Problem Definition and Assumptions

C HAPTER 3

3. Problem Definition and Assumptions

The problem being analyzed concerns a producer who meets sales and collection center demand with new, repaired and remanufactured products. It is assumed that the factory, distribution center, repair center, sales, and collection center in the sustainable supply chain network belong to one enterprise.

The sales and collection center sell the products it receives from the factory and purchases EOLPs from customers.

IoT provides information about a product when they are returned and plays a significant role in the recovery process and backup. This information reduces and eliminates the uncertainty of the condition and remaining lives of components in an EOLP. The price paid for EOLPs is based on their level of value. The returned products are processed via one of three recycling procedures: repair, disassembly, or disposal. The products that have little damage and can be reused are repaired. The broken components of these products are replaced with new components received from the factory, and the products are sent to the distribution center as needed to meet demand. If the returned products cannot be repaired, they are disassembled. The components salvaged from disassembly are sorted by value and sent to the sales and collection center to be sold to the factory for use in new products or to the waste center for disposal. The factory must outsource for new components to meet the demand for products and components and optimize total production costs by making the correct recycling decision for each returned product.

New parts and spare parts are also sold in the sales and collection center. When the demand is high for spare parts, it is met with new parts. Sales and collection centers bear the cost of stocking new parts.

This present model is a single product, the multi-stage model that includes the cost and recycling evaluation process of CO₂ emission for different types of vehicles. It is a linear mathematical model. This network supply chain network design presents in Figure 1.

Model Assumptions

1. This product is modular and contains lifecycle information.

2. There is no difference between new products and recovered products.

re

Fig. 1: Sustainable Supply Chain Network Design with the Internet of Things.

3. All cost and sale prices are known.

4. End-of-life products (EOLPs) contain both functional and non-functional components.

5. The components of the product have importance weights that range from new to one, and the sum of them is 1.

6. It is assumed that the product value level is calculated according to the current component value levels as follows:

Product value rate (diot_j) = ∑ Component value level (diot)_j * Importance weight of component 7. New products and components are sold in the sales and collection center.

8. Inventory costs exist and no shortage cost is allowed.

9. Sales and collection centers have the capacity for the product/components.

10. The factory has a production and modular capacity.

11. Sales from the inventory of the sales collection center are not allowed.

12. For a single product type, a dynamic, multi-stage, and mixed linear model has been developed.

13. Carbon emission amounts of the vehicles were considered, and it was punished by a penalty coefficient.

14. It is assumed that vehicle capacities are limitless.

3.1 Model Indices and Parameters

Based on the above assumptions, a uniform product (automobile, computer, phone, etc.) is selected that is modular. A multi-stage, single-product and mixed whole number model was developed by considering environmental factors.

Notations

i Returned products (i = 1, 2, …, I) j Parts (j = 1, 2, …, J)

l Returned product value range (l = 1, 2, …, L) s Number of supplier (s = 1,……, S)

p Number of factory (p = 1,…..., P)

d Number of distribution centers (d = 1,……..D) st Number of sales and collection center (st = 1,……..,ST) t Vehicle types (t = 1, 2, …, T)

Model Parameters

a_j : Assembly cost of component j in factory and sales collection center d1_j : Disassembly cost of component j

e_j : Waste cost of component j

g2_j : Unit transportation cost of component j p1_sj : Ordering cost of component j from s. supplier

pp_j : Purchasing value of j component obtaining by disassembly

rr_l : Purchasing cost of an l-level product from sales and collection center

f_st,j : Cost of replacing the j used component in st. sales center

h2_st,j : Unit sales price of j. original component in st. sales collection center

h3_st,j : Unit sales price of j. used component in st. sales collection center

rc_j : Number of component j in a product

R_st,l : Amount of used product in the l-level are purchased from sales and collection center

bro_ij : 1 if component j of the returned product I is the quality deficit in period t, zero otherwise C_i : Value level of the returned product

aa_st,i : 1 if the returned product i is purchased, 0 otherwise in period t

dm_st : Product demand of st. sales and collection center

dms_st,j : j. new component demand of st. sales and collection center

56 Logistics 4.0: Digital Transformation of Supply Chain Management dmc_st,j

Capmax_st,j CapmaxU_st Capp1_s Capp2_p Capp3_d Capp4_dj K1_spt K2_sdt K3_pdt K4_d,st,t CC1_spt CC2_sdt CC3_d,st,t CC4_d,st,t h1_st Q_st M_jt g1 rw_j teta_j tww Weight Recycling Recy_j Recy1 Wcost pn

