Optimal Stock Levels Research Articles

Current trends in management practices for European larch in North America

European larch (Larix decidua Miller) was introduced to North America in the mid-19th century. Its rapid growth led to its use as a reforestation species in northeastern North America during the early part of the 20th century. Proper site selection and vegetation management are crucial to the successful establishment and productivity of this species. On comparable sites, yields of European larch commonly exceed those of native species. Management practices and applied research for this species in North America include the refinement of 1) site selection criteria, 2) growth and yield tables, and 3) optimal density management and stocking levels, 4) product utilization and marketing, and 5) the advancement of tree improvement programs. Key words: growth and yield, productivity, silviculture, tree improvement

The Demand for Food Products: An Analysis of Interpurchase Times and Purchased Quantities

In this paper we study household purchase behaviour of storable food products. An inventory model is developed in which the household chooses an optimal stock level of the product. Storage of the product is costly, there is a fixed cost per purchase occasion, and the market price is sometimes discounted because of price promotions. We show that the optimal purchase policy is an s, S policy. The model is used to derive predictions on the correlations between interpurchase times and purchased quantities on the one hand, and prices on the other. These predictions are empirically verified using consumer panel data.

Management of Multi-Item Retail Inventory Systems with Demand Substitution

Customers for retail merchandise can often be satisfied with one of several items. Accounting for demand substitution in defining customer service influences the choice of items to stock and the optimal inventory level for each item stocked. Further, when certain items are not stocked, the resulting substitutions increase the demand for other items, which also affects the optimal stock levels. In this paper, we develop a probabilistic demand model for items in an assortment that captures the effects of substitution and a methodology for selecting item inventory levels so as to maximize total expected profit, subject to given resource constraints. Illustrative examples are solved to provide insights concerning the behavior of the optimal inventory policies, using the negative binomial demand distribution, which has performed well in fitting retail sales data.

Capacity Choice and Allocation: Strategic Behavior and Supply Chain Performance

We consider a simple supply chain in which a single supplier sells to several downstream retailers. The supplier has limited capacity, and retailers are privately informed of their optimal stocking levels. If retailer orders exceed available capacity, the supplier allocates capacity using a publicly known allocation mechanism, a mapping from retailer orders to capacity assignments. We show that a broad class of mechanisms are prone to manipulation: Retailers will order more than they need to gain a more favorable allocation. Another class of mechanisms induces the retailers to order exactly their needs, thereby revealing their private information. However, there does not exist a truth-inducing mechanism that maximizes total retailer profits. We also consider the supplier's capacity choice. We show that a manipulable mechanism may lead the supplier to choose a higher level of capacity than she would under a truth-inducing mechanism. Nevertheless, her choice will appear excessively restrictive relative to the prevailing distribution of orders. Furthermore, switching to a truth-inducing mechanism can lower profits for the supplier, the supply chain, and even her retailers. Hence, truth-telling is not a universally desirable goal.

The Effects of Selling Packaged Goods on Inventory Decisions

In this paper, we study within a newsboy type modeling framework the common business practice of retail firms to sell products not only as independent items, but also as part of multiproduct packets (packaged goods). Our emphasis is on understanding the effects of such practices on the inventory decisions of the firm. We provide insights on the resulting level of suboptimality when inventory decisions are made with demand information only on the independent items and without accounting for the demand substitution structure induced between independent items and packaged goods. Our stylized model studies an environment with two products that are not direct substitutes for each other, sold either independently or as part of a packet that contains one unit of each. We provide necessary and sufficient optimality conditions for this model and suggest an efficient numerical search for obtaining the optimal stocking levels. An extensive computational study allowed us to provide insights on the nature of the optimal stocking policies, the suboptimality of independent newsboy policies, the effects of demand correlation among individual products and multiproduct packets, and the determining role of induced substitution structure among products during stockout occasions on the profitability of the inventory system.

A net present value approach to safety stocks in a multi-level MRP system

The Laplace transform and input–output Analysis have been used for formulating a basic theory for material requirements planning (MRP) in a sequence of recent papers. The transform has been used for describing time developments and lags of the relevant production, demand and inventory variables in a compact way including effects of order flows and lead times. Secondly, the transform has functioned as a generating function, and thirdly, the transform has been applied for assessing cash flows adopting the net present value (NPV) principle (or the annuity stream which is a variation of NPV). Input-output Analysis, in particular, the input matrix, has been applied for describing multi-level product structures. This has made the analysis compact and distinct. In the current paper the analysis of determining optimal safety stock levels in MRP systems is extended from a single-level model recently investigated to a multi-level system assuming production to take place according to a lot-for-lot (L4L) policy when applying the NPV as the objective criterion and disregarding the opportunities for joint set-ups. Relaxing the L4L assumption is also discussed.

