Nomenclature

Index set

Dimension

Unit

Definition

s є S

{s}

-

Supplier

p є P

{p}

-

Production plant

r є R

{r}

-

Distribution center

c ϵ C

{c}

-

Customer

t ϵ T

{T}

-

Time period, t = 1, 2, 3, …, n

f ϵ F

{F}

-

Type of raw material, f = 1, 2, 3, ..., n

g ϵ G

{G}

-

Type of product, e.g., Product g

General data

Definition

RMC

{s}

$/unit

Raw material cost of product g

BOM

{p}

unit

Bill of raw material, BOM. Amount of raw material needed to make g

MIC

{p}

unit

Maximum inventory capacity of plant p

MRC

{r}

unit

Maximum inventory capacity of distribution center r

Decision Variables

Definition

BQ

{s}

unit

Purchase quantity of raw material f from supplier s in time period t

PQ

{p}

unit

Manufacturer product quantity of g from plant p in time period t

ILR

{p}

unit

k’th inventory level of raw material remain in plant p in time period t

ILG

{p}

unit

k’th inventory level of finished product g in plant p in time period t

IL

{p}

unit

Inventory level of plant p which keep raw material and finished product g in time period t

IR

{r}

unit

k’th inventory level of distribution center r in time period t

PR

{p}

unit

Quantity of product g shipped from plant p to distribution center r in time period t

PE

{r}

unit

Quantity of product g shipped from retailer r to customer c in time period t

DB

{p}

unit

Quantity of demand backlog in plant p in time period t