: j. used component demand of st. sales and collection center : j. the component capacity of st. sales and collection center : Capacity of st. sales and collection center for product : Capacity of s. supplier

: Capacity of p. factory

: Capacity of d. distribution center

: j component capacity in d distribution center

: Unit transportation cost of t vehicle from s supplier to p factor : Unit transport cost of t vehicle from s supplier to p factory : Unit transport cost of t vehicle from s supplier to p factory

: Unit transport cost of t vehicle from d distribution center to p factory

: Amount of CO emission of truck t during the transportation of s supplier to p factory₂

: Amount of CO emission of truck t during the transportation from s supplier to d distribution center ₂ : Amount of CO emission truck t during the transportation from p factory to d distribution center ₂ : Amount of CO emission truck t vehicle the transportation from d distribution center to st sales₂

collection center

: Unit product sales price in the sales collection centers : Amount of products repaired in the sales collection center : Amount of components can be disposed

: Transportation cost of unit product : Weight of j component per product

: Rate of the material to can be recycled for j component (%) : recycling rate for product one another (%)

: Unit weight of a product (kg) : Amount of product can be recycled

: Return gained in recycling of sale of j component : Unit recycling return of a product

: Unit disposal cost of a product : Unit penalty cost of CO₂ emission Expression of some parameters

Binary parameters bro_ijt determine how to process components according to their value levels. Accordingly, components whose value level is sufficient are refurbished and reused after the disassembly process. If the value level of a component is insufficient, the component is sent for disposal. The threshold value to determine if components should be refurbished is represented by n.

bro_ijt = 1  0

if component j is non − functional, 0 ≤ diot _j ≤ n

"i and 0 < n (1) component j is functional ( Again used ), diot _j ≥ n

Assuming the value level of components and their importance weights of return are known, there are three value ranges that can be calculated for product value levels (diot_i). C_i (the product value range) is determined where n₁ and n₂ represent value range limits. According to the information on which recovery process (repair, disassembly or disposal) is applied for each EOLP, the parameter C_i can be calculated as follows:

{

1 (Disposal) 0 ≤ diot_i < n₁

C_i = 2 (Disassembly) n₁ ≤ diot_i < n₂ "i and 0 < n₁ < n₂ (2)

3 (Repair) diot_i ≥ n₂

(Ondemir and Gupta 2014b)

Returned products are repaired in sales and collection points if they are purchased in t period and at 3rd level of importance.

Therefore;

C_i.α– _st,i = 3 then yy_st,i = 1 (3)

If returned products are purchased in t period and at 2nd importance value, they are disassembled. Disassembled products are determined in sales and collection centers and they are brought to decomposition centers. Then, they are subjected to the disassembly process. Therefore;

C_i.α– _st,i = 2 then xx_st,i = 1 (4)

If returned products are in 1st importance value, they are directly eliminated. Product parts are eliminated during disassembly and repair. Therefore;

C_i = 1 then Σ _t xx_st,i + yy _st,i = 0 (5) Amount of total renewed parts after disassembly (rfc_jt ) is calculated as the following:

rfc = _{st,j {i∊I|a}

∑

– _st,i .(1 – bro ) _ij (6)

st,i = 1} xx Amount of product repaired in sales and collection centers;

Q = ^st

∑

^{yy st,i (7)}

i

Components with inadequate levels came out of repair and disassembly periods are directly sent to waste in decomposition centers.