A net present value approach to safety stocks in planned production

In a number of recent papers, the Laplace transform together with input-output analysis has been applied for the sake of formulating a basic theoretical description of material requirements planning (MRP). The transform approach has had a threefold use; on the one hand, it has been useful for describing time developments of the relevant production, demand and inventory properties in a compact way including effects of order flows and lead times. Second, the transform also captures stochastic properties by functioning as a generating function, and, third, the transform is easily applied for assessing the resulting cash flows when adopting the net present value (NPV) principle (or the annuity stream principle which is a variation of NPV). Input-output analysis, in particular the input matrix, is applied for describing multi-level product structures, which has made the analysis concise and distinct. In this paper we extend the analysis of determining optimal safety stock levels for a sequence of planned production decisions (a one-level MRP system) by applying the annuity stream as a criterion to a simple model instead of the average cost approach previously used.

A note on the convexity of the objective function for a simple common component inventory problem

We prove the convexity of the objective function for any continous demand distribution for a common component inventory problem as considered in Jönsson and Silver (Engineering Costs and Production Economics 16 (1989) 257–267). This result guarantees that a local optimum is the global optimum. It facilitates the determination of optimal stock levels for the components.

Analysis of a Production/Inventory System Subject to Random Disruptions

In this paper we study an unreliable bottleneck production/inventory system with a constant production and demand rate that is subject to random disruptions. We assume that the restoration times are constant, the time between breakdowns is exponential, the production setup cost and/or setup time is positive, and excess demand is backordered. We propose an (s, S) production policy for such systems and develop expressions for the operating characteristics of the system. The properties of the policy parameters that minimize the expected total cost rate are investigated and a procedure for finding their optimal values is developed. In addition, we devise and test a simple heuristic procedure for finding near optimal production policies. The results of a numerical experiment suggest that (i) setup cost reduction is more effective in reducing total operating cost when the production system is more reliable, (ii) setup cost reduction in unreliable production systems results in higher optimal safety stock level, and (iii) proper determination of the safety stock levels is extremely important in Just-in-Time systems, which are susceptible to disruptions.

Optimal Steady States and the Effects of Discounting

A simple expression for finding and characterizing the optimal steady state of a general dynamic optimization problem is derived. This expression is easy to interpret and easy to apply for various purposes as, for example, to analytically investigate the effect of the discount rate upon optimal steady state stock levels. It is shown that an increase in the discount rate may result in higher optimal stock levels even in the one-dimensional (single species) case in nonlinear models. An important result is that if demand is inelastic at the optimal steady state, a higher discount rate will unequivocally imply higher standing stock(s). Increasing marginal cost of harvest will further strengthen this result. In the multidimensional case it is demonstrated that an increased discount rate may result in higher optimal stock levels for all stocks included in the model.

A Contingent-Claims Approach to the Inventory-Stocking Decision

This paper presents option-pricing solutions to the inventory-stocking problem when demand is distributed discretely or continuously. The model readily incorporates inventory salvage values and stockout costs, and shows that option-pricing models can be used to determine the optimal stocking levels. The contingent-claims approach is a straightforward extension of the traditional inventory framework, and allows the technology of financial economics to be applied to this important class of assets. The conventional approach to inventory decisions relies on an expected profit-maximization criterion, which takes as its starting point a distribution of demand for the inventory item. The starting point for the contingent-claims approach presented here is to associate the demand for an inventory item to the price of an underlying state variable. Inventory payoffs depend on demand and the quantity stocked as well as the selling price, salvage value, and penalties for stockouts. To apply the contingent-claims approach, we construct a portfolio of options that replicates these inventory payoffs, value the portfolio, and then subtract the inventory investment to establish the net present value (NPV) of an inventory policy.

A lost sales (S — 1, S) perishable inventory system with renewal demand

This article analyzes a one-to-one ordering perishable inventory model with renewal demands and exponential lifetimes. The leadtimes are independently and exponentially distributed and the demands that occur during stock out periods are lost. Although the items are assumed to decay at a constant rate, the output process is not renewal and the Markov renewal techniques are successfully employed to obtain the operating characteristics. The problem of minimizing the long run expected cost rate is discussed and numerical values of optimal stock level are also provided. © 1996 John Wiley & Sons, Inc.

