Problems (Aggregate Planning)
I. Develop a production plan and calculate the annual cost for a firm whose unit demand forecast is fall. 10,000; winter, 8,000; spring. 7,000; summer, 12,000. Inventory at the beginning of fall is 500 units. At the beginning of fall you currently have 30 workers, but you plan to hire temporary workers at the beginning of summer and lay them off at the end of summer. In addition, you have negotiated with the union an option to use the regular workforce on overtime during winter or spring if overtime is necessary to prevent stock outs at the end of those quarters. Overtime is not available during the fall. Relevant costs are hiring, $100 for each temp; layoff, $200 for each regular worker laid off; inventory holding, $S per unit per quarter; back order, S 10 per unit per quarter; straight time, $S per hour; overtime, $8 per hour. Assume that worker productivity is two hours per unit, with eight hours per day and 60 days per season.
2. Develop an aggregate production plan for a four-month period: February through May. For February and March, you should produce to exactly meet the demand forecast. For April and May, you should use overtime. and inventory with a stable workforce. However, government constraints put a maximum of S,OOOhours of overtime labor per month in April arid May (zero overtime in February and March). If demand exceeds supply', then back orders occur. There are I00 workers on January 31. You are given the following unit demand forecast: February, 80,000; March, 64,000; April, 100,000; May, 40,000. Worker productivity is four units per hour. Assume/eight hours per day, 20 days per month and zero inventory on February 1. Costs are hiring, $Soper new worker; layoff, $70 per worker laid off; inventory holding, $10 per unit per month; straight-time labor, S10 per hour; overtime. SIS per hour; back order, $20 per unit per month. Find the total cost of this plan.
3. Develop an aggregate production plan for the next year. The unit demand forecast is spring, 20,000; summer, 10.000; fall, IS,OOO; winter, 18,000. At the beginning of spring you have 70 workers and 1,000 units in inventory. The union contract specifies that you may layoff workers only once a-.year, at the beginning of summer. Also, you may hire new workers only at the end of summer to begin regular work in the fall. The number of workers laid off at the beginning of summer and the number hired at the end of summer should result in planned production levels for summer and fall that equal the demand forecasts for summer and fall respectively. If demand exceeds supply, use overtime in spring only, which means that back orders could occur in winter. You are given these costs: hiring, $100 per new worker; layoff, $200 per worker laid off; holding, 520 per unit per quarter; back order costs, $8 per unit per
quarter; straight-time labor, S10 per hour; overtime. $15 per hour. Worker productivity is two hours per unit. Assume eight hours per day and 50 days per quarter. Find the total cost.
4. DAT, Inc. needs to develop an aggregate plan for its product line. Relevant data are
Management prefers to keep a constant workforce and production level, absorbing variations in demand through inventory excesses and shortages. Demand that is not met is carried over to the following month.
Develop an aggregate plan that will meet the demand and other conditions of the problem. Do not try to find the optimum: just find a good solution and state the procedure you might use to test for a better solution. Make any necessary assumptions.
5. Shoney Video Concepts produces a line of CD players to be linked to personal computers for video games. CDs have much faster access time than does tape. With such a computer/CD link, the game becomes a very realistic experience. In a simple driving game where the joystick steers the vehicle, for example, rather than seeing computer
graphics on the screen, the player is actually viewing a segment of a CD shot from a real moving vehicle. Depending on the action of the player (hitting a guard rail, for example) the disc moves virtually instantaneously to that segment and the player becomes part of an actual accident of real vehicles (staged, of course).
Shoney is trying to determine a production plan for the next 12 months. The main criterion for this plan is that the employment level is to be held constant over the period. Shoney is continuing in its R&D efforts to develop new applications and prefers not to cause any adverse feeling with the local workforce. For the same reasons, all employees should put in full work weeks, even if this is not the lowest-cost alternative. The number of CD players forecast for the next 12 months is
Manufacturing cost is $200 per player. equally divided between materials and labor. Inventory storage costs are $5 per CD player per month. A shortage results in lost sales and is estimated to cost an overall S20 per unit short. (Shortages are not carried forward since the sales are lost.)