M – _j

∑∑

bro . (xx + yy ) = 0 ∀j _{ij st,i st,i} (8)

i st

Geridon_j : Amount of material of j component to be sent to recycling in kg;

Geridon = M . rw . teta _{j j j j} (9)

Amount of product to be recycled;

Recycling =

∑∑

^TWst,i . weight.tww (10)

st i

Model Decision Variables

b _j : Auxiliary decision variable used to decide the value of SS precisely (takes the value 0 or 1)_st,j

X_spjt : Amount of j. new component transported by t truck from s supplier to p factory

Y_sdjt : Amount of j. unused component transported by t truck from s supplier to d distribution

center

Z_pdt : Amount of component transported by t truck from p factory to d distribution center

W _d,st,j,t : Amount of j. component transported by t truck from d distribution center to st. sales and

collection center

V _d,st,t : Amount of product transported by t truck from s supplier to p factory

SS_st,j : Amount of j. used component transported from st. sales and collection center to dismantling

center

58 Logistics 4.0: Digital Transformation of Supply Chain Management

N_pj : Amount of j. renewed components transported from p factory to dismantling center

Icc_st,j : Amount of j component stored in the st. sales and collection center

3.2 Objective Functions

The objective function is the Maximization of the total revenue. Total revenue (TR) and Total Cost (TC) and Objective Function (Z) is shown below:

Z = TR – TC

Total Revenue (TR): Companies regard the sale of a brand-new product, original components and used components as income for the company. The sales of used components, which are in good condition after the disassembly process, returns to the company as revenue.

TR =

∑∑

^{dmt,st .h1st +}

∑∑∑

^{(dmst,st,j + dmct,st,j −SSst, j,t ).h2st, j +}

∑∑∑

^{SSst, j,t .h3st, j +}

st t t st j st j t

(11)

∑∑

^{Npj.ppj +}

∑∑

^{Geridon jt.recyj +}

∑

recy1.recylingt

p j j t t

Total Cost (TC): Total cost consists of total purchasing cost (TPC), total manufacturing cost (TMC), total transport cost (TTC), Total Waste Cost (TWC), Total Renting Car cost (TRC), total emission Cost (TCC), and Total Fixed Cost (TFC).

TC = TPC + TMC + TTC + TWC + TRC + TCC + TFC (12)

Total Purchasing Cost (TPC): Purchasing cost is defined as the sum of purchasing costs made in order to meet the demand of factory and sales collection centers in original components from the suppliers and purchasing costs of the products returned from customers to sales collection centers.

TPC =

∑∑∑∑

^{p1sjXspjt +}

∑∑∑∑

^{p1sjYsdjt +}

∑

^rrl

∑∑

^{Rst,l,t (13)}

s p j t s d j t l st t

Total Manufacturing Cost (TMC): In factories, manufacturing costs are composed of repair costs in sales and collection centers and assembly costs in disassembly centers and remanufacturing costs in the plant.

TMC =

∑

^{a jrcj}

∑∑∑

^{Zpdt +}

∑∑∑∑

^{(d1j + aj +}

∑

^{p1sj )broijtyyst,i,t}

j p d t st i j t s (14)

+

∑∑∑

xx ^st,i,t

∑

d1 ^j + f (1 ^j − bro ))^ijt

st i t j

Total Transport Cost (TTC): Transport costs consists of both product and component cost. Products are transported from factory to distribution centers and from distribution center to sales collection center.

TTC =

∑∑∑

^{Zpdt .g1 +}

∑∑∑

^{Vd,st,t .g1 +}

∑∑∑∑

^{wd,st, j,t .g2j +}

∑∑

^{SSst, j.g (15)}

p d t d st t d st j t st j

Total Waste Cost (TWC): Original components are disposed if they are broken in the repair and disassembly processes.

These original components are sent to the disposal center.

TWC =

∑∑

^{ejbroij (16)}

i j

Total Renting Truck Cost (TRC): Renting costs of trucks associated with the amount of transported products and components.

