Discrete Lot-sizing And Scheduling Problem Research Articles

Discrete lot-sizing and scheduling problems considering renewable energy and CO2 emissions

Scheduling research increasingly focuses on reducing carbon emissions. Curbing carbon emissions during production and operation processes based on renewable energy sources is thus of priority concern. Therefore, this study analyzes two variants of the discrete lot-sizing and scheduling problem (DLSP): (1) a bi-objective DLSP in which renewable energy is considered and earliness tardiness and CO2 emissions are minimized simultaneously; (2) a DLSP in which renewable energy is considered and earliness tardiness is minimized, subject to a constraint on the CO2 emissions. Non-dominated solutions for the bi-objective DLSP are subsequently derived using the lexicographic weighted Tchebycheff (LWT) method. Experimental results clearly demonstrate that the LWT method is superior to the conventionally used weighted-sum method. In terms of practical applications, guidelines on how to set the number of periods, battery capacity, and carbon emissions constraints are also studied. Results of this study have significant managerial implications for actual production.

Exact solution approaches for the discrete lot-sizing and scheduling problem with parallel resources

We consider a production planning problem known as the discrete lot-sizing and scheduling problem (DLSP) and study a variant of the DLSP involving several identical parallel resources. We show how to solve the resulting discrete optimisation problem as a mixed-integer linear program using a commercial MIP solver. To achieve this, we exhibit a family of strong valid inequalities for which the associated separation problem is efficiently solvable. Our computational results show that the proposed solution algorithm is capable of providing optimal solutions for medium-sized instances.

Heuristic lot size scheduling on unrelated parallel machines with applications in the textile industry

In this paper, we present an industrial problem found in a company that produces acrylic fibres to be used by the textile industry. The problem is a particular case of the discrete lot sizing and scheduling problem (DLSP). In this problem, lots of similar products must be generated and sequenced in ten unrelated parallel machines, in order to minimize tool changeovers and the quantity of fibre delivered after the required due date. The company problem is original because a changeover can occur between two lots of the same product due to tool wear. We analyse the problem in detail and present an adaptation of a heuristic found in the literature to solve it. Results obtained with the proposed heuristic are compared with results that used to be obtained by the production planner, using historical data.

Simultaneous lot sizing and scheduling for multi-product multi-level production

The paper deals with the multi-level lot sizing and scheduling problem for job shop production in capacitated, dynamic and deterministic cases. Demand is to be fulfilled without backlogging. The multi-level lot sizing and scheduling models of the literature are small bucket problems such as the discrete lot sizing and scheduling problem (DLSP) and the proportional lot sizing and scheduling problem (PLSP). In contrast we develop a big bucket model for multi-product multi-level production. The multi-level general lot sizing and scheduling problem with multiple machines (MLGLSP_MM) is based on the general lot sizing and scheduling problem (GLSP) for single-level production. Our focus is on minimising the sum of sequence dependent setup costs, inventory costs, production costs and the costs of maintaining the setup conditions of the machines. Inventory costs will be calculated exactly. In addition sequence dependent setup times are considered. Finally, our approach minimises the lead-time of semi-finished goods and the throughput time of finished goods.

Problems, Models and Complexity. Part II: Application to the DLSP

In Part I of this study, we suggest to identify an operations research (OR) problem with the equivalence class of models describing the problem and enhance the standard computer-science theory of computational complexity to be applicable to this situation of an often model-based OR context. The Discrete Lot-sizing and Scheduling Problem (DLSP) is analysed here in detail to demonstrate the difficulties which can arise if these aspects are neglected and to illustrate the new theoretical concept. In addition, a new minimal model is introduced for the DLSP which makes this problem eventually amenable to a rigorous analysis of its computational complexity.

The discrete lot-sizing and scheduling problem: Complexity and modification for batch availability

The discrete lot-sizing and scheduling problem (DLSP) has been suggested for the simultaneous choice of lot sizes and production schedules. In the context of computational complexity, it turns out that literature results for the DLSP are incorrect. Therefore, we prove that the decision version of the DLSP is NP-hard in the strong sense. The common assumption of instantaneous availability of the manufactured units is not satisfied in practice if the units arrive in inventory only in one batch after the whole lot has been completed. Therefore, additional constraints are presented for this case of batch availability on a single machine. The resulting modified DLSP is formulated as a mixed-integer linear program. This problem can be shown to be NP-hard again using ideas similar to the item-availability case. Hence, a two-phase simulated-annealing (SA) heuristic is suggested for solving the DLSP in the case of batch availability. Numerical results are presented for different problem classes.

