Christian Van Delft

Efficient scheduling rules in a combined make-to-stock and make-to-order manufacturing system

In this paper, we consider a mixed MTS/MTO policy to manage a single manufacturing facility producing two classes of end-products. A few end-products have high volume demands, whereas a fairly large number of end-products have low volume demands. In this situation, it is appealing to try to produce the high volume products according to an MTS policy and the low volume products according to an MTO policy. The purpose of this paper is to analyze and compare the impact of the choice of the scheduling policy on the overall performance of the system. We consider two policies: the classical FIFO policy and a priority policy (PR). The PR policy gives priority to production orders corresponding to low volume products over production orders corresponding to high volume products. Under some simple stochastic modeling assumptions, we develop analytical/numerical solutions to optimise each system. We then provide insights regarding this issue with the help of numerical examples. It appears that for some range of parameters, the PR rule can outperform the FIFO rule in the sense that, to achieve the same service level constraint, the corresponding cost under the PR rule is much lower. This situation is encountered when the low volume products can be managed with an MTO policy under the PR scheduling rule, while they have to be managed according to an MTS policy under the FIFO scheduling rule. We also derive some theoretical properties that support our empirical findings.

Convergence of stochastic approximation coupled with perturbation analysis in a class of manufacturing flow control models

This paper deals with a class of piecewise determinstic control systems for which the optimal control can be approximated through the use of an optimization-by-simulation approach. The feedback control law is restricted to belong to an a priori fixed class of feedback control laws depending on a (small) finite set of parameters. Under some general conditions developed in this paper, infinitesimal perturbation analysis (IPA) can be used to estimate the gradient of the objective function with respect to these parameters for finite horizon simulation and the consistency of the IPA estimators, as the simulation length goes to infinity, is assured. Also, the parameters can be optimized through a stochastic approximation (SA) algorithm combined with IPA. We prove that in this context, under appropriate conditions, such an approach converges towards the optimum.

Staffing a call center with uncertain non-stationary arrival rate and flexibility

We consider a multi-period staffing problem in a single-shift call center. The call center handles inbound calls, as well as some alternative back-office jobs. The call arrival process is assumed to follow a doubly non-stationary stochastic process with a random mean arrival rate. The inbound calls have to be handled as quickly as possible, while the back-office jobs, such as answering emails, may be delayed to some extent. The staffing problem is modeled as a generalized newsboy-type model under an expected cost criterion. Two different solution approaches are considered. First, by discretization of the underlying probability distribution, we explicitly formulate the expected cost newsboy-type formulation as a stochastic program. Second, we develop a robust programming formulation. The characteristics of the two methods and the associated optimal solutions are illustrated through a numerical study based on real-life data. In particular we focus on the numerical tractability of each formulation. We also show that the alternative workload of back-office jobs offers an interesting flexibility allowing to decrease the total operating cost of the call center.

Discounted costs, obsolescence and planned stockouts with the EOQ formula

Abstract In this paper, we propose a simple economic order quantity for a class of inventory management problems concerning items with a short and stochastic lifetime. The analysis is relevant to the management of items in industries subject to fast technological progress, where the obsolescence rate is large. The approach is performed in the framework of the total discounted cost criterion. A new economic order quantity is computed; it may turn out to be significantly smaller than the one given by Wilson formula. Finally, we show that a policy maker who faces the risk of obsolescence, can plan stockouts if sufficiently many customers accept late delivery.

Automatic formulation of stochastic programs via an algebraic modeling language

This paper presents an open source tool that automatically generates the so-called deterministic equivalent in stochastic programming. The tool is based on the algebraic modeling language ampl. The user is only required to provide the deterministic version of the stochastic problem and the information on the stochastic process, either as scenarios or as a transitions-based event tree.

Two-stage flexible supply contract with payback and information update

In this paper, we consider a two-stage supply contract model for advanced reservation of capacity, with payback option at the beginning of the selling season. Between the two decision stages, external information is collected that serves to update the demand forecast and permits to adjust the decisions of the first stage by exercising options or by returning some units to the supplier. The demand occurs during a single selling period. At the end of the period, the remaining inventory, if any, is sold at a salvage value. During the selling season, any satisfied demand is charged with a unit selling price and any unsatisfied demand is lost. The objective of the model is to determine the quantities to be ordered before the beginning of the selling season which can be interpreted as the amount of capacity to be reserved, in order to satisfy optimally the demand.

A generalized single product and single-period inventory problem with non-linear parameters

In this paper, we extend the study of the classical single-period newsboy inventory problem by considering costs that are non-linear functions of the decision variable. We assume that the demand probability density function is known to the decision maker. We prove that, under some much more relaxed conditions, the total expected profit function remains concave and classical optimization methods can thus be used to obtain the global optimal solution. After that, we provide numerical examples for illustrative purpose.

A Newsvendor Model with Initial Inventory and Two Salvage Opportunities

In this paper, we develop an extension of the newsvendor model with initial inventory. In addition to the usual quantity ordered at the beginning of the horizon and the usual quantity salvaged at the end of the horizon, we introduce a new decision variable: a salvage opportunity at the beginning of the horizon, which might be used in the case of high initial inventory level. We develop the expression of the optimal policy for this extended model, for a general demand distribution. The structure of this optimal policy is particular and is characterized by two threshold levels. Some managerial insights are given via numerical examples.

Analysis and Optimization of a Combined Make-to-Stock and Make-to-Order Multiproduct Manufacturing System

We consider a single-stage multiproduct manufacturing facility producing several end-products for delivery to customers with a required customer lead-time. The end-products can be split in two classes: few products with high volume demands and a large number of products with low-volume demands. In order to reduce inventory costs, it seems efficient to produce the high-volume products according to an MTS policy and the low volume products according to an MTO policy. The purpose of this paper is to analyze and compare the impact of the scheduling policy on the overall inventory costs, under customer lead-time service level constraints. We consider two policies: the classical FIFO policy and a priority policy (PR) which gives priority to low volume products over high volume products. We show that for some range of parameters, the PR rule can significantly outperform the FIFO rule. In these ranges, the service level constraints are satisfied by the PR rule with much lower inventory costs.

Some New Classroom Cases for Teaching Statistical Quality Control Methods

Many graduates of basic courses in quality control and operations management do not understand the potential benefits arising from a real understanding of the main principles of probability theory and statistics. In Ref. 1, Savage said that many graduates of basic statistics courses do not understand the central limit theorem or even the concept of probability distribution. A primary reason for such disinterest in Operations Research, and Management Sciences in general, is the complexity of the models and mathematics involved. Nevertheless, another principal cause corresponds to the fact that often too much effort is spent in teaching the technicalities of the mathematical models (and optimization techniques). Moreover, not enough time is given to connecting the students with actual problems they are going to face in their future company. Along such lines, several very interesting methods have been developed for training in the design of experiments (see Ref. 2). Most of them rely on the use of classroom experimentation. The aim of the present article is to describe new inclass experiments and cases for training in statistical quality control. These new tools complement more classical teaching methods in quality control, which can use the ISO 2859 standard as a reference, as well as an interesting source of examples. Several other books (see, e.g., Refs 3– 6) provide numerous examples and cases. The first case is about inspection and analysis and conception of sampling plans in the framework of a long-term producer– customer relationship. The second experiment deals with the statistical control of a process and the analysis of drift by control charts.