Question

NYY is a winter jacket manufacturer company with manufacturing facilities in the U.S.A. Winter jacket demand is seasonal peaking in the winter as the temperatures along the East Coast dipping well below zero. Production of winter jackets requires some certain amount of work and NYY jacket manufacturer has multiple options to handle seasonal demand. The first option is NYY can prefer to increase number of workers by adding workers during the peak season. Second option is NYY can subcontract out partial work to outside companies. Third option is NYY can build up inventory capacity to produce and store extra winter jackets during slow seasons. Fourth option is that NYY can make late order deliveries by creating backlog of orders. President of NYY wants to know how to make best use of these available options through an aggregate plan. Demand forecast for entire year is shown in following Table 1.

Demand forecast for NYY jacket manufacturer

Month	demand	month	demand
January	5500	July	600
February	3900	August	700
March	3000	September	1900
April	1700	October	2800
May	700	November	4900
June	500	December	6800

NYY has 1,000 jackets in their inventory as well as 80 workers working with the company at the beginning of January. Each month consists of 20 working days and each worker works 8 hours per day straight and rest on overtime. $4 is paid to each worker regular time. Please note that production operation is not limited by the machine capacity as production operation is directly related to the number of labor hours worked. Overtime per employee per month is limited to 10 hours. Table 2 shows the related costs. Keep it in mind that NYY does not have any limits on subcontracting out, backlogging, and inventories. Cost of inventory is paid at the end of inventory in the month. All stockouts are supplied from the following month’s production or previous month’s inventory. President of NYY wants to find the optimal plan that will let them stock 1000 jackets in inventory, have no stockouts, and 80 workers are hired at the end of December for the next year production plan.

Costs for manufacturing jackets (table 2)

item	cost
Materials cost	$10/unit
Adding more workers cost	$300/worker
Backlogging cost	$5/unit/month
Subtracting cost	$32/unit
Inventory cost	$2/unit/month
Regular time cost	$4/hour
Overtime cost	$5/hous
Layoff cost	$500/worker
Labor hours required	4 hours/unit

2. Create an AMPL code to solve the formulated LP and run it. In addition to the main report, you need to turn in four files: (a) a model file, (b) a data file, (c) a script file containing the commands you issue in AMPL to solve the model and display the result, and (d) an output file containing the result of running your script file. These files should be named miniprj.mod, miniprj.dat, miniprj.run, and miniprj.out, respectively. • Comments in the code are absolutely necessary. Comments should be such that one could understand the whole problem and model just by reading your code. In particular all sets, parameters, variables, objective function, and constraints should have associated comments clearly defining/explaining them. The comments should be self-contained and not refer to the problem description. • Use meaningful and short names for all elements of the model consistent with the terminology used in the description.

Answer 1