Assignment:
The demand forecast for a company's gardening tools are shown in the table below. The company needs to meet the demand and end June with at least 500 tools (i.e., no stockouts at the end of June and at least 500 tools in inventory). At the beginning of January the company has a workforce of 50 employees and 600 tools in inventory. The material cost for each tool is $10 The company has a total of 20 working days in each month, and each employee earns $4 per hour regular time and $6 per hour overtime. Each employee works eight hours per day on regular time and the rest on overtime. No employee works more than 10 hours of overtime each month. Each employee can produce 40 tools per month on regular time and one tool for every four hours of overtime. At the beginning of each month, the company decides how many additional employees are hired or how many current employees are laid off. The cost of hiring an employee $300 and the cost of laying off an employee is $500. To meet the demand, the company can build up inventory during the slow months (i.e., months in which the demand is low) or building up a backlog of orders (stockouts) that will be delivered late to customers. The cost of carrying inventory is per month, and the cost of stocking out is $5 per tool per month. In addition to manufacturing tools in its facility, the company can subcontract out some of the work. The subcontracting cost is $30/tool. (i.e., the company can purchase one at $30 from suppliers to meet the demand. Please formulate an LP model to help the company minimize the total cost. Please use GAMS to find the optimal solution and optimal value.
|
Month
|
Demand Forecast (Number of Tools)
|
|
January
|
2000
|
|
February
|
3200
|
|
March
|
3000
|
|
April
|
2400
|
|
May
|
4000
|
|
June
|
3200
|
Your answer must be typed, double-spaced, Times New Roman font (size 12), one-inch margins on all sides, APA format and also include references.