1. Aggregate Planning Model
GlobalCell is a cell phone producer in Europe, the demand for the first half of the coming year is forecasted in the table below.
|
Month
|
Demand in Unites
|
|
1
|
1000
|
|
2
|
1200
|
|
3
|
1000
|
|
4
|
1300
|
|
5
|
1500
|
|
6
|
1700
|
The plant operates for 20 days a month, eight hours each day. One worker can assemble a cell phone every 10 minutes. Workers are paid 20 euros per hour and a 50% premium for over time. The plant currently employs 1250 workers. Each cell phone costs 20 euros to make. The inventory carrying cost of a cell phone is 3 euros per phone per month. The company has no layoff policy in place. Overtime is limited to a maximum of 20 hours per month per worker. Assume that the company has a starting inventory of 5000 unites and wants to have the same level of inventory at the end of the schedule.
Develop an aggregate planning schedule for GobalCell for the next 6 months.
2. Inventory Management/Multi-item Joint Replenishment EOQ - Model
The Lamps Store sells 2 types of table lamps: classic and contemporary. The annual demand for the classic table lamp is 200 units while the annual demand for the contemporary table lamp is 300 units.
Assume each lamp costs Lamps Store $50 to purchase from its supplier, and the fixed ordering cost is $300 each time. For each type of table lamps ordered and delivered on the same truck, an additional fixed handling cost of $100 is charged. The company has a holding cost of 20 percent of the unit purchasing cost.
The Lamps Store decides to order 2 models of lamps at the same time using the same truck. What is the optimal lot size for each model?
3. Transportation Model
Frost Generators Co. operates factories in Cleveland, Bedford, and York. Production volumes over the next 3 months planning period for a particular generator is as follows
|
Factory
|
3-month production volume (units)
|
|
Cleveland
|
5000
|
|
Bedford
|
6000
|
|
York
|
2500
|
The company sells the generators through four regional warehouses in Boston, Chicago, St Louis, and Lexington. The 3-month demand of the warehouses is as follows
|
Warehouse
|
3-month demand forecast (units)
|
|
Boston
|
6000
|
|
Chicago
|
4000
|
|
St Louis
|
2000
|
|
Lexington
|
1500
|
The transportation cost per unit from factories to warehouses are given as follows
|
Factory to Warehouse
|
Boston
|
Chicago
|
St Louis
|
Lexington
|
|
Cleveland
|
3
|
2
|
7
|
6
|
|
Bedford
|
7
|
5
|
2
|
3
|
|
York
|
2
|
5
|
4
|
5
|
Management wants to use linear programming method to determine how much of its production units should be shipped from each factory to each warehouse such that the total transportation costs would be minimized.
1) What are the decision variables and definitions?
2) What is the objective function?
3) What are the constraints?