Case study: Developing an Aggregate Plan-Bradford Manufacturing You are the operations manager for a manufacturing plant that produces pudding food products. One of your important responsibilities is to prepare an aggregate plan for the plant. This plan is an important input into the annual budget process. The plan provides information on production rates, manufacturing labor requirements, and projected finished goods inventory levels for the next year. You make those little boxes of pudding mix on packaging lines in your plant. A packaging line has a number of machines that are linked by conveyors. At the start of the line the pudding is mixed; it is then placed in small packets. These packets are inserted into the small pudding boxes, which are collected and placed in cases that hold 48 boxes of pudding. Finally, 160 cases are collected and put on a pallet. The pallets are staged in a shipping area from which they are sent to four distribution centers. Over the years, the technology of the packaging lines has improved so that all the different flavors can be made in relatively small batches with no setup time to switch between flavors. The plant has 15 of these lines, but currently only 10 are being used. Six employees are required to run each line. The demand for this product fluctuates from month to month. In addition, there is a seasonal component, with peak sales before Thanksgiving, Christmas, and Easter each year. To complicate matters, at the end of the first quarter of each year the marketing group runs a promotion in which special deals are made for large purchases. Business is going well, and the company has been experiencing a general increase in sales. The plant sends product to four large distribution warehouses strategically located in the United States. Trucks move product daily. The amounts shipped are based on maintaining target inventory levels at the warehouses. These targets are calculated based on anticipated weeks of supply at each warehouse. Current targets are set at two weeks of supply. In the past, the company has had a policy of producing very close to what it expects sales to be because of limited capacity for storing finished goods. Production capacity has been adequate to support this policy. A sales forecast for next year has been prepared by the marketing department. The forecast is based on quarterly sales quotas, which are used to set up an incentive program for the salespeople. Sales are mainly to the large U.S. retail grocers. The pudding is shipped to the grocers from the distribution warehouses based on orders taken by the salespeople. Your immediate task is to prepare an aggregate plan for the coming year. The technical and economic factors that must be considered in this plan are as follows: 1. Currently the plant is running 10 lines with no overtime. Each line requires six people to run. For planning purposes, the lines are run for 7.5 hours each normal shift. Employees, though, are paid for 8 hours' work. It is possible to run up to 2 hours of overtime each day, but it must be scheduled for a week at a time, and all the lines must run overtime when it is scheduled. Workers are paid $20.00/ hour during a regular shift and $30.00/ hour on overtime. The standard production rate for each line is 450 cases/hour. 2. The marketing forecast for demand is as follows: Q1-2,000; Q2 2,200;Q32,500; Q4-2,650; and Q1 (next year)-2,200. These numbers are in 1,000-case units. Each number represents a 13-week forecast. 3. Management has instructed manufacturing to maintain a two-week supply of pudding inventory in the warehouses. The two-week supply should be based on future expected sales. The following are ending inventory target levels for each quarter: Q1338; Q2-385; Q3-408; Q4-338. 4. Inventory carrying cost is estimated by accounting to be $1.00 per case per year. This means that if a case of pudding is held in inventory for an entire year, the cost to just carry that case in inventory is $1.00. If a case is carried for only one week, the cost is $1.00/52, or $.01923. The cost is proportional to the time carried in inventory. There are 200,000 cases in inventory at the beginning of Q1 (this is 200 cases in the 1,000 case units that the forecast is given in). 5. If a stockout occurs, the item is backordered and shipped at a later date. The cost when a backorder occurs is $2.40 per case due to the loss of goodwill and the high cost of emergency shipping. 6. The human resource group estimates that it costs $5,000 to hire and train a new production employee. It costs $3,000 to lay off a production worker. 7. Make the following assumptions: - Inventory costs are based on inventory in excess of safety stock. - Backorder costs are incurred on negative deviation from planned safety stock, even though planned inventory may be positive. - Overtime must be used over an entire quarter and should be based on hours per day over that time. Prepare an aggregate plan for the coming year, assuming that the sales forecast is perfect. a. Use heuristic worksheet in the provided Excel file. In the spreadsheet an area has been designated for your aggregate plan solution. Supply the number of packaging lines to run and the number of overtime hours for each quarter (your final solution needs an integer number of lines and an integer number of overtime hours for each quarter). You will need to set up the cost calculations in the spreadsheet. b. Using the model template in the LP worksheet, complete the missing formulas to obtain a linear programming model and then find the optimal solution. Remember that your final solution needs an integer number of lines and an integer number of overtime hours for each quarter. Note: recent versions of Excel for Apple computers has problems in finding the optimal solution, I recommend that you solve the model on a Windows computer. All production/demend we in 1000-cae usits