A lost sales (S ? 1, S) perishable inventory system with renewal demand

This article analyzes a one-to-one ordering perishable inventory model with renewal demands and exponential lifetimes. The leadtimes are independently and exponentially distributed and the demands that occur during stock out periods are lost. Although the items are assumed to decay at a constant rate, the output process is not renewal and the Markov renewal techniques are successfully employed to obtain the operating characteristics. The problem of minimizing the long run expected cost rate is discussed and numerical values of optimal stock level are also provided. © 1996 John Wiley & Sons, Inc.

( S − 1, S) Perishable systems with stochastic leadtimes

This article discusses a one-to-one ordering perishable system, in which reorders are processed in the order of their arrival and the processing times are arbitrarily distributed, and as such, the leadtimes are not independent. The Markov renewal techniques are employed to obtain the various operating characteristics for the case of Poisson demand and exponential lifetimes. The problem of minimizing the steady state expected cost rate is also discussed, and in the special case of exponential processing times, the optimal stock level is derived explicitly.

Continuous time inventory control for wiener process demand

This paper discusses a continuous time inventory system without backlogging allowed under the condition that the demand follows a Wiener process. We propose the explicit formula of the expected total discounted cost for an infinite time span by applying the familiar technique of optimal stopping problem. Further, it is shown that the asymptotic value of the expected total discounted cost by perturbation of the discount rate gives the long-run average cost. Finally, the optimal inventory policies, which are given as the optimal stock levels minimizing the expected total discounted and the long-run average costs, are numerically obtained and compared with ones in the deterministic inventory system. It is made apparent that the discount rate and the diffusion parameter of the demand process are very sensitive for the optimal inventory policies.

Master Production Scheduling Under Rolling Planning Horizons with Fixed Order Intervals

Fixed interval scheduling is studied in the context of a rolling horizon framework that is developed by building on previous work in the master scheduling area. The rolling horizon framework includes a stationary scheduling model which uses the “time fencing’concept by partitioning the planning horizon into three sections. The lengths of these sections and the frequency at which the stationary problem is updated and resolved are discussed as parameters of the rolling horizon model. Two different interpretations of the freeze interval parameter are examined, enabling confirmation and clarification of results presented in an earlier study. Details are given for three methods of calculating safety stocks as a function of rolling horizon parameters, including a method which results in optimal safety stock levels. A comparison of the safety stock methods shows that the constant safety stock method can result in inventories that are significantly above optimal under certain conditions, whereas the constant service level method consistently yields nearly optimal results.

Optimal Stock Levels and Service Channel Allocations in a Multi-Item Repairable Asset Inventory System

Abstract A methodology is described for determining the optimum allocation of repairable item inventories and repair channels to support operating systems consisting of different components. The steady-state probability distribution for die number of failed components is based upon the M/M/s finite population queueing model. Dynamic programming is then used to allocate a fixed budget among the components in order to maximize system availability. At each stage of the dynamic program, optimum trade-offs between stock levels and repair channels are made. An illustrative example is provided.

Optimal inventory policies for substitutable commodities with stochastic demand

In this article we consider a stochastic model for two products which have a single-period inventory structure and which can be used as substitutes for each other should the need arise. Substitution will occur with probability one, but at perhaps a different revenue level. We prove that the expected profit function is concave, allowing us to find optimal stocking levels for the two products. We compare optimum inventory levels for the case of single substitution with that where there is no substitution. It is demonstrated for the case of single substitution that total optimum order quantities can actually increase or decrease with the substitution revenue.

Bioeconomics of sustainable harvest of competing species

The concept of maximum sustainable yield frontier (MSF) is applied to a Gause model of competing species. Maximizing the present value of economic rent under costless harvesting with positive discount rate implies optimal stock levels below the locus of MSF stocks. Maximizing economic rent with positive harvesting costs and zero discount rate implies optimal stock levels above the locus of MSF stocks. It is shown how the optimal steady state stock levels are altered by changes in the exogenous discount rate, harvest prices, and harvest costs. Optimal harvesting might imply harvesting of one of the two species at a loss.

Temporary Equilibrium Model and Optimal Capital Stock: An Application to Japanese Electric Utilities

This paper provides empirical evidence on scale economies and the capacity utilization of Japanese electric utilities. Panel data of Japanese electric utilities are analyzed using a static equilibrium with a quasi-fixed factor. Optimal capital stock level is estimated, using the envelope relationship. Scale economies and capacity utilization are also estimated at the optimal capital stock level. Scale economies exist in the short-run, but not in the long-run. Most of capacity utilization are less than one in Japanese electric utilities. However comparing with other studies, we can not certainly say the existence of excess capacity.