A factory produces m (i = 1, 2, ..., m) products, each of which requires processing on n (j = 1, 2, ..., n) workstations. Let a_ij be the amount of processing time that one unit of the i^th product requires on the j^th workstation. Let the revenue from selling one unit of the i^th product be r_i and h_i be the holding cost per unit per time period for the i^th product. The planning horizon consists of T (t = 1, 2,..., T) time periods. The minimum demand that must be satisfied in time period t is d_it, and the capacity of the j^th workstation in time period t is c_jt. Consider the aggregate planning formulation below, with decision variables S_it (amount of product i sold in time period t), X_it (amount of product i manufactured in time period t) and I_it (amount of product i held in inventory at the end of time period t).
max‌
T
∑
t=1
⁡
m
∑
i=1
⁡(riSit−hiIit)
Subject to
S_it ≥ d_it ∀ i, t
< capacity constraint >
< inventory balance constraint >
X_it, S_it, I_it ≥ 0; I_i0 = 0
The capacity constraints and inventory balance constraints for this formulation respectively are

Question

Examsnet · Accepted Answer

Correct Answer is : m∑iaijXit≤cjt‌∀j,t and Iit=Ii,t−1+Xit−Sit‌∀i,t

GATE Mechanical Engineering (ME) 2021 Shift 2 Solved Paper