A two-stage heuristic for disassembly scheduling with assembly product structure

Disassembly scheduling, one of the important operational problems in disassembly systems, is the problem of determining the ordering and disassembly schedules of used or end-of-life products while satisfying the demand of their parts or components over a certain planning horizon. This paper considers products with assembly structure for the objective of minimizing the sum of purchase, set up, inventory holding, and disassembly operation costs, and suggests a two-stage heuristic, in which an initial solution is obtained in the form of the minimal latest ordering and disassembly schedule, and then improved iteratively considering trade-offs among different cost factors. To show the performance of the heuristic, computational experiments were done on the example obtained from the literature and a number of randomly generated test problems, and the results show that the heuristic can give optimal or very near-optimal solutions within very short computation times.     

A branch and bound algorithm for disassembly scheduling with assembly product structure

This paper considers a production planning problem in disassembly systems, which is the problem of determining the quantity and timing of disassembling end-of-use/life products in order to satisfy the demand of their parts or components over a planning horizon. The case of single product type without parts commonality is considered for the objective of minimizing the sum of setup and inventory holding costs. To show the complexity of the problem, we prove that the problem is NP-hard. Then, after deriving the properties of optimal solutions, a branch and bound algorithm is suggested that incorporates the Lagrangean relaxation-based upper and lower bounds. Computational experiments are performed on a number of randomly generated problems and the test results indicate that the branch and bound algorithm can give optimal solutions up to moderate-sized problems in a reasonable computation time. A Lagrangean heuristic for a viable alternative for large-sized problems is also suggested and compared with the existing heuristics to show its effectiveness.     

A Heuristic for a Resource-capacitated Multi-stage Lot-sizing Problem with Lead Times

In this paper we propose a heuristic for the resource-capacitated multi-stage lot-sizing problem with general product structures, set-up costs and resource usage, work-in-process inventory costs and lead times. To facilitate the functioning of the heuristic, we use the formulation of the problem based on Echelon Stock in a rolling horizon scheme. The heuristic first obtains a reasonable solution to the corresponding uncapacitated problem and then tries to attain capacity feasibility by shifting production backwards in time. The concept of echelon stock makes the task of checking the inventory feasibility of proposed shifts easier than would be the case with conventional installation stock. The heuristic is first tested computationally for problems with a five-component product structure over a 12 period planning horizon for which optimal solutions were available and for which optimality precision guarantees were also obtained via Lagrangian Relaxation. The heuristic's performance is also explored with two different 40-component product structures, with high and low set-up costs, and is compared with the Lagrangian precision guarantees.     

A Lagrangian relaxation approach to multi-period inventory/distribution planning

We consider a multi-period inventory/distribution planning problem (MPIDP) in a one-warehouse multiretailer distribution system where a fleet of heterogeneous vehicles delivers products from a warehouse to several retailers. The objective of the MPIDP is to minimise transportation costs for product delivery and inventory holding costs at retailers over the planning horizon. In this research, the problem is formulated as a mixed integer linear programme and solved by a Lagrangian relaxation approach. A subgradient optimisation method is employed to obtain lower bounds. We develop a Lagrangian heuristic algorithm to find a good feasible solution of the MPIDP. Computational experiments on randomly generated test problems showed that the suggested algorithm gave relatively good solutions in a reasonable amount of computation time.     

A heuristic for the multi-period petrol station replenishment problem

In the multi-period petrol station replenishment problem (MPSRP) the aim is to optimize the delivery of several petroleum products to a set of petrol stations over a given planning horizon. One must determine, for each day of the planning horizon, how much of each product should be delivered to each station, how to load these products into vehicle compartments, and how to plan vehicle routes. The objective is to maximize the total profit equal to the revenue, minus the sum of routing costs and of regular and overtime costs. This article describes a heuristic for the MPSRP. It contains a route construction and truck loading procedures, a route packing procedure, and two procedures enabling the anticipation or the postponement of deliveries. The heuristic was extensively tested on randomly generated data and compared to a previously published algorithm. Computational results confirm the efficiency of the proposed methodology.     

