Hervé Camus

A New Cyclic Scheduling Algorithm for Flexible Manufacturing Systems

Flexible manufacturing system control is an NP-hard problem. A cyclic approach has been demonstrated to be adequate for an infinite scheduling problem because of maximal throughput reachability. However, it is not the only optimization criterion in general. In this article we consider the minimization of the work in process (WIP) as an economical and productivity factor. We propose a new cyclic scheduling algorithm giving the maximal throughput (a hard constraint) while minimizing WIP. This algorithm is based on progressive operations placing. A controlled beam search approach has been developed to determine at each step the schedule of the next operations. After presenting the main principles of the algorithm, we compare our approach to several most known cyclic scheduling algorithms using a significant existing example from the literature.

Optimal Control of a Nested-Multiple-Product Assemble-to-Order System

In this paper, we study an assemble-to-order system consisting of n products assembled from a subset of m distinct components where the products have a modular nested design, i.e. product i has only one additional component more than product i − 1. In particular, we study the optimal production and inventory allocation policies of such systems. Components are produced on independent production facilities one unit at a time, each with a finite production rate and exponentially distributed production times. The components are stocked ahead of demand and therefore incur a holding cost per unit per unit of time. Demand from each product occurs continuously over time according to a Poisson process. The demand for a particular product can be either satisfied (provided all its components are available in stock) or rejected. In the latter case, a product-dependent lost sale cost is incurred. In this situation, a manager is confronted with two decisions: when to produce a component and whether or not to satisfy an incoming product order from on-hand inventory. We show that, for the production of a component, the optimal policy is a base-stock type where the base-stock level depends on all other components’ inventory. We also show that, for inventory allocation, the optimal policy is a multi-level rationing policy where the rationing levels depend on all other components’ inventory. We propose a simple heuristic that we numerically compare against the optimal policy and show that, when carefully designed, it can be very effective.

Heuristic for the resolution of the general FMS cyclic scheduling problem

The aim of this paper is to present a new heuristic for the resolution of the general cyclic scheduling problem. This approach consists in determining a cyclic command which respects the hard constant of optimal production speed while minimizing the work in process (WIP). In fact we choose the cyclic behavior to reduce the complexity of the general scheduling problem. In addition we will minimize the WIP to satisfy the economical constraints and the access conflicts to the shared resources of the shop. One of the main interests of our method is to get close to the exact algorithm to solve the cyclic scheduling problem. Thats why we consider overlapping cycles, that means that an operation can start in a cycle and end at the next one. The obtained cyclic and deterministic command can be modeled by a Petri net subclass called marked graph and represented by a dual Gantt diagram with both resources and operating sequences points of view.

An assemble-to-order system with product and components demand with lost sales

This paper studies a single end product assemble-to-order system serving both the demand of the end product and the individual components. Demands are assumed to form independent Poisson streams with different rates. Unsatisfied demand, both for the end product and for components, is assumed lost and thus incurs a per unit lost sale penalty. The end product is assembled from K distinct components each produced on a different production facility (or procured from independent suppliers). Production lead times are non-identical and are assumed to be independent and exponentially distributed. Produced components are held in stock in anticipation of future demands. The goal is to determine the optimal component production and inventory allocation policy. The optimal policy is characterised using a Markov Decision Process model. It is shown that, in addition to the state-dependent threshold type, the optimal policy exhibits counter-intuitive features which have not been observed in systems without components demand. In particular, for certain combinations of system parameters, the optimal inventory allocation policy switches priority as the inventory level of components changes. Furthermore, for a particular component k, as the inventory level of other components increases, the desirability of satisfying Component k demand decreases. Finally, because in general the optimal policy is fairly complicated and is difficult to obtain numerically, due to the curse of dimensionality of dynamic programming, three heuristic policies are proposed. Extensive numerical experiments indicate that the three heuristics perform very well compared to the optimal policy.

