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Solution of aggregate planning problems by linear programming,…
Solution of aggregate planning problems by linear
programming
Cost parameters
worker
CH = Cost of hiring one worker
CF = Cost of firing one worker
Wo = initial workforce at the start of the planning horizon
Stock
CI= Cost of holding one unit of stock for one period
lo = Initial inventory on hand at the start of the planning horizon
producing
CR = cost of producing one unit on regular time
co = incremental cost of producing one unit on overtime
CU= Idle cost per unit of production
Production
Cs = Cost to subcontract one unit of production
nt = Number of production days in period t
K = Number of aggregate units produced by one worker in one day
Dt = Forecast of demand in period t
Problem Variables
worker
Wt = Workforce level in period t
Ht = Number of workers hired in period t
Ft = Number of workers fired in period t
Capacity
Pt = Production level in period t
Ot = Overtime production in units
Ut = Worker idle time in units
St = Number of units subcontracted from outside
Stock
i = Inventory level in period t
Conservation of Unit Constraints
I(t) = I(t-1) + P(t) +S(t) -D(t)
in period t
实际产量Pt 理论产能K
nt
Wt
Pt = K
nt
Wt + Ot -Ut
Ot * Ut = 0
同一周期内，企业要么因产能不足需要加班，要么因需求不足导致产能闲置，两者不能同时存在
Production vs. Workforce Constraints
Conservation of Workforce Constraints
W(t) = W(t-1) + H(t) - F(t)
Ht*Ft = 0
同一周期内，企业不会同时雇佣和解雇工人