# Case Study The Bi-Objective Economic Lot Scheduling Problem

In this research, we study the bi-objective economic lot scheduling problem (ELSP) considering deteriorating items in which the shortage is allowed. The considered problem is NP-hard since the ELSP is already shown as NP-hard problem. The goal of this study is to minimize two objectives simultaneously; 1) setup and inventory holding costs including deteriorating factor, 2) total number of stock out units of each item during each period. The studied ELSP problem, adopts extended basic period (EBP) approach under Power-of-Two (PoT) policy to make sure of having feasible replenishment cycles, called SDELSP_EBP_PoT. To solve the considered problem, three multi-objective algorithms, i.e., 1) non-dominated sorting genetic algorithm II (NSGAII), 2) …show more content…
The BP approach assumes that production runs of all products should be made in each BP and must be long enough to accommodate the production of all the products. Also, the replenishment cycle of each item, Ti, is an integer multiple of B, i.e., Ti = ki × B. In such a case, the objective will be changed to find a set of multipliers ki instead of a set of replenishment cycles. The solution of the ELSP is represented using a set of multipliers {ki}; i=1,2,..,n as well as the basic period (BP) in which each product is produced. The time-varying lot size approach is more flexible than CC and BP approaches and allows different lot sizes for different products in a cycle. Dobson (1987) showed that the time varying lot size approach always produce a feasible schedule, besides giving a better quality solution. The BP's in the ELSP could be segmented as either the 'BP' or the 'extended basic period' ¬(EBP) approach. The EBP method develops upon the BP by employing two consecutive cycles however forcing them an integer multiple, ki (for ith product), of some BP. EBP definitely dominates BP in solution quality however an effort should be made in developing the solution. While this approach could be generalized to load more than two consecutive basic periods, the increases in modeling and computational complexity rule this out. In addition to the aforementioned reason, one of the motivations of shifting from the BP approach to EBP is to obviate waste of capacity of the production facility due to the restrictive feasibility condition. Feasible solutions for the conventional ELSP (production schedules and lot sizes) should satisfy production plan (single machine), with no stock-out in addition to the capacity constraints. Capacity constraint is to check whether the