingdao Port before Nov 1st 00:00am for Thanksgiving / Christmas selling season. In the case of late delivery, PQ will charge TK $1,000 per day as penalty. For example, if TK delivers on Nov 2rd noon, PQ will charge $1,000*1.5=$1,500 as penalty. TK does not know exactly how long it would take to product this batch of 400 tea sets due to yield uncertainty. Therefore, TK is trying to utilize historical data to estimate its production time. The historical production times for batches of similar tea sets are shown in Table 1 in Q4. Since these are similar tea sets, the average per-unit product time and the yield rate will be similar for this upcoming batch. PQ will pay TK immediately by cash on Nov 1st 00:00am or on delivery, whichever is later: Even if TK delivers on Oct 30th 00:00am, TK still needs to wait until Nov 1st 00:00am to get the payment. If TK delivers on Nov 2nd noon, however, the payment will be made on Nov 2nd noon. TK is relying on bank loan to start its production, which incurs $400 daily interest once the production starts and until paid using payment from PQ. For example, if TK starts production on Oct 30th noon and delivers on Nov 2nd 00:00am, TK pays $400/day*2.5days = $1000 interest to the bank. Please help TK to determine when to start the production. Hint: Apply newsvendor model for this problem. Consider order quantity as the time between starting the production and Nov 1st 00:00am, and demand as the actual production time for this batch.Name: ______________________ Q1 If order quantity turns out to be larger than demand (i.e., TK finishes its production before Nov 1st 00:00am), how much it could have saved by ordering one unit less (i.e., by starting its production one day later)? This is the overage cost. Answer : __________________________ Q2 Following similar idea as in Q1, how much is the underage cost? Answer : __________________________ Q3 What is the critical fractile? Enter a number with two digits after decimal. Answer : __________________________Name: ______________________ Q4 Come up with the demand distribution (i.e., a distribution for the production time) using the historical data. Follow the steps below, and fill the blanks in Table 1 and Table 2. For each of the historical batches, compute its average production time per tea set. Multiple those per-unit production times by 400 these are the product times if the batch quantity was 400. Copy the production time in the last column of Table 1 to the first column of Table 2, but in ascending order. Use Table 2 to get the demand distribution.

Q5 TK should start its production on Oct ____________. Enter an integer number in the blank, and justify your answer.

Table 1 Table 2 Table 1 Table 2