TRC =

∑∑∑∑

^{Xspjt .K1spt +}

∑∑∑∑

^{Ysdjt .K2sdt +}

∑∑∑

^{Zpdt.K3pdt +}

s p j t s d j t p d t (17)

∑∑∑

^{Vd,st,t .K4d,st,t +}

∑∑∑∑

^{Wd,st, j,t .K4d,st,t}

d st t d st j t

Total Emission Cost (TCC): Carbon emission cost varies by the type of trucks and it is multiplied by a penalty cost coefficient as well.

TCC =

∑∑∑∑

^{Xspjt .CC1spt +}

∑∑∑∑

^{Ysdjt .CC2sdt +}

∑∑∑

^Zpdt.CC3pdt

s p j t s d j t p d t

+

∑∑∑

^{Vd,st,t .CC4d,st,t +}

∑∑∑∑

^{Wd,st, j,t .CC4d,st,t} (18)

d st t d st j t

Total Fixed Cost of Facilities (TFC): The fixed cost of facilities includes the selection cost of suppliers, the opening cost of plant and distribution centers.

TFC =

∑

f1 k11 ^{s s} +

∑

f 2 k12 ^{p p} +

∑

f 3 k13 ^{d d} (19)

s p d

3.3 Constraints

The number of original components coming from factories to distribution centers and the number of original components going from distribution centers to sales and collection centers should be equal to each other.

∑∑

^{Ysdjt =}

∑∑

^{Ws,st, jt "d, j (20)}

s t st t

The number of products coming from factories to distribution centers and the number of products going from distribution centers to sales and collection centers should be equal.

∑∑

^{Z pdt =}

∑∑

^{Vd,st,t "d (21)}

p t st t

Products are disassembled in decomposition center and then useable parts are sent to sales and collection centers in order to meet the demand of usable components.

∑

^{rfcst, jt =}

∑

^{SSst, j,t +}

∑

^{Npjt "j (22)}

st st p

A certain part of components used in the factory to remanufacture is supplied by the dismantling center and the other parts are supplied by suppliers. Therefore, the sum of the parts that arrived should meet the need for the component of the factory.

∑∑

^{Xspjt + Npj − rcj}

∑∑

^Zpdt = 0,"p, j (23)

s t d t

Product demand of sales and collection centers supplied by final products in distribution centers.

∑∑

^{Vd,st,t = dmst ,"st (24)}

d t

The customer has two different demands as an original component and used components. The amount of original components coming from distribution centers to sales and collection centers is equal to original component stock remaining from the previous period in sales and collection centers, demand in original component and stock amount remain at the end of the period.

Sst, j +

∑∑

^{Wd,st, jt = dmsst, j + dmcst, j} "st, j (25)

d t

Certain components are renewed after the dismantling process is sent to sales and collection centers in order to meet the demand in usable and new components are send to remanufacture in the factory. As priority is to meet the demand in used component, it must be as either total amount of refurbished components after the disassembly or used component demand.

∑

^{SSst, j,t =}

∑

^{rfcst, j,t .bjt +}

∑

^{dmcst, j,t (1 − bjt} ),"j,t (26)

st st st

   

60 Logistics 4.0: Digital Transformation of Supply Chain Management

Capacity constraints for sales and collection centers are considered for each product and component.

∑∑

^{Vd,st,t ≤Capmax Ust,"st (27)}

d t

∑∑

^{Wd,st, j,t +SSjt ≤Cap maxst, j} ,"st, j (28)

d t

Capacity constraint for each supplier.

∑ ∑ ∑

_{p d t} ^Zpdt ≤Capp2_p, "p, t (29) Capacity constraint both product and components in the distribution center.

∑ ∑

st t ^{Vd,st,t ≤Capp3d, "d (30)}

∑ ∑

st t ^{Wd,st, j,t ≤Capp4djt, "d, j (31)}

The variables should be greater than zero.

X _spjt ,Y_sdjt ,Z_pdt ,W _{d st} , , jt ,V _{d st t} , ,,SS_{st , j} , N _pj ,Icc_{st , j} ≥0, "s, p, j,t,d, st (32)

4.  A Computation Experiment