El-Houssaine Aghezzaf

An integrated production and preventive maintenance planning model

We are given a set of items that must be produced in lots on a capacitated production system throughout a specified finite planning horizon. We assume that the production system is subject to random failures, and that any maintenance action carried out on the system, in a period, reduces the system’s available production capacity during that period. The objective is to find an integrated lot-sizing and preventive maintenance strategy of the system that satisfies the demand for all items over the entire horizon without backlogging, and which minimizes the expected sum of production and maintenance costs. We show how this problem can be formulated and solved as a multi-item capacitated lot-sizing problem on a system that is periodically renewed and minimally repaired at failure. We also provide an illustrative example that shows the steps to obtain an optimal integrated production and maintenance strategy.

Capacity planning and warehouse location in supply chains with uncertain demands

We discuss the strategic capacity planning and warehouse location problem in supply chains operating under uncertainty. In particular, we consider situations in which demand variability is the only source of uncertainty. We first propose a deterministic model for the problem when all relevant parameters are known with certainty, and discuss related tractability and computational issues. We then present a robust optimization model for the problem when the demand is uncertain, and demonstrate how robust solutions may be determined with an efficient decomposition algorithm using a special Lagrangian relaxation method in which the multipliers are constructed from dual variables of a linear program.

Modeling inventory routing problems in supply chains of high consumption products

Given a distribution center and a set of sales-points with their demand rates, the objective of the inventory routing problem (IRP) is to determine a distribution plan that minimizes fleet operating and average total distribution and inventory holding costs without causing a stock-out at any of the sales-points during a given planning horizon. We propose a new model for the long-term IRP when demand rates are stable and economic order quantity-like policies are used to manage inventories of the sales-points. The proposed model extends the concept of vehicle routes (tours) to vehicle multi-tours. To solve the nonlinear mixed integer formulation of this problem, a column generation based approximation method is suggested. The resulting sub-problems are solved using a savings-based approximation method. The approach is tested on randomly generated problems with different settings of some critical factors to compare our model using multi-tours as basic constructs to the model using simple tours as basic constructs.

Optimising part feeding in the automotive assembly industry: deciding between kitting and line stocking

In a synchronous and fast-paced assembly line operation, it is crucial that the right parts are being supplied at the right time and at the right place. In automotive assembly, the need for efficient material handling part delivery is particularly great because of extensive product customisation and the lack of space to stock all the required parts at the assembly line. This paper introduces a mathematical cost model for evaluating the assignment of parts to one of two possible material supply systems: kitting or line stocking. Case data from an automotive company in Belgium is used to test the model. The results demonstrate that hybrid policies, where some parts will be kitted while others will be stocked in bulk at the line, are preferred to the exclusive use of either material delivery system. The factors influencing the preferred delivery method for individual parts are explored. Numerical results are presented.

Models for robust tactical planning in multi-stage production systems with uncertain demands

We consider the problem of designing robust tactical production plans, in a multi-stage production system, when the periodic demands of the finished products are uncertain. First, we discuss the concept of robustness in tactical production planning and how we intend to approach it. We then present and discuss three models to generate robust tactical plans when the finished-product demands are stochastic with known distributions. In particular, we discuss plans produced, respectively, by a two-stage stochastic planning model, by a robust stochastic optimization planning model, and by an equivalent deterministic planning model which integrates the variability of the finished-product demands. The third model uses finished-product average demands as minimal requirements to satisfy, and seeks to offset the effect of demand variability through the use of planned capacity cushion levels at each stage of the production system. An experimental study is carried out to compare the performances of the plans produced by the three models to determine how each one achieves robustness. The main result is that the proposed robust deterministic model produces plans that achieve better trade-offs between minimum average cost and minimum cost variability. Moreover, the required computational time and space are by far less important in the proposed robust deterministic model compared to the two others.

Safety stock placement problem in capacitated supply chains

Todays highly competitive business environment forces supply chain managers to maintain high service levels while keeping inventory-related costs as low as possible. Therefore, placing the right amount of safety stock at the right places in the supply chain is an important aspect of effective inventory management. This safety stock placement problem, for which some solution strategies have been proposed in the case of uncapacitated supply chains, becomes much more complicated when, in addition to the variability of the demand, capacity constraints also come into play. In this paper we propose a model to locate safety stocks in a capacitated supply chain with the objective of maintaining the required service level. The underlying relationships linking excess capacity, demand variability, and service levels are analysed to gain deeper understanding of the safety stock placement problem in capacitated supply chains. Based on these relationships a solution approach for the problem is proposed and is tested with Monte Carlo simulation.

