John Betts

Should Start-up Companies Be Cautious? Inventory Policies Which Maximise Survival Probabilities

New start-up companies, which are considered to be a vital ingredient in a successful economy, have a different objective than established companies: They want to maximise their chance of long-term survival. We examine the implications for their operating decisions of this different criterion by considering an abstraction of the inventory problem faced by a start-up manufacturing company. The problem is modelled under two criteria as a Markov decision process; the characteristics of the optimal policies under the two criteria are compared. It is shown that although the start-up company should be more conservative in its component purchasing strategy than if it were a well-established company, it should not be too conservative. Nor is its strategy monotone in the amount of capital it has available. The models are extended to allow for interest on investment and inflation.

On finding safe regions for moving range queries

Abstract The cost of monitoring and keeping the location of a Moving Query updated is very high, as the calculation of the range query needs to be re-evaluated whenever the query moves. Many methods have been proposed to minimize the computation and communication costs for the continuous monitoring of Moving Range Queries. However, because this problem has been only partly solved, more radical efforts are needed. In response, we propose an efficient technique by adopting the concept of a safe region. The safe region is an area where the set of objects of interest does not change. If a moving query is roaming within the safe region then there is no need to update the query. This paper presents efficient techniques to create a competent safe region to reduce the communication costs. We use Monte-Carlo simulation to calculate the area of the safe region due to the irregularity of its shape. As long as the query remains inside its specified safe region, expensive re-computation is not required, which reduces the computational and communication costs in client–server architectures.

Just-in-time replenishment decisions for assembly manufacturing with investor-supplied finance

While JIT ideas have been enthusiastically embraced by manufacturing practitioners, the small replenishment batch sizes advocated are difficult to reconcile with the standard management science cost trade-off approach. The difficulty is diagnosed as being due to the standard assumption that capital for inventory is borrowed and hence boundless. We present a new analysis of inventory reduction decisions, such as adopting JIT replenishment or component substitution, using a deterministic batch sizing model which assumes that inventory is financed by the investors in the company and is thus finite. As a consequence, the investment level is treated as an additional variable of the decision analysis. Using the well established technique of constrained optimisation it is shown that for investor-financed operations the effective value of money invested in inventory is the marginal return on investment of the company, and increases with the degree of constraint. Thus, JIT policy options are especially favourable when low levels of inventory investment are sought, even without setup cost reduction, because the capital formerly invested in stock holdings of the JIT components can be reinvested in the inventory of other components to make their replenishment more efficient using larger batch sizes. The analysis is illustrated using an actual case study of a small manufacturing enterprise seeking to reduce inventory and increase return on investment. The analysis has interesting practical implications for inventory managers including a proposed simple method for identifying candidate components for JIT replenishment.

Monitoring Moving Queries inside a Safe Region

With mobile moving range queries, there is a need to recalculate the relevant surrounding objects of interest whenever the query moves. Therefore, monitoring the moving query is very costly. The safe region is one method that has been proposed to minimise the communication and computation cost of continuously monitoring a moving range query. Inside the safe region the set of objects of interest to the query do not change; thus there is no need to update the query while it is inside its safe region. However, when the query leaves its safe region the mobile device has to reevaluate the query, necessitating communication with the server. Knowing when and where the mobile device will leave a safe region is widely known as a difficult problem. To solve this problem, we propose a novel method to monitor the position of the query over time using a linear function based on the direction of the query obtained by periodic monitoring of its position. Periodic monitoring ensures that the query is aware of its location all the time. This method reduces the costs associated with communications in client-server architecture. Computational results show that our method is successful in handling moving query patterns.

Dynamic safe regions for moving range queries in mobile navigation

The cost of monitoring and updating the location of Moving Queries is very high, as the calculation of a range query needs to be re-evaluated whenever the query moves. Previous efforts to reduce this cost have proposed reducing the frequency of communication between query and server. However, because all possible objects continue to be surveyed using these approaches, substantial cost reduction is not possible. This paper introduces two novel techniques: the continuous basic safe region, by calculating the closest objects to the border of the moving query, and the continuous extended safe region, by calculating the intersections among several range objects. Inside these safe regions there is no need to update the query as the set of objects of interest does not change. We compare the size of the safe regions obtained using these two methods and show their potential to greatly reduce computations and communications cost in client-server architectures.

