The document contains solutions to three operations management assignment questions. The first question involves scheduling employee work to meet demand. The second question calculates lot sizes and costs using different lot sizing methods. The third question develops a production plan to meet seasonal demand forecasts and calculates the associated costs.
2. 1.) The Glendale Electronics Store employs five people. Customer Traffic is highest on the weekends and
lowest during midweek. Accordingly, demand for employee help is given in the following table. Make
an employee work schedule that will meet staffing requirements and guarantee each employee two
consecutive days off per week.
Sol.)
DAYS
Monday Tuesday Wednesday Thursday Friday Saturday Sunday
Requirements 4 3 2 3 4 5 4
Adams 4 3 2 3 4 5 4
Chang 3 2 2 3 3 4 3
Klein 2 2 2 2 2 3 2
Ramirez 1 1 1 2 2 2 1
Sampson 0 1 1 1 1 1 0
Here 5 worker work for 25 worker days although slight different assignments may be equally satisfactory
The Schedule is
ADAM is assigned Wednesday & Thursday OFFs
CHANG is assigned Tuesday & Wednesday OFFs
KLEIN is assigned Thursday & Friday OFFs
RAMIREZ is assigned Tuesday & Wednesday OFFs
SIMPSON is assigned Sunday & Monday OFFs
3. 2.) An item has a setup cost of $100 and a weekly holding cost of $0.50 per unit. Given the following net
requirements, what should the lot sizes be using Lot-for-Lot (L4L), economic order quantity (EOQ) and
least total cost (LTC)? Also what is the total cost associated with each lot sizing?
WEEKS Net Requirements
1 10
2 30
3 10
4 50
5 20
6 40
7 50
8 30
Sol.)
LOT-4-LOT (L4L)
Week Net Production Ending Holding Setup Total
Requirements Quantity Inventory Cost Cost Cost
1 10 10 0 0 100 100
2 30 30 0 0 100 200
3 10 10 0 0 100 300
4 50 50 0 0 100 400
5 20 20 0 0 100 500
6 40 40 0 0 100 600
7 50 50 0 0 100 700
8 30 30 0 0 100 800
ECONOMIC ORDER QUANTITY
Annual Holding Cost, H = 0.50 * 52
= $26 per unit
Setup Cost, S = $100
E= ((2DS)/ H)
= 110 units
Week Net Production Ending Holding Setup Total
Requirements Quantity Inventory Cost Cost Cost
1 10 110 100 50 100 150
2 30 0 70 35 100 135
3 10 0 60 30 100 130
4 50 0 10 5 100 105
5 20 110 100 50 100 150
6 40 0 60 30 100 130
7 50 0 10 5 100 105
8 30 110 90 45 100 145
4. Que 3. Develop a production plan and calculate the annual cost for a firm whose demand forecast is
fall, 10,000; winter, 8,000; spring, 7,000; summer, 12,000. Inventory at the beginning off all 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 the 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 worker
laid off; inventory holding, $5 per unit-quarter; backorder, $10 per unit; straight time, $5 per hour;
overtime, $8 per hour. Assume that the productivity is 0.5 units per worker hour, with eight hours
per day and 60 days per season.
Solution:
Productivity = 0.5 units/hour, 8 hours/day, 60 days/season
Labor RT = $5/hour, OT = $8/hour
RT unit cost = $5/0.5 units = $10/unit
OT unit cost = $8/0.5 units = $16/unit
Inventory holding = $5/unit/quarter, Backorder = $10/unit
Hiring = $100/worker, Firing = $200/worker, Fall Inventory = 500 units
Number of units produced by 1 worker in one season = 0.5*8*60 = 240 units
5. Que: Plan production for the next year. The demand forecast is spring, 20,000; summer, 10,000; fall,
15,000; 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 lay off 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 backorders could occur in winter. You are given these costs: hiring, $100 per new
workers; layoff, $200 per worker laid off; holding, $20 per unit-quarter, backorder cost, $8 per unit;
straight-time labor, $10 per hour; overtime, $15 per hour. Productivity is 0.5 units per worker hour,
eight hours per day, 50 days per quarter. Find the total cost.
Solution:
Productivity = 0.5 units/hour, 8 hours/day, 50 days/season
Labor RT = $10/hour, OT = $15/hour
RT unit cost = $10/0.5 units = $20/unit, OT unit cost = $15/0.5 units = $30/unit
Inventory holding = $20/unit/quarter, Backorder = $8/unit
Hiring = $100/worker, Firing = $200/worker, Spring Inventory = 1,000 units
Number of units produced by 1 worker in one season = 0.5*8*50 = 200 units
*Laid off 20 workers at the beginning of summer
** Hired 20 workers at the end of summer to begin regular work in the fall
*** Hired 25 workers at the end of summer to begin regular work in the fall
