A Novel MILP Model for the Production, Lot Sizing, and Scheduling of Automotive Plastic Components on Parallel Flexible Injection Machines with Setup Common Operators

Table 2

Nomenclature for the model.

Index
i	Index of machines i ∈ {1, …, I}
j	Index of tools j ∈ {1, …, J}
k	Index of products (parts) k ∈ {1, …, K}
t	Index of time periods t ∈ {1, …, T}
Data
aj	Total amount of tools j available for production
cbk	Backorder cost of product k
cik	Inventory cost of product k
covkt	Stock coverage defined as the number of time periods for the stock minimum coverage of product k during time period t
crij	Setup cost of tool j on machine i
csj	Setup cost of preparing tool j
cstk	Coverage stockout cost of product k
dkt	Demand of product k during time period t
INVk0	Initial inventory of product k
INVMAXk	Maximum inventory units for product k during time period t
INVMINk	Minimum inventory units for product k during time period t
nct	Amount of tool changes allowed during time period t
npjk	Amount of products k no longer produced when tool j is set up
pjk	Amount of products k produced when tool j is set up
rij	1 if tool j can be set up on machine i; 0 otherwise
tpt	Production time available during time period t
Decision variables
Bkt	Backorder of product k during time period t
INVkt	Inventory level of product k at the end of time period t
SAijt	1 if tool j is set up on machine i during time period t and is not set up on machine i during time period t − 1; 0 if tool j is set up on machine i during time period t − 1
Sijt	1 if tool j is set up on machine i during time period t; 0 otherwise
STktt	Coverage stockout of product k during time period
TPijt	Production time of tool j set up on machine i during time period t
Xkt	Amount of product k to produce during time period t
Xnpkt	Amount of product k no longer produced during time period t, while a tool is set up
	Amount of product k to produce during time period t by subtracting Xnpkt