A fast solution method for the time-dependent orienteering problem

This paper introduces a fast solution procedure to solve 100-node instances of the time-dependent orienteering problem (TD-OP) within a few seconds of computation time. Orienteering problems occur in logistic situations were an optimal combination of locations needs to be selected and the routing between the selected locations needs to be optimized. In the time-dependent variant, the travel time between two locations depends on the departure time at the first location. Next to a mathematical formulation of the TD-OP, the main contribution of this paper is the design of a fast and effective algorithm to tackle this problem. This algorithm combines the principles of an ant colony system (ACS) with a time-dependent local search procedure equipped with a local evaluation metric. Additionally, realistic benchmark instances with varying size and properties are constructed. The average score gap with the known optimal solution on these test instances is only 1.4% with an average computation time of 0.5seconds. An extensive sensitivity analysis shows that the performance of the algorithm is insensitive to small changes in its parameter settings.

Robust distribution planning for supplier-managed inventory agreements when demand rates and travel times are stationary

Supplier-managed inventory (SMI) is a partnering agreement between a supplier and his customers. Under this SMI agreement, inventory monitoring and ordering responsibilities are entirely transferred to the supplier. Subsequently, the supplier decides both the quantity and timing of his customer deliveries. The inventory routing problem is an underlying optimization model for SMI partnerships to cost-effectively coordinate and manage customer inventories and related replenishments logistics. This paper discusses the case where customer demand rates and travel times are stochastic but stationary, and proposes a version of the inventory routing optimization model that generates optimal robust distribution plans. The approach proposed to obtain and deploy these robust plans combines optimization and Monte Carlo simulation. Optimization is used to determine the robust distribution plan and simulation is used to fine-tune the plans critical parameters such as replenishment cycle times and safety stock levels. Results of a simplified real-life case implementing the proposed optimization-simulation approach are shown and discussed in detail.

Selective maintenance optimization when quality of imperfect maintenance actions are stochastic

Abstract This paper addresses the selective maintenance optimization problem in a multi-component system, carrying out several missions with scheduled inter-mission breaks. To improve the probability of the system successfully completing the next mission, maintenance is performed on the system׳s components during the break. Each component is assigned a list of eligible maintenance actions ranging from minimal repair, through intermediate imperfect maintenance actions, to replacement. The quality of a maintenance action is assumed to be stochastic, reflecting the degree of expertise of the repairman and the tools used to perform the maintenance action. This quality is thus treated as a random variable with an identified probability distribution. The selective maintenance problem aims thus at finding a cost-optimal subset of maintenance actions, to be performed on the system during the limited duration of the break, which guarantees that the pre-set minimum probability of successfully completing the next mission is attained. The fundamental constructs and the relevant parameters of this nonlinear and stochastic optimization problem are developed and thoroughly discussed. It is then put into practice for a series–parallel system and the added value of solving it as a stochastic problem is demonstrated on some test cases.

Optimizing production and imperfect preventive maintenance planning׳s integration in failure-prone manufacturing systems

Abstract This paper investigates the issue of integrating production and maintenance planning in a failure-prone manufacturing system. It is assumed that the system׳s operating state is stochastically predictable, in terms of its operating age, and that it can accordingly be preventively maintained during preplanned periods. Preventive maintenance is assumed to be imperfect, that is when performed, it brings the manufacturing system to an operating state that lies between ‘as bad as old’ and ‘as good as new’. Only an overhauling of the system brings it to a ‘as good as new’ operating state again. A practical integrated production and preventive maintenance planning model, that takes into account the system׳s manufacturing capacity and its operational reliability state, is developed. The model is naturally formulated as a mixed-integer non-linear optimization problem, for which an extended mixed-integer linear reformulation is proposed. This reformulation, while it solves the proposed integrated planning problem to optimality, remains quite demanding in terms of computational time. A fix-and-optimize procedure, that takes advantage of some properties of the original model, is then proposed. The reformulation and the fix-and-optimize procedure are tested on some test instances adapted from those available in the literature. The results show that the proposed fix-and-optimize procedure performs quite well and opens new research direction for future improvements.