Calculating target inventory levels for constrained production: A fast simulation-based approximation

Abstract An accurate model for the inventory shortfall distribution is necessary to calculate the target level required to give a desired service level in manufacturing systems under stochastic demand and production capacity constraint. Existing methods for modelling the inventory shortfall require that the demand distribution be expressible in functional form and that the coefficient of demand variation be small. When these conditions cannot be met, the only recourse to a practitioner is to set target levels using simulation-based optimisation, which is computationally intensive and time consuming. By contrast, this paper presents a model in which the inventory shortfall is approximated by sampling from a single simulation run of the inventory process. The target level required for a given service level can then be calculated efficiently, to a high degree of reliability, using an iterative search. This new model is thus an efficient alternative to conventional simulation-based optimisation. Because the shortfall distribution is generated by simulating demand directly, the model makes no assumptions about the form of the demand distribution. By requiring no user modelling of the functional form or parameters of the demand distribution, this new method is easily used by inventory managers in practice or implemented in software.

A robust approximation for setting target inventory levels in a constrained production environment

A model is developed to calculate the inventory target level required to provide a specified service level in a single-item single-stage inventory when production is subject to a capacity constraint. The model provides a reliable alternative when the exact Markov chain method is intractable, and where known approximations become unreliable due to high demand variability. The model derives the inventory shortfall distribution by simulating the unconstrained inventory process, from which the parameters of a continuous approximation are estimated. The inventory target level required to provide a desired service level can then be calculated efficiently. This new model requires that only one simulation trial is conducted, from which the optimization is then performed. It is thus an efficient alternative to conventional simulation-based optimization. By simulating the shortfall directly, the model makes no assumptions about the form of the demand distribution. By requiring no user modeling this new method is easily used by inventory managers in practice. The model is robust, with accuracy diminishing only by small degree under increased demand variability or production constraint. The degree of reliability increases as the desired service level increases. Sample size has little effect on the accuracy of forecast service levels.

Optimised robust treatment plans for prostate cancer focal brachytherapy

Abstract Focal brachytherapy is a clinical procedure that can be used to treat low-risk prostate cancer with reduced side-effects compared to conventional brachytherapy. Current practice is to man- ually plan the placement of radioactive seeds inside the prostate to achieve a desired treatment dose. Problems with the current practice are that the manual planning is time-consuming and high doses to the urethra and rectum cause undesirable side-effects. To address this problem, we have designed an optimisation algorithm that constructs treatment plans which achieve the desired dose while minimizing dose to organs at risk. We also show that these seed plans are robust to post-operative movement of the seeds within the prostate.

Minimizing Inventory Costs for Capacity-constrained Production Using a Hybrid Simulation Model☆

Abstract A hybrid simulation model is developed to determine the cost-minimizing target level for a single-item, single-stage production-inventory system. The model is based on a single discrete-event simulation of the unconstrained production system, from which an analytical approximation of the inventory shortfall is derived. Using this analytical expression it is then possible to evaluate inventory performance, and associated costs, at any target level. From these calculations, the cost-minimizing target level can then be found efficiently using a local search. Computational experiments show that model accuracy is preserved at high levels of demand variation, where existing analytical methods are known to be unreliable. By deriving an expression for the shortfall distribution via simulation, no user modelling of the demand distribution or estimation of demand parameters is required. Thus this model can be applied to situations when the demand distribution does not have an identifiable analytical form

Optimal Hedging Decisions for Gold Miners: How Much Future Production Should a Gold Miner forward Sell?

This paper attempts to answer the question of how much of its current production a gold producer should hedge by forward selling. We develop a model which allows a company manager to determine the optimal (profit-maximising) hedge, and an estimate of the risk of company failure, based on an estimate of the forward price of gold; the mine’s operating costs; and the company’s tolerance to debt. The model is illustrated with data drawn from historical gold prices and recent Australian company data. By simulating multiple instances of companies operating with different degrees of forward selling under varying levels of volatility in the price of gold, it was shown that the optimal degree of forward selling increased as volatility increased. The model allows managers to gain insights into the effect of volatility on a company’s return given its particular cost structure which in turn, supports more informed decision making. The model illustrates why, during the recent period of constant growth and low volatility in gold prices, gold producers are reducing their hedge books.