Evaluation of cycle-count policies for supply chains with inventory inaccuracy and implications on RFID investments

Inventory record inaccuracy leads to ineffective replenishment decisions and deteriorates supply chain performance. Conducting cycle counts (i.e., periodic inventory auditing) is a common approach to correcting inventory records. It is not clear, however, how inaccuracy at different locations affects supply chain performance and how an effective cycle-count program for a multi-stage supply chain should be designed. This paper aims to answer these questions by considering a serial supply chain that has inventory record inaccuracy and operates under local base-stock policies. A random error, representing a stock loss, such as shrinkage or spoilage, reduces the physical inventory at each location in each period. The errors are cumulative and are not observed until a location performs a cycle count. We provide a simple recursion to evaluate the system cost and propose a heuristic to obtain effective base-stock levels. For a two-stage system with identical error distributions and counting costs, we prove that it is more effective to conduct more frequent cycle counts at the downstream stage. In a numerical study for more general systems, we find that location (proximity to the customer), error rates, and counting costs are primary factors that determine which stages should get a higher priority when allocating cycle counts. However, it is in general not effective to allocate all cycle counts to the priority stages only. One should balance cycle counts between priority stages and non-priority stages by considering secondary factors such as lead times, holding costs, and the supply chain length. In particular, more cycle counts should be allocated to a stage when the ratio of its lead time to the total system lead time is small and the ratio of its holding cost to the total system holding cost is large. In addition, more cycle counts should be allocated to downstream stages when the number of stages in the supply chain is large. The analysis and insights generated from our study can be used to design guidelines or scorecard systems that help managers design better cycle-count policies. Finally, we discuss implications of our study on RFID investments in a supply chain.     

REBUILDING THE EASTERN BALTIC COD STOCK UNDER ENVIRONMENTAL CHANGE (PART II): TAKING INTO ACCOUNT THE COSTS OF A MARINE PROTECTED AREA

Abstract This study adds a cost analysis of the Eastern Baltic cod fishery to the existing model presented in Röckmann et al. [2007a] . As cost data on this international fishery do not exist, data from Denmark are extrapolated to the whole international fishery. Additionally, unit and total variable costs are simulated, and the sensitivity to a set of different cost–stock and cost–output elasticities is tested. The study supports preliminary conclusions that a temporary marine reserve policy, which focuses on protecting the Eastern Baltic cod spawning stock in the International Council for the Exploration of the Sea (ICES) subdivision 25, is a valuable fisheries management tool to (i) rebuild the overexploited Eastern Baltic cod stock and (ii) increase operating profits. The negative effects of climate change can be postponed for at least 20 years—depending on the assumed rate of future climate change. Including costs in the economic analysis does not change the ranking of management policies as proposed in the previous study where costs were neglected.     

Age-dependent production planning and maintenance strategies in unreliable manufacturing systems with lost sale

In this paper, we formulate an analytical model for the joint determination of an optimal age-dependent buffer inventory and preventive maintenance policy in a production environment that is subject to random machine breakdowns. Traditional preventive maintenance policies, such as age and periodic replacements, are usually studied based on simplified and non-realistic assumptions, as well as on the expected costs criterion. Finished goods inventories and the age-dependent likelihood of machine breakdowns are usually not considered. As a result, these policies could significantly extend beyond the anticipated financial incomes of the system, and lead to crises. In order to solve this problem, a more realistic analysis model is proposed in this paper to consider the effects of both preventive maintenance policies and machine age on optimal safety stock levels. Hence, a unified framework is developed, allowing production and preventive maintenance to be jointly considered. We use an age-dependent optimization model based on the minimization of an overall cost function, including inventory holdings, lost sales, preventive and corrective maintenance costs. We provide optimality conditions for the manufacturing systems considered, and use numerical methods to obtain an optimal preventive maintenance policy and the relevant age-dependent threshold level production policy. In this work, this policy is called the multiple threshold levels hedging point policy. We include numerical examples and sensitivity analyses to illustrate the importance and the effectiveness of the proposed methodology. Compared with other available optimal production and maintenance policies, the numerical solution obtained shows that the proposed age-dependent optimal production and maintenance policies significantly reduce the overall cost incurred.     

