The Synchronized and Integrated Two-Level Lot Sizing and Scheduling Problem: Evaluating the Generalized Mathematical Model

Table 1

Guideline for line and tank constraints.

Line constraints	Tank constraints	Meaning
(2)	(30)	Assignments not allowed for lines and tanks
(3)	(31)	Assignments of products or raw materials to slots
(4), (16), and (17)	(32)–(34)	Link between the products or raw material assignments and the respective lot size produced or stored.
(7)	(35) and (36)	Products or raw materials changeover.
(8) and (9)	(37) and (38)	Changeover setup time
(10)	(39)	Macro-period capacity
(5) and (6)	(64) and (65)	Inventory balance
(11)–(13)	(41)–(43)	Available capacity between endings of two consecutive slots.
(14) and (15)	(44)–(47)	Define only one beginning and only one ending for each slot.
(18)–(21), (23)–(24)	(51)–(57), (59)–(61)	Define the beginning and the ending for a slot effectively used or not.
(22)	(58)	Define an order for slot occupation
(25), (28), and (29)	(40), (48), (64), and (65)	Synchronize when a slot of raw material is taken from tanks and produced by lines.
(26) and (27)	—	Use of the capacity of the first micro-period of each slot.
—	(62), (63), and (65)	Refilling of tanks