Capacity planning for phased implementation of flexible manufacturing systems under budget restrictions

We consider a problem of gradually replacing conventional dedicated machines with flexible manufacturing modules (FMMs) under budget restrictions over a finite planning horizon assuming that dedicated machines cannot be purchased during the planning horizon and acquired FMMs are kept until the end of the horizon. In the problem, a replacement schedule is to be determined and operations are to be assigned to the FMMs or the dedicated machines with the objective of minimizing the sum of discounted costs of acquisition and operation of FMMs and operation costs of conventional dedicated machines. In this research, the problem is formulated as a mixed integer linear program and solved by a Lagrangean relaxation approach. A subgradient optimization method is employed to obtain lower bounds of solutions and a multiplier adjustment method is devised to improve the lower bounds. We develop a linear programming-based Lagrangean heuristic algorithm to find a good feasible solution of the original problem in a reasonable amount of computation time. The algorithm is tested on randomly generated test problems and the results are reported.     

A multi-period order selection problem in flexible manufacturing systems

We consider a multi-period order selection problem in flexible manufacturing systems, which is the problem of selecting orders to be produced in each period during the upcoming planning horizon with the objective of minimising earliness and tardiness costs and subcontracting costs. The earliness and tardiness costs are incurred if an order is not finished on time, while subcontracting cost is incurred if an order is not selected within the planning horizon (and must be subcontracted) due to processing time capacity or tool magazine capacity. This problem is formulated as a 0–1 integer program which can be transformed into a generalised assignment problem. To solve the problem, a heuristic algorithm is developed using a Lagrangian relaxation technique. Effectiveness of the algorithm is tested on randomly generated problems and results are reported.     

Dynamic economic lot size model with perishable inventory and capacity constraints

In this study, we consider a dynamic economic lot sizing problem for a single perishable item under production capacities. We aim to identify the production, inventory and backlogging decisions over the planning horizon, where (i) the parameters of the problem are deterministic but changing over time, and (ii) producer has a constant production capacity that limits the production amount at each period and is allowed to backorder the unmet demand later on. All cost functions are assumed to be concave. A similar problem without production capacities was studied in the literature and a polynomial time algorithm was suggested (Hsu, 2003 [1]). We assume age-dependent holding cost functions and the deterioration rates, which are more realistic for perishable items. Backordering cost functions are period-pair dependent. We prove the NP-hardness of the problem even with zero inventory holding and backlogging costs under our assumptions. We show the structural properties of the optimal solution and suggest a heuristic that finds a good production and distribution plan when the production periods are given. We discuss the performance of the heuristic. We also give a Dynamic Programing-based heuristic for the solution of the overall problem.     

Simple dynamic location problem with uncertainty: a primal-dual heuristic approach

Abstract

In this paper, the simple dynamic facility location problem is extended to uncertain realizations of the potential locations for facilities and the existence of customers as well as fixed and variable costs. With limited knowledge about the future, a finite and discrete set of scenarios is considered. The decisions to be made are where and when to locate the facilities, and how to assign the existing customers over the whole planning horizon and under each scenario, in order to minimize the expected total costs. Whilst assignment decisions can be scenario dependent, location decisions have to take into account all possible scenarios and cannot be changed according to each scenario in particular. We first propose a mixed linear programming formulation for this problem and then we present a primal-dual heuristic approach to solve it. The heuristic was tested over a set of randomly generated test problems. The computational results are provided.     

Multi-Item Single-Level Capacitated Dynamic Lot-Sizing Heuristics: A General Review

The multi-item single-level capacitated lot-sizing problem consists of scheduling N different items over a horizon of T periods. The objective is to minimize the sum of set-up and inventory-holding costs over the horizon, subject to a capacity restriction in each period. Different heuristic approaches have been suggested to solve this difficult mathematical problem. So far, only a few limited attempts have been made to analyse and compare these approaches. The paper can be divided into two main parts. The first part shows that current heuristics can be classified in two different categories: single-resource heuristics, which are special-purpose methods, and mathematical-programming-based heuristics, which can usually deal with more general problem environments. The second part is devoted to an extensive computational review. The general idea is to find relationships between the performance of the heuristic and the computational burden involved in finding the solution. Based on these computational results, suggestions can be given with respect to the usefulness of the various heuristics in different industrial settings.     

