Solving Fuzzy Multiproduct Aggregate Production Planning Problems Based on Extension Principle

Table 2

Notation for parameters of the fuzzy APP model.

Parameter	Definition
𝐶^𝑛𝑝𝑡	Unit production cost excluding labour cost of 𝑛th product in period 𝑡 ($/unit)
𝐶^𝑛𝑜𝑡	Overtime labour cost of 𝑛th product in period 𝑡 ($/man-hour)
𝐶^𝑛𝑟𝑡	Labour cost of 𝑛th product in period 𝑡 ($/man-day)
𝐶^𝑛𝑖𝑡	Inventory carrying cost of 𝑛th product in period 𝑡 ($/unit-period)
𝐶^𝑛ℎ𝑡	Cost to hire one worker of 𝑛th product in period 𝑡 ($/man-day)
𝐶^𝑛𝑙𝑡	Cost to layoff one worker of 𝑛th product in period 𝑡 ($/man-day)
𝐶^𝑛𝑏𝑡	Unit backorder cost of 𝑛th product in period 𝑡 ($/unit)
𝑘𝑛	Conversion factor in hours of labour per unit of production (man-hour/unit)
𝛿	Regular working hours per worker per day (man-hour/man-day)
𝛽^𝑛𝑡	Fraction of working hours available for overtime production
𝑇	Planning horizon or number of periods
𝐼^𝑛0	Initial inventory level of 𝑛th product (units)
𝑊^𝑛0	Initial work force level of 𝑛th product (man-day)
𝐵^𝑛0	Initial backorder level of 𝑛th product (units)
(𝑊𝑡^max)𝑛	Maximum workforce available of 𝑛th product in period 𝑡 (man-day)
(𝐹𝑡^min)𝑛	Minimum demand of the 𝑛th product in period 𝑡 (units)
𝑁	The number of products