The inventory on hand at the beginning of the planning period is 200 units. Ten labor hours are required per CD player. The workday is eight hours. Develop an aggregate production schedule for the year using a constant workforce. For simplicity, assume 22 working days each month except July. when the plant closes down for three weeks' vacation (leaving seven working days). Make any a assumptions you need.
6. The Bentley Chemical Company (BCC) is vitally concerned about generating a production schedule for their products for the coming fiscal year (1uly-June). The operations manager at BCC, Mr. Perspa Cassidy. has been charged with generating an Aggregate aggregate plan for this time period so that BCC can meet their demand with the minimum utilization of resources. Mr. Cassidy first aggregates the various products that BCC sells into a single "aggregate" production unit and forecasts the demand for the following four quarters:
On March I (prim to quarter # I) there are 1,200 units in BCC's inventory and the forecast demand for the fourth quarter of the previous year is 9,900 units. Mr. Cassidy knows that to keep one unit in inventory for one month costs $5; further, BCC uses average inventory when computing inventory costs. The workforce on March I consists of 40 employees, each of whom produces exactly four (4) units in an 8-hour day. For the coming four quarters, Mr. Cassidy has determined the number of productive days for-each quarter to be as follows:
Each of the regular employees is paid at the rate of $53 per day; however, overtime is available at the rate of $80 per day. BCC has a very strict quality control policy and does not allow any subcontracting. In addition, BCC wishes to maintain their reputation with their customers and has adopted a policy that all demand must be met on time. Mr. Cassidy recognizes that meeting all demand can be difficult. He is faced with two limitations: (I) he is using aggregate units and (2) he has only his forecasts as a basis for his aggregate plan. However, he believes that his forecasts are quite good and decides to use his figures objectively (i.e., he decides not to keep any safety stock).
The workforce can be increased or decreased at the discretion of Mr. Cassidy, but no more than a 25 percent increase or decrease (using integer values) is allowed in any given quarter due to union regulations. Mr. Cassidy knows that should he wish to hire and/or fire, the total increase/decrease in the workforce (when using whole people) cannot exceed the 25 percent mark. Fortunately, BCC is located in an area where there is no shortage of skilled labor. To hire a new individual and train Himmler requires exactly one-quarter and costs $1,200. All new employees always start on the first day of a given quarter. Hence, they cannot be considered part of the productive labor force until after their first quarter. To fire an individual costs $1.000, and when an individual is fired, he remains part of the productive workforce until the end of the quarter in which he was fired. Mr. Cassidy believes that he has all the data he needs; hence, he starts to determine the aggregate capacity plan. He selects a strategy of trying to maintain a relatively
stable workforce, while letting the inventory levels fluctuate. a. Perform the initial calculations Mr. Cassidy would need prior to completing the grid that follows.
b. Develop an aggregate plan for Mr. Cassidy by filling in the grid.
7. Nelson's Marina on Cape Cod, as part of the service it offers to its customers, stores boats during the winter months. In addition, the marina. at the request of the customer, also will paint the hull of the boat, which must be done every year to prevent barnacles from attaching to the hull.
Dave Nelson, the owner of the marina. has received orders for the following sizes of boats to be stored and painted, and also has estimated the number of hours required to paint each size boat
Dave currently employs one handyman during the summer months who does a wide variety of tasks. As one option, Dave can continue to employ this person during the six winter months (November-April) and have him paint the boat hulls. With this option the person would work 160 hours per month for each of the six months. Dave estimates the cost of painting the boats to be $30.00 per hour, which includes both labor and materials ($20.00 for labor and $10.00 for materials). Inasmuch as the boat owners will not pay Dave until the spring when their boats go in the water, Dave will have to borrow the money from his bank for the labor and materials at an annual rate of 18 percent, or 1.5 percent per month. As a second alternative, Dave can let the handyman go at the end of the season and then hire the necessary number of workers to get all of the boats painted in April, just before they go into the water. At the end of the month, he would let all but the handyman go. The cost of hiring a worker for this kind of work is estimated to be $100.00 per person and the layoff cost is estimated at $75.00 per person. .A third option would be to hire
A third option would be to hire less workers in April and have them all work overtime. In this ca e, each worker would work 60 hours a week, or 240 hours for the month. The overtime premium is 50 percent of the cost of labor, or $10.00 per hour. Develop an -aggregate plan for each of these alternatives. Which one do you recommend?