Disassembly EOQ models with price-sensitive demands

The disassembly economic order quantity problem is to determine the quantities of a product to be disassembled at different times over an infinite planning horizon by considering ordering, operation, and inventory costs. The demands for the components are independent, which can lead to accumulations of unnecessary inventories over time. This article proposes the models which integrate price-sensitive demands and disposal decisions in disassembly economic order quantity problems to maximize the profit of disassembly systems without inventory accumulations. Three models are developed and analyzed to obtain solution approaches that give prices, the replenishment cycle time (or, equivalently, the order quantity), and the disposal quantity. The inventory policy integrating both pricing and disposal decisions allows higher profits to be achieved. A numerical experiment shows its efficiency and highlights its potential implementation in practical cases.     

Asymptotic Analysis of a Greedy Heuristic for the Multi-Period Single-Sourcing Problem: The Acyclic Case

The multi-period single-sourcing problem that we address in this paper can be used as a tactical tool for evaluating logistics network designs in a dynamic environment. In particular, our objective is to find an assignment of customers to facilities, as well as the location, timing and size of production and inventory levels, that minimizes total assignment, production, and inventory costs. We propose a greedy heuristic, and prove that this greedy heuristic is asymptotically optimal in a probabilistic sense for the subclass of problems where the assignment of customers to facilities is allowed to vary over time. In addition, we prove a similar result for the subclass of problems where each customer needs to be assigned to the same facility over the planning horizon, and where the demand for each customer exhibits the same seasonality pattern. We illustrate the behavior of the greedy heuristic, as well as some improvements where the greedy heuristic is used as the starting point of a local interchange procedure, on a set of randomly generated test problems. These results suggest that the greedy heuristic may be asymptotically optimal even for the cases that we were unable to analyze theoretically.     

A two-phase heuristic approach to the bike repositioning problem

An approach to overcome the bike imbalance problem is to transfer excess bikes to branches with bike shortages. This study develops a constrained mathematical model to deal with a multi-vehicle bike-repositioning problem, and aims to minimize the sum of transportation and unmet demand costs over a planning horizon through bike-transfer strategies under a minimum service requirement. A two-phase heuristic based on linear programming was proposed to solve the problem and produce compromising solutions. In the first phase, the paper developed a linear programming model to quickly develop decisions related to bike inventory, unloading, and loading for all stations for each time slot. In the second phase, this paper proposed an iterative approach through two parameter sensitive mathematical models to sequentially reduce the problem scale to develop decisions related to bike transfers. Computational results show that the proposed approach is superior to a CPLEX optimizer and a hybrid heuristic based on a genetic algorithm. The proposed approach was used to analyze the bicycle system in Taiwan. The impacts of various system parameters on the system were also investigated.     

Furniture supply chain tactical planning optimization using a time decomposition approach

We study the supply chain tactical planning problem of an integrated furniture company located in the Province of Québec, Canada. The paper presents a mathematical model for tactical planning of a subset of the supply chain. The decisions concern procurement, inventory, outsourcing and demand allocation policies. The goal is to define manufacturing and logistics policies that will allow the furniture company to have a competitive level of service at minimum cost. We consider planning horizon of 1 year and the time periods are based on weeks. We assume that customer’s demand is known and dynamic over the planning horizon. Supply chain planning is formulated as a large mixed integer programming model. We developed a heuristic using a time decomposition approach in order to obtain good solutions within reasonable time limit for large size problems. Computational results of the heuristic are reported. We also present the quantitative and qualitative results of the application of the mathematical model to a real industrial case.     

Production strategies for a stochastic lot-sizing problem with constant capacity

This paper presents a single item capacitated stochastic lot-sizing problem motibated by a Dutch company operating in a Make-To-Order environment. Due to a highly fluctuating and unpredictable demand, it is not possible to keep any finished goods inventory. In response to a customer's order, a fixed delivery date is quoted by the company. The objective is to determine in each period of the planning horizon the optimal size of production lots so that delivery dates are met as closely as possible at the expense of minimal average costs. These include set-up costs, holding costs for orders that are finished before their promised delivery date and penalty costs for orders that are not satisfied on time and are therefore backordered. Given that the optimal production policy is likely to be too complex in this situation, attention is focused on the development of heuristic procedures. In this paper two heuristics are proposed. The first one is an extension of a simple production strategy derived by Dellaert [5] for the uncapacitated version of the problem. The second heuristic is based on the well-known Silver-Meal algorithm for the case of deterministic time-varying demand. Experimental results suggest that the first heuristic gives low average costs especially when the demand variability is low and there are large differences in the cost parameters. The Silver-Meal approach is usually outperformed by the first heuristic in situations where the available production capacity is tight and the demand variability is low.     

New heuristic for the dynamic layout problem

The dynamic layout problem addresses the situation where the traffic among the various units within a facility changes over time. Its objective is to determine a layout for each period in a planning horizon such that the total of the flow and the relocation costs is minimized. The problem is computationally very hard and has begun to receive attention only recently. In this paper, we present a new heuristic scheme, based on the idea of viable layouts, which is easy to operationalize. A limited computational study shows that, depending upon how it is implemented, this scheme can be reasonably fast and can yield results that are competitive with those from other available solution methods.     

Optimal policy for a dynamic,non-stationary,stochastic inventory problem with capacity commitment

This paper studies a single-product, dynamic, non-stationary, stochastic inventory problem with capacity commitment, in which a buyer purchases a fixed capacity from a supplier at the beginning of a planning horizon and the buyer’s total cumulative order quantity over the planning horizon is constrained with the capacity. The objective of the buyer is to choose the capacity at the beginning of the planning horizon and the order quantity in each period to minimize the expected total cost over the planning horizon. We characterize the structure of the minimum sum of the expected ordering, storage and shortage costs in a period and thereafter and the optimal ordering policy for a given capacity. Based on the structure, we identify conditions under which a myopic ordering policy is optimal and derive an equation for the optimal capacity commitment. We then use the optimal capacity and the myopic ordering policy to evaluate the effect of the various parameters on the minimum expected total cost over the planning horizon.     

Heuristic algorithms for a multi-period multi-stop transportation planning problem

We consider a multi-period multi-stop transportation planning problem (MPMSTP) in a one-warehouse multi-retailer distribution system where a fleet of homogeneous vehicles delivers products from a warehouse to retailers. The objective of the MPMSTP is to minimize the total transportation distance for product delivery over the planning horizon while satisfying demands of the retailers. We suggest two heuristic algorithms based on the column generation method and the simulated annealing algorithm. Computational experiments on randomly generated test problems showed that the suggested algorithms gave better solutions than an algorithm currently used in practice and algorithms modified from existing algorithms for vehicle routing problems.     

Economic lot sizes and vehicle scheduling

In this paper a relationship between the vehicle scheduling problem and the dynamic lot size problem is considered. For the latter problem we assume that order quantities for different products can be determined separately. Demand is known over our n-period production planning horizon. For a certain product our task is to decide for each period if it should be produced or not. If it is produced, what is its economic lot size? Our aim here is to minimize the combined set-up and inventory holding costs. The optimal solution of this problem is given by the well-known Wagner-Whitin dynamic lot size algorithm. Also many heuristics for solving this problem have been presented. In this article we point out the analogy of the dynamic lot size problem to a certain vehicle scheduling problem. For solving vehicle scheduling problems the heuristic algorithm developed by Clark and Wright in very often used. Applying this algorithm to the equivalent vehicle scheduling problem we obtain by analogy a simple heuristic algorithm for the dynamic lot size problem. Numerical results indicate that computation time is reduced by about 50% compared to the Wagner-Whitin algorithm. The average cost appears to be approximately 0.8% higher than optimum.     

Joint replacement in an operational planning phase

We consider the problem of combining replacements of multiple components in an operational planning phase. Within an infinite or finite time horizon, decisions concerning replacement of components are made at discrete time epochs. The optimal solution of this problem is limited to only a small number of components. We present a heuristic rolling horizon approach that decomposes the problem; at each decision epoch an initial plan is made that addresses components separately, and subsequently a deviation from this plan is allowed to enable joint replacement. This approach provides insight into why certain actions are taken. The time needed to determine an action at a certain epoch is only quadratic in the number of components. After dealing with harmonisation and horizon effects, our approach yields average costs less than 1% above the minimum value.