Using JIT in a Green Supply Chain

Read this article on the Green Supply Chain. The authors analyzed the JIT approach to a transportation supply chain. As you read, think about what JIC materials, goods, and labor must be on hand in order to deliver JIT products?

Modeling and Assumptions

Objective Functions and Constraints

Objective Function 1: Minimum the total Cost:

$\begin{aligned} \min \mathrm{Z}_{1} &=P S M T C+P W M T C+P R W T C+P W M T C+P W C T C+T M S T C \\ &+T S W T C+T W R T C+T R M T C+I W T C+I M T C+F G T C \\ &+F C T C \end{aligned}$ (23)

Objective Function 2: Minimum CO₂

$\min \mathrm{Z}_{2}=E C P C+E M S C+E S W C+E W R C+E R M C+E M W C$ (24)

Model Constraints:

1. Each can choose either Scenario 1 or Scenario 2 for transportation and cross usage is not allowed for 120 working days.

$\chi_{(a, b), 1, n}+\chi_{(a, b), 2, n} \leq 1 \text { for } \mathrm{a}=1,2,3,4, \mathrm{~b}=1,2, \ldots, 5, \mathrm{n}=\mathrm{S}, \mathrm{S}+1, \ldots, \mathrm{S}+120$ (25)

$\chi_{(a, b), T M, n+10} \geq \chi_{(a, b), T M, n}$ (26)

2. he goods arrive once every ten days.

$\sum_{n=1}^{10} \chi_{(a, b), T M, n}=1 \text { for } \mathrm{a}=1,2,3,4, \mathrm{~b}=1,2, \ldots, 5, \mathrm{TM}=1,2$ (27)

$\sum_{n=11}^{20} \chi_{(a, b), T M, n}=1 \text { for } \mathrm{a}=1,2,3,4, \mathrm{~b}=1,2, \ldots, 5, \mathrm{TM}=1,2$ (28)

$\sum_{n=21}^{30} \chi_{(a, b), T M, n}=1 \text { for } \mathrm{a}=1,2,3,4, \mathrm{~b}=1,2, \ldots, 5, \mathrm{TM}=1,2$ (29)

$\sum_{n=31}^{40} \chi_{(a, b), T M, n}=1 \text { for } \mathrm{a}=1,2,3,4, \mathrm{~b}=1,2, \ldots, 5, \mathrm{TM}=1,2$ (30)

$\sum_{n=41}^{50} \chi_{(a, b), T M, n}=1 \text { for } \mathrm{a}=1,2,3,4, \mathrm{~b}=1,2, \ldots, 5, \mathrm{TM}=1,2$ (31)

$\sum_{n=51}^{60} \chi_{(a, b), T M, n}=1 \text { for } \mathrm{a}=1,2,3,4, \mathrm{~b}=1,2, \ldots, 5, \mathrm{TM}=1,2$ (32)

$\sum_{n=61}^{70} \chi_{(a, b), T M, n}=1 \text { for } \mathrm{a}=1,2,3,4, \mathrm{~b}=1,2, \ldots, 5, \mathrm{TM}=1,2$ (33)

$\sum_{n=71}^{80} \chi_{(a, b), T M, n}=1 \text { for } \mathrm{a}=1,2,3,4, \mathrm{~b}=1,2, \ldots, 5, \mathrm{TM}=1,2$ (34)

$\sum_{n=81}^{90} \chi_{(a, b), T M, n}=1 \text { for } \mathrm{a}=1,2,3,4, \mathrm{~b}=1,2, \ldots, 5, \mathrm{TM}=1,2$ (35)

$\sum_{n=91}^{100} \chi_{(a, b), T M, n}=1 \text { for } \mathrm{a}=1,2,3,4, \mathrm{~b}=1,2, \ldots, 5, \mathrm{TM}=1,2$ (36)

$\sum_{n=101}^{110} \chi_{(a, b), T M, n}=1 \text { for } \mathrm{a}=1,2,3,4, \mathrm{~b}=1,2, \ldots, 5, \mathrm{TM}=1,2$ (37)

$\sum_{n=111}^{120} \chi_{(a, b), T M, n}=1 \text { for } \mathrm{a}=1,2,3,4, \mathrm{~b}=1,2, \ldots, 5, \mathrm{TM}=1,2$ (38)