A two-phase genetic algorithm to solve variants of the batch sequencing problem

We introduce the batch sequencing problem (BSP) with item and batch availability for the single-machine and two-machine flow-shop case. We propose a genetic algorithm which solves the BSP through a decomposition into a phase I-batching and a phase II-scheduling decision. The batch sequencing problem is closely related to the discrete lotsizing and scheduling problem (DLSP). Computational experience shows that the genetic algorithm for solving the BSP favourably compares with procedures for solving the DLSP.

Remarks on: “Some Extensions of the Discrete Lotsizing and Scheduling Problem”

Saloman et al. (Salomon, M., L. G. Kroon, R. Kuik, L. N. Van Wassenhove. 1991. Some extensions of the discrete lotsizing and scheduling problem. Management Sci. 37 801–812.) claim the NP-completeness of different variants of the discrete lot-sizing and scheduling problem (DLSP) which are differentiated by using a six-field notation. However, some of the given proofs are incorrect because the transformations employed map certain data values of the preimage problem to the number of data in the resulting instance and are hence not polynomial. As an example, we concentrate here on the 1/*/SI/G/A-optimization problem (Salomon et al. [Salomon, M., L. G. Kroon, R. Kuik, L. N. Van Wassenhove. 1991. Some extensions of the discrete lotsizing and scheduling problem. Management Sci. 37 801–812.], Theorem 3). Similar arguments pertain to the 1/*/A/G/SI-DLSP, too.

DLSP for two-stage multi-item batch production

Abstract The standard mixed-integer linear model formulation for the multi-item discrete lot-sizing and scheduling problem (DLSP) is extended by additional partially nonlinear constraints for the case of two-stage batch production. The corresponding feasibility problem is NP-complete in the case of non-zero setup limes. A simulated annealing approach is suggested for computing production schedules on both stages. Numerical results are presented.

The single-item discrete lotsizing and scheduling problem: optimization by linear and dynamic programming

This paper considers the single-item discrete lotsizing and scheduling problem (DLSP). DLSP is the problem of determining a minimal cost production schedule, that satisfies demand without backlogging and does not violate capacity constraints. We formulate DLSP as an integer programming problem and present two solution procedures. The first procedure is based on a reformulation of DLSP as a linear programming assignment problem, with additional restrictions to reflect the specific (setup) cost structure. For this linear programming (LP) formulation it is shown that, under certain conditions on the objective, the solution is all integer. The second procedure is based on dynamic programming (DP). Under certain conditions on the objective function, the DP algorithm can be made to run very fast by using special properties of optimal solutions.

A Dual Ascent and Column Generation Heuristic for the Discrete Lotsizing and Scheduling Problem with Setup Times

In this paper the Discrete Lotsizing and Scheduling Problem (DLSP) with setup times is considered. DLSP is the problem of determining the sequence and size of production batches for multiple items on a single machine. The objective is to find a minimal cost production schedule such that dynamic demand is fulfilled without backlogging. DLSP is formulated as a Set Partitioning Problem (SPP). We present a dual ascent and column generation heuristic to solve SPP. The quality of the solutions can be measured, since the heuristic generates lower and upper bounds. Computational results on a personal computer show that the heuristic is rather effective, both in terms of quality of the solutions as well as in terms of required memory and computation time.

Some Extensions of the Discrete Lotsizing and Scheduling Problem

In this paper the Discrete Lotsizing and Scheduling Problem (DLSP) is considered. DLSP relates to capacitated lotsizing as well as to job scheduling problems and is concerned with determining a feasible production schedule with minimal total costs in a single-stage manufacturing process. This involves the sequencing and sizing of production lots for a number of different items over a discrete and finite planning horizon. Feasibility of production schedules is subject to production quantities being within bounds set by capacity. A problem classification for DLSP is introduced and results on computational complexity are derived for a number of single and parallel machine problems. Furthermore, efficient algorithms are discussed for solving special single and parallel machine variants of DLSP.