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.Markov decision processes;optimal critical claim size;order statistics

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.Markov decision processes;bonus—malus systems;automobile insurance

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

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 simulation study 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-off between permanent and temporary workforce levels, and between capacity shortages and budget deviations. Simulation 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

A stochastic inventory policy with limited transportation capacity

In this paper we consider a stochastic single-item inventory problem. A retailer keeps a single product on stock to satisfy customers stochastic demand. The retailer is replenished periodically from a supplier with ample stock. For the delivery of the product, trucks with finite capacity are available and a fixed shipping cost is charged whenever a truck is dispatched regardless of its load. Furthermore, linear holding and backorder costs are considered at the end of a review period. A replenishment policy is proposed to determine order quantities taking into account transportation capacity and aiming at minimizing total average cost. Every period an order quantity is determined based on an order-up-to logic. If the order quantity is smaller than a given threshold then the shipment is delayed. On the other hand, if the order quantity is larger than a second threshold then the initial order size is enlarged and a full truckload is shipped. An order size between these two thresholds results in no adaption of the order quantity and the order is shipped as it is. We illustrate that this proposed policy is close to the optimal policy and much better than an order-up-to policy without adaptations. Moreover, we show how to compute the cost optimal policy parameters exactly and how to compute them by relying on approximations. In a detailed numerical study, we compare the results obtained by the heuristics with those given by the exact analysis. A very good cost performance of the proposed heuristics can be observed