Forecast accuracy, information technologies and the performance of inventory policies under multi-level rolling schedule environments

Our incentive is to study the behaviour of lot-sizing rules in a multi-level context when forecast demand is subject to changes within the forecast window. To our knowledges, only Bookbinder and Heath (1988) have proposed a lot-sizing study in a multi-echelon rolling schedule with probabilistic demands. But their simulation study was limited to two arborescent structures with 6 nodes. By means of an extensive simulation study we show that it is always worth decreasing the error magnitude. This should encourage companies to develop Electronic Data Interchange to ameliorate demand forecast.Although the presence or absence of forecast errors matters more than the error level, we show that lot-sizing rules exhibit significant differences in their behaviour as the level of error is augmented. This paper also provides a clear description of the rolling procedure when applied to general product structures, probabilistic demand within the forecast window and positive lead times.economics of technology ;

Budget Allocation for Permanent and Contingent Capacity under Stochastic Demand.

We develop a model of budget allocation for permanent and contingent workforce under stochastic demand. The level of permanent capacity is determined at the beginning of the horizon and is kept constant throughout, whereas the number of temporary workers to be hired must be decided in each period. Compared to existing budgeting models, this paper explicitly considers a budget constraint. Under the assumption of a restricted budget, the objective is to minimize capacity shortages. When over-expenditures are allowed, both budget deviations and shortage costs are to be minimized. The capacity shortage cost function is assumed to be either linear or quadratic with the amount of shortage, which corresponds to different market structures or different types of services. We thus examine four variants of the problem that we model and solve either approximately or to optimality when possible. A comprehensive experimental design is designed to analyze the behavior of our models when several levels of demand variability and parameter values are considered. The parameters consist of the initial budget level, the unit cost of temporary workers and the budget deviation penalty/reward rates. Varying these parameters produce several trade-offs between permanent and temporary workforce levels, and between capacity shortages and budget deviations. Numerical results also show that the quadratic cost function leads to smooth and moderate capacity shortages over the time periods, whereas all shortages are either avoided or accepted when the cost function is linear.Stochastic; Capacity planning; Contingent workers; Budget allocation; Non-linear stochastic dynamic programming; Optimization;

Heuristic procedures for a stochastic lot-sizing problem in make-to-order manufacturing

We consider a single item, uncapacitated stochastic lot-sizing problem motivated by a Dutch make-to-order company producing steel pipes. Since no finished goods inventory is kept, a delivery date is fixed upon arrival of each order. The objective is to determine the optimal size of production lots so that delivery dates are met as closely as possible with a limited number of set-ups. Orders that are not satisfied on time are backordered and a penalty cost is incurred in those cases. We formulate the problem as a Markov Decision Process and determine the optimal production policy by dynamic programming. Since this approach can only be applied to very small examples, attention is given to the development of three simple lot-sizing rules. The first strategy consists of producing the orders for a fixed number T of periods whenever the demand for the current period reaches a pre-specified limit x. A simple set of tests is proposed leading to cost improvements in situations where the best combination for the decision variables x and T deviates from the optimal policy. The second lot-sizing rule is based on the well-known Silver-Meal heuristic for the case of deterministic time-varying demand. A fixed cycle production strategy is also derived. Numerical examples taking into account different demand patterns are provided. The analysis of the results suggests that the first heuristic is particularly suitable for the problem under consideration. Finally, the model is incorporated in the operations control level of the hierarchical production planning system of the Dutch company and assists the management in the evaluation of the quality of the aggregate decisions. A consequence of this feedback mechanism is the modification of the aggregate plans

On non-negative auto-correlated integer demand processes

Methods to generate realistic non-stationary demand scenarios are a key component for analyzing and optimizing decision policies in supply chains. Typical forecasting techniques recommended in standard inventory control textbooks consist of some form of simple exponential smoothing (SES) for both the estimates for the mean and standard deviation. We study demand generating processes (DGPs) that yield non-stationary demand scenarios, and that are consistent with SES, meaning that SES yields unbiased estimates when applied to the generated demand scenarios. As demand in typical practical settings is discrete and non-negative, we study consistent DGPs on the non-negative integers. We derive conditions under which the existence of such DGPs can be guaranteed, and propose a specific DGP that yields autocorrelated, discrete demands when these conditions are satisfied. Our subsequent simulation study gains further insights into the proposed DGP. It demonstrates that from a given initial forecast, our DGPs yields a diverse set of demand scenarios with a wide range of properties. To show the applicability of the DGP, we apply it to generate demand in a standard inventory problem with full backlogging and a positive lead time. We find that appropriate dynamic base-stock levels can be obtained using a new and relatively simple algorithm, and we demonstrate that this algorithm outperforms relevant benchmarks

Optimal claim behaviour for third-party liability insurances or to claim or not to claim: that is the question

It is proved that the optimal decision rule to claim or not to claim for damage is of the form: ‘to claim for damage only if its amount exceeds a certain limit’. Optimal critical claim sizes are derived, and a sensitivity analysis is given with respect to changes in (the parameters of) the distributions of the number of claims and the claim size

Optimal claim behaviour for vehicle damage insurances

In this paper we analyse the optimal claim behaviour of a risk sensitive policy holder having a vehicle damage insurance. It is proved that the optimal decision is of the form: to claim for damages only if its amount exceeds a certain limit. Moreover, we also derive the optimal stopping rule to terminate the insurance. Finally, some computational results are presented

Optimal claim behaviour for third-party liability insurances with perfect information

In this paper we analyse the optimal claim behaviour of a policy holder having a third-party liability insurance in which one is allowed to decide at the end of an insurance year which damages occurred during that year should be claimed. This analysis can only be carried out in detail in case the damages are negative exponentially distributed. Moreover, we present some computational results using an existing bonus—malus system and a horizon of 10 and 25 years and compare these results with similar computations for a corresponding third-party liability insurance in which the policy holder has to decide within a limited time period after the accident to claim or not to claim

Insurers' profits in the third-party liability insurance

In this note we derive the expected total discounted profit of an insurer due to a single policy holder within a third-party liability insurance. We consider both a policy holder claiming optimally and non-optimally

Self-adaptive randomized constructive heuristics for the multi-item capacitated lot-sizing problem

Capacitated lot-sizing problems (CLSPs) are important and challenging optimization problems in production planning. Amongst the many approaches developed for CLSPs, constructive heuristics are known to be the most intuitive and fastest method for finding good feasible solutions for the CLSPs, and therefore are often used as a subroutine in building more sophisticated exact and metaheuristic approaches. Classical constructive heuristics, such as the period-by-period heuristics and lot elimination heuristics, are first introduced in the 1990s, and thereafter widely used in solving the CLSPs. This paper evaluates the performance of period-by-period and lot elimination heuristics, and improves the heuristics using perturbation techniques and self-adaptive methods. We have also proposed a procedure for automatically adjusting the parameters of the proposed heuristics so that the values of the parameters can be chosen based on features of individual instances. Experimental results show that the proposed self-adaptive randomized period-by-period constructive heuristics are efficient and can find better solutions with less computational time than the tabu search and lot elimination heuristics. When the proposed constructive heuristic is used in a basic tabu search framework, high-quality solutions with 0.88% average optimality gap can be obtained on benchmark instances of 12 periods and 12 items, and optimality gap within 1.2% for the instances with 24 periods and 24 items