1. Goodrice Company is importing a new variety of rice into Hong Kong. The sales data for ten weeks are given as follows in the unit of one thousand kg). Answer the following questions, Keep two decimal places for any values in your calculation. a. Using the trend adjusted exponential smoothing model, fill in the shaded blanks below, compute the overall at the end of period 10) ME, MAD, and MAPE. Also compute and plot the tracking signals over time in these ten periods. Comment on the forecasts. Trend Adjusted Exponential Smoothing Smoothing Constants: 0-0.4, 8-0.6 At Period Actual Ft Forecast Not Including Trend 200,00 Trend FIT Forecast Including Trend 300.00 1 310 100.00 406 304.00 02.40 406.40 3 525 4 578 5 673 6 735 7 773 8 820 9 837 10 872 ME = MAD- MAPE = Compute and plot the tracking signals over time in these ten weeks: Comment: b. Using the linear regression model, fill in the shaded blanks below, derive the linear relationship coefficients a and b, compute the standard error of the estimate, Syx. Forecast the demand for the 11th and 50th weeks, and comment on your forecast numbers. Least Square Linear Regression Period Demand Fitted Value X X? XY Y 1 310 1 2 406 4 3 525 9 4 578 16 5 673 25 6 735 36 7 773 49 8 820 64 9 837 81 10 872 100 Total: 55 6529 385 Mean: 5.5 652.9 38.5 a- b= Syx = Forecast for the 11th and 50th wecks: Comment: 2. The ABC Clothing is experiencing a general increase in sales over years. The company wants to develop a production plan for the next 6 months based on the following demand forecast: Period Total 1 Jan 5600 2 Feb 7100 3 Mar 5600 4 Apr 9500 5 May 9200 6 Jun 5700 Forecasted demand 42700 The company currently has 15 workers in its factory. In order to satisfy the production requirement, the company can vary its capacity by hiring or laying off workers, running overtime production, and using subcontractors. The following assumptions are made. a. Overtime is planned in integer number of hours. All workers need to work the same number of overtime hours within a month, if overtime production is planned in that month. b. Inventory and backorder costs are calculated using ending inventory/backorder of each month. Once scheduled, all workers will produce at their ull potential cach month. C. Beginning Inventory Productivity Current number of workers Hiring and training workers Laying off workers Regular time salary Overtime salary Marginal subcontracting cost (not including material) Inventory holding cost Back-ordering cost Regular hours per month Maximum allowed overtime hours in each month Required Ending Inventory at the end of June 0 units 2 units/worker hour 15 $4000 per worker $2500 per worker $10/hour/worker $15/hour/worker $15/unit $3 per unit per month $20 per unit per month 200 30 hours per worker At least 500 units Consider the following three different strategies. 1) Level production over six months. That is, hiring or layoff only happens at the beginning of January, and the number of workers keeps constant over six months. No overtime or subcontracting. 2) Use subcontracting, when necessary, to eliminate backlog in every month. No hiring, layoff, or overtime. 3) A combination of overtime and subcontracting. No hiring or layoff. Develop three plans using the above three strategies, respectively. Your plans should be cost- efficient among the plans that satisfy the requirements. For example, subcontracting 5000 units obviously satisfies the requirement of 2); however, doing so is not cost-efficient because you subcontract too many than what are needed. Which one of these three plans would you recommend? (Note: If you are not confident about your plan, especially plan 3), show some key steps in your calculation of the optimal decisions (the yellow cells). The instructor will mark accordingly.) Instructions: Plan 1): Calculate the overall production requirement first and then the number of workers needed. Plan 2): Calculale the required subcontracting quantity month by month. Plan 3); Compure the costs of overtime and subcontracting, Then, aljust your decisions based on Plan2). Further adjustment can be made if you carefully examine the costs of working overtime, holding inventory, and subcontracting, and their combinations. In particular, consider the options of keeping appropriate amount of inventory and backorders. Use the following template to present your plans. You need to make decisions in the yellow cells. The numbers of other cells depend on your decisions. 4 9500 5 9200 6 5700 Total 42700 5600 7100 5600 Period Demand Number of workers Overtime hours per worker --- Beginning Inventory Regular production quantity Overtime production quantity Subcontract quantity Ending Inventory Hiring cost Laying off cost Regular labor cost Overtime labor cost Marginal subcontract cost Inventory holding cost Backorder cost Total: 3. Jason oversees a job shop which runs two processes sequentially on products. In the morning, Jason receives seven orders that require the following processing times (in hours). Process 1 (cutting) Job A B C D E F G 3 3 6 1 4 Process 2 (polishing) 3 1 5 2 6 4 8 a) Use Johnson's rule to find the processing sequence for these jobs and draw the Gantt chart. How long does it take to finish all jobs? b) What is the total idle time for Polishing in this schedule? c) Suppose that there are only 29 hours left before a scheduled long maintenance of the job shop, which requires both processes being shut down. Therefore, Jason cannot accept all these seven orders. The profits of these orders are A:S45, B:120, C:$40, D:$60, E:S30, F:S70. G:$80. Which order(s) should Jason reject so that he can make highest profit from the remaining 29 hours? Why