Managing an Integrated Production Inventory System with Information on the Production and Demand Status and Multiple Non-Unitary Demand Classes

In this paper, we study a system consisting of a manufacturer or supplier serving several retailers or clients. The manufacturer produces a standard product in a make-to-stock fashion in anticipation of orders emanating from n retailers with different contractual agreements hence ranked/prioritized according to their importance. Orders from the retailers are non-unitary and have sizes that follow a discrete distribution. The total production time is assumed to follow a k0-Erlang distribution. Order inter-arrival time for class l demand is assumed to follow a kl-Erlang distribution. Work-in-process as well as the finished product incur a, per unit per unit of time, carrying cost. Unsatisfied units from an order from a particular demand class are assumed lost and incur a class specific lost sale cost. The objective is to determine the optimal production and inventory allocation policies so as to minimize the expected total (discounted or average) cost. We formulate the problem as a Markov decision process and show that the optimal production policy is of the base-stock type with base-stock levels non-decreasing in the demand stages. We also show that the optimal inventory allocation policy is a rationing policy with rationing levels non-decreasing in the demand stages. We also study several important special cases and provide, through numerical experiments, managerial insights including the effect of the different sources of variability on the operating cost and the benefits of such contracts as Vendor Managed Inventory or Collaborative Planning, Forecasting, and Replenishment. Also, we show that a heuristic that ignores the dependence of the base-stock and rationing levels on the demands stages can perform very poorly compared to the optimal policy.

Two stages optimization problem: New variant of Bin Packing Problem for decision making

In this paper, we present a new multi-criteria assignment problem that groups characteristics from the well known bin packing problem (BPP) and generalized assignment problem (GAP). Similarities and differences between these problems are discussed, and a new variant of BPP is presented. The new variant will be called generalized assignment problem with identified first-use bins (GAPIFB). The GAPIFB will be used to supply decision makers with quantitative and qualitative indicators in order to optimize a business process. An algorithm based on the GAP problem model and on GAPIFB is proposed.

Optimal control of a continuous-time W-configuration assemble-to-order system

We analyze a W-configuration assemble-to-order system with random lead times, random arrival of demand, and lost sales, in continuous time. Specifically, we assume exponentially distributed production and demand inter-arrival times. We formulate the problem as an infinite-horizon Markov decision process. We deviate from the standard approach by first characterizing a region (the recurrent region) of the state space where all properties of the cost function hold. We then characterize the optimal policy within this region. In particular, we show that within the recurrent region components are always produced. We also characterize the optimal component allocation policy which specifies whether an arriving product demand should be fulfilled. Our analysis reveals that the optimal allocation policy is counter-intuitive. For instance, even when one product dominates the other, in terms of lost sale cost and lost sale cost rate (i.e., demand rate times the lost sale cost), its demand may not have absolute priority over the other products demand. We also show that the structure of the optimal policy remains the same for systems with batch production, Erlang distributed production times, and non-unitary product demand. Finally, we propose efficient heuristics that can be either used as an approximation to the optimal policy or can be used as a starting policy for the common algorithms that are used to obtain the optimal policy in an effort to reduce their computational time.

Scheduling of FMS: An exact method based on CLP related to a cyclic scheduling approach

Abstract This paper deals with the contribution of Petri net (PN) modelling used for the computation of the scheduling of Flexible Manufacturing Systems (FMS). Two recent techniques of scheduling ((Korbaa and Gentina, 1997) and (Benasser et al., 1996)) are proposed using both PN (see (Murata, 1989) for concepts and notations). The first one deals with a heuristic in order to compute a cyclic command. The second one is based on an efficient reachability search in timed Petri nets by means of constraints propagation techniques. An example will be developed in this paper to illustrate the main results.

A mixed integer linear programming approach to schedule the operating room

The problem studied in this paper is to allocate and to sequence the elective operation on operating rooms (ORs). We develop a mixed integer linear programming (MILP) model to solve this problem. Decisions in this model include the allocation of operations to material resources and human resources, the starting time of them and the starting time for each surgeon. To show the efficiency of this model, we decide to compare it with a constraints programming (CP) approach. The performance of these models is tested using a benchmark of the literature. The results indicate the efficiency of the MILP model compared with the CP model in terms of computational time.

SHMP solution for surface treatment line using an hybrid constraints satisfaction algorithm

For single-hoist multi-products job shop scheduling problems, a constraints satisfaction algorithm CSA is successfully applied in this paper to find the optimal move sequence of the hoist that minimize the cycle period. Then, the CSA is hybridized with two classical heuristics to impose a criterion of selection of tasks according to their processing times. This hybridization generates better quality of solution. A real surface treatment line is studied with consideration of the minimization of the cycle time obtained by applying different algorithms. Comparative study is then presented to show the efficiency of the three proposed approaches and the preferment one is then selected.