On a production-inventory system of deteriorating items subject to random machine breakdowns with a fixed repair time

This paper considers the impact of random machine breakdowns on the classical Economic Production Quantity (EPQ) model for a product subject to exponential decay and under a no-resumption (NR) inventory control policy. A product is manufactured in batches on a machine that is subject to random breakdowns in order to meet a constant demand over an infinite planning horizon. The product is assumed to have a significant rate of deterioration and time to deterioration is described by an exponential distribution. Also, the time-to-breakdown is a random variable following an exponential distribution. Under the NR policy, when a breakdown occurs during a production run, the run is immediately aborted. A new run will not be started until all available inventories are depleted. Corrective maintenance of the production system is carried out immediately after a breakdown and it takes a fixed period of time to complete such an activity. The objective is to determine the optimal production uptime that minimizes the expected total cost per unit time consisting of setup, corrective maintenance, inventory carrying, deterioration, and lost sales costs. A near optimal production uptime is derived under conditions of continuous review, deterministic demand, and no shortages.     

CONSERVATION OF WILDLIFE. A BIO‐ECONOMIC MODEL OF A WILDLIFE RESERVE UNDER THE PRESSURE OF HABITAT DESTRUCTION AND HARVESTING OUTSIDE THE RESERVE

ABSTRACT. Biodiversity is today threatened by many factors of which destruction and reduction of habitats are considered most important for terrestrial species. One way to counteract these threats is to establish reserves with restrictions on land use and exploitation. However, very few reserves can be considered islands, wildlife species roam over large expanses, often via some density dependent dispersal process. As a consequence, habitat destruction, and exploitation, taking place outside will influence the species abundance inside the conservation area. The paper presents a theoretical model for analyzing this type of management problem. The model presented allows for both the common symmetric dispersal as well as what is called asymmetric dispersal between reserve and outside area. The main finding is that habitat destruction outside may not necessarily have negative impact upon the species abundance in the reserve. As a consequence, economic forces working in the direction of reducing the surrounding habitat have unclear effects on the species abundance within the protected area. We also find that harvesting outside the reserve may have quite modest effect on the species abundance in the reserve. This underlines the attractiveness of reserves from a conservation viewpoint.     

Approximate analysis and optimization of batch ordering policies in capacitated supply chains

Devising manufacturing/distribution strategies for supply chains and determining their parameter values have been challenging problems. Linking production management to stock keeping processes improves the planning of the supply chain activities, including material management, culminating in improved customer service levels. In this study, we investigate a multi-echelon supply chain consisting of a supplier, a plant, a distribution center and a retailer. Material flow between stages is driven by reorder point/order quantity inventory control policies. We develop a model to analyze supply chain behavior using some key performance metrics such as the time averages of inventory and backorder levels, as well as customer service levels at each echelon. The model is validated against simulation, yielding good agreement of robust performance metrics. The metrics are then used within an optimization framework to design the supply chain so as to minimize expected total system costs. The outcome of the optimization framework specifies how to move inventory throughout the supply chain and how to set inventory control parameters, i.e., reorder levels and replenishment batch sizes.     

Nonlinear reserving in life insurance: Aggregation and mean-field approximation

We suggest a unified approach to claims reserving for life insurance policies with reserve-dependent payments driven by multi-state Markov chains. The associated prospective reserve is formulated as a recursive utility function using the framework of backward stochastic differential equations (BSDE). We show that the prospective reserve satisfies a nonlinear Thiele equation for Markovian BSDEs when the driver is a deterministic function of the reserve and the underlying Markov chain. Aggregation of prospective reserves for large and homogeneous insurance portfolios is considered through mean-field approximations. We show that the corresponding prospective reserve satisfies a BSDE of mean-field type and derive the associated nonlinear Thiele equation.     

A MODEL OF TROPICAL MARINE RESERVE‐FISHERY LINKAGES

ABSTRACT. The excessive and unsustainable exploitation of our marine resources has led to the promotion of marine reserves as a fisheries management tool. Marine reserves, areas in which fishing is restricted or prohibited, can offer opportunities for the recovery of exploited stock and fishery enhancement. In this paper we examine the contribution of fully protected tropical marine reserves to fishery enhancement by modeling marine reserve‐fishery linkages. The consequences of reserve establishment on the long‐run equilibrium fish biomass and fishery catch levels are evaluated. In contrast to earlier models this study highlights the roles of both adult (and juvenile) fish migration and larval dispersal between the reserve and fishing grounds by employing a spawner‐recruit model. Uniform larval dispersal, uniform larval retention and complete larval retention combined with zero, moderate and high fish migration scenarios are analyzed in turn. The numerical simulations are based on Mombasa Marine National Park, Kenya, a fully protected coral reef marine reserve comprising approximately 30% of former fishing grounds. Simulation results suggest that the establishment of a fully protected marine reserve will always lead to an increase in total fish biomass. If the fishery is moderately to heavily exploited, total fishery catch will be greater with the reserve in all scenarios of fish and larval movement. If the fishery faces low levels of exploitation, catches can be optimized without a reserve but with controlled fishing effort. With high fish migration from the reserve, catches are optimized with the reserve. The optimal area of the marine reserve depends on the exploitation rate in the neighboring fishing grounds. For example, if exploitation is maintained at 40%, the ‘optimal’ reserve size would be 10%. If the rate increases to 50%, then the reserve needs to be 30% of the management area in order to maximize catches. However, even in lower exploitation fisheries (below 40%), a small reserve (up to 20%) provides significantly higher gains in fish biomass than losses in catch. Marine reserves are a valuable fisheries management tool. To achieve maximum fishery benefits they should be complemented by fishing effort controls.     

On upper bounds of sequential stochastic production planning problems

In this paper we consider a class of problems that determine production, inventory and work force levels for a firm in order to meet fluctuating demand requirements. A production planning problem arises because of the need to match, at the firm level, supply and demand efficiently. In practice, the two common approaches to counter demand uncertainties are (i) carrying a constant safety stock from period to period, and (ii) planning with a rolling horizon. Under the rolling horizon (or sequential) strategy the planning model is repeatedly solved, usually at the end of every time period, as new information becomes available and is used to update the model parameters. The costs associated with a rolling horizon strategy are hard to compute a priori because the solution of the model in any intermediate time period depends on the actual demands of the previous periods.In this paper we derive two a priori upper bounds on the costs for a class of production planning problems under the rolling horizon strategy. These upper bounds are derived by establishing correspondences between the rolling horizon problems and related deterministic programs. One of the upper bounds is obtained through Lagrangian relaxation of the service level constraint. We propose refinements to the non-Lagrangian bounds and present limited computational results. Extensions of the main results to the multiple item problems are also discussed. The results of this paper are intended to support production managers in estimating the production costs and value of demand information under a rolling horizon strategy.     

Optimal maintenance of two stochastically deteriorating machines with an intermediate buffer

We consider a manufacturing system in which an input generating installation transfers a raw material to a subsequent production unit. Both machines deteriorate stochastically with usage and may fail. For each machine the deteriorating process is described by some known transition probabilities between different degrees of deterioration. A buffer has been built between the two machines in order to cope with unexpected failures of the installation. A discrete-time Markov decision model is formulated for the optimal preventive maintenance of both machines. The maintenance times are geometrically distributed and the cost structure includes operating costs, storage costs, maintenance costs and costs due to the lost production. It is proved that for fixed buffer content and for fixed deterioration degree of one machine, the average-cost optimal policy initiates a preventive maintenance of the other machine if and only if its degree of deterioration exceeds some critical level. We study, by means of numerical results, the effect of the variation of some parameters on the optimal policy and on the minimum average cost. For the case in which the maintenance times follow continuous distributions, an approximate discrete-time Markov decision model is proposed.     

CREATION OF MARINE RESERVES AND INCENTIVES FOR BIODIVERSITY CONSERVATION

Abstract Despite a number of benefits, marine reserves provide neither incentives for fishermen to protect biodiversity nor compensation for financial loss due to the designation of the reserves. To obtain fishermen's support for marine reserves, some politicians have suggested that managers of new marine reserves should consider subsidizing or compensating those fishermen affected by the new operations. The objective of this paper is to apply principal–agent theory, which is still infrequently applied to fisheries, to define the optimal reserve area, fishing effort, and transfer payments in the context of symmetric and asymmetric information between managers and fishermen. The expected optimal reserve size under asymmetric information is smaller than that under symmetric information. Fishing efforts encouraged with a transfer payment are always less compared to those without payment. This reflects the fact that as the manager induces the fishermen to participate in the conservation program, the fishermen will take into account their effects on fish stock by decreasing their effort. Examples are also supplied to demonstrate these concepts.     

The use of simple calibrations of individual locations in making transshipment decisions in a multi-location inventory network

Demands occur at each location in a network of stock-holding retail outlets. Should a location run out of stock between successive replenishments, then subsequent demands may be met either by transshipping from another location in the network or by an emergency supply from a central depot. We deploy an approximate stochastic dynamic programming approach to develop a class of interpretable and implementable heuristics for making transshipment decisions (whether and from where to transship) which make use of simple calibrations of the candidate locations. The calibration for a location depends upon its current stock, the time to its next replenishment and the identity of the location needing stock. A numerical investigation shows strong performance of the proposed policies in comparison with standard industry practice (complