Mohamed Aly Ould Louly

A reactive GRASP and path relinking for a combined production-distribution problem

An NP-hard production-distribution problem for one product over a multi-period horizon is investigated. The aim is to minimize total cost taking production setups, inventory levels and distribution into account. An integer linear model is proposed as a compact problem specification but it cannot be solved to optimality for large instances. Instead of using a classical two-phase approach (production planning and then route construction for each day), metaheuristics that simultaneously tackle production and routing decisions are developed: a GRASP (greedy randomized adaptive search procedure) and two improved versions using either a reactive mechanism or a path-relinking process. These algorithms are evaluated on 90 randomly generated instances with 50, 100 and 200 customers and 20 periods. The results confirm the interest of integrating production and distribution decisions, compared to classical two-phase methods. Moreover, reaction and path-relinking give better results than the GRASP alone.

Fast heuristics for a combined production planning and vehicle routing problem

This paper studies a problem of production and distribution of one product on a multi-period horizon. The value of co-ordinating production and distribution planning is investigated. The particular scenario addressed here concerns a plant that manufactures one product that can be stored at the plant or shipped to customers who can also store it. The product is distributed by a limited fleet of vehicles to the customers whose the demands are known for each period of the planning horizon. The objective is to determine, for each period, the amount produced and the delivery trips, in order to minimise the total cost of production and distribution over the whole horizon. Two greedy heuristics followed by two local search procedures are proposed for this difficult problem. The first heuristic or uncoupled approach computes in a classical way a production plan and then a distribution plan. The second one or coupled approach determines the two plans simultaneously. The one product hypothesis is not restricted since our heuristics can be extended to cases of several products if these products can be mixed in the same vehicles without creating resource conflicts in production. These heuristics are tested on randomly generated instances with up to 200 customers and 20 periods: they are all very fast and significant savings are obtained by the coupled approach.

Decomposition approach for a problem of lot-sizing and sequencing under uncertainties

The paper addresses a problem of optimal lot-sizing and sequencing of manufacturing items for production lines. The following factors are taken into account: processing times, set-up times, random machine breakdowns and rejects. The goal is to maximize the probability of a desired output for a given period. A mathematical model of the problem and an optimization approach are discussed. This approach is based on the decomposition of the initial problem in three sub-problems: an enumeration, a travelling salesman problem and a knapsack problem. An iterative optimization procedure is proposed, based on this decomposition.

Balancing of Transfer Lines with Simultaneously Activated Spindles

Abstract A balancing problem for transfer lines with parallel spindles is investigated. All spindle heads of the same workstation are activated simultaneously. The relations of the necessity of executing some operations at the same workstation, the possibility of combining the spindles at the same workstation as well as precedence constraints are given. The problem is to choose spindle heads from a given set and allocate them to workstations in such a way that i) all the operations are performed, ii) all constraints are satisfied, iii) the cycle time is provided, and iv) the line cost is minimal. The proposed method for solving the problem is based on its formulation as a mixed integer problem (MIP).

A MEMETIC ALGORITHM WITH POPULATION MANAGEMENT FOR A PRODUCTION-DISTRIBUTION PROBLEM

Abstract This paper studies an NP-hard multi-period production-distribution problem to minimize the sum of three costs: production setups, inventories and distribution. This problem is solved by a very recent form of metaheuristic called Memetic Algorithm with Population Management (MA|PM). Contrary to classical ***two-phase methods (production planning followed by vehicle routing in each period), the algorithm simultaneously tackles production and distribution decisions. It is compared with a two-phase heuristic and a Greedy Randomized Adaptive Search Procedure (GRASP) on 90 randomly generated instances with 50, 100 or 200 customers and 20 periods. The significant savings obtained compared to the two other methods confirm both the interest of integrating production and distribution decisions and of using the MA|PM template.

Integrated optimization of production and distribution for several products

This paper proposes an integrated approach for optimizing production, inventory and distribution in a multi-period, multi-item and less-than-truckload configuration. The value of coordinating production with distribution is investigated. The objective is to minimize the sum of setup production costs, holding costs and distribution costs on the planning horizon. An iterative approach is developed for this NP-hard problem. A first production plan is obtained using integer linear programming and the distribution plan (set of vehicle trips in each period) is built using a tabu search metaheuristic that does not change the production plan. In the following iteration, an improved production plan is first determined considering the distribution plan of the previous interaction as a constraint. Then, a new distribution plan is computed given the new production plan. This iterative process stops when the two plans become stable. The iterative method is evaluated on a set of randomly generated instances. The impact of various parameters is evaluated. A comparison with a classical two-phase method shows significant savings ranging from 3.50% to 27.73%. These results underline the relevance of integrating distribution and production planning decisions

Supply Planning in Multilevel Assembly Systems Under Lead Times uncertainties

A multilevel assembly system with one type of finished product and several types of components is considered in this paper. The component lead times at each level are discrete independent random variables, and the finished product demand is fixed. The assembly of the components at each level is carried out as soon as the components necessary are available. The demand of finished product should be satisfied by the end of each period. Otherwise a backlogging cost is incurred. Components necessary to assemble the same semi-finished product that are delivered not at same time will cause holding cost. The objective is to find the optimal release dates for the components in order to minimize the total expected costs composed of the finished product backlogging cost and the component holding cost. We propose a model that gives the optimal release dates values for the components. From a theoretical point of view, it is a generalization of the well known discrete Newsboy Model

A model for an assembly system under lead time uncertainty

This paper studies a customized product assembly scenario where some of components cannot be stocked due to high component cost and risk. These key components are ordered after a demand has been registered with promised delivery date. Components lead times are stochastic and associated distribution function is known in advance. The objective is to find the ordering date for each component minimizing the expected holding and backlogging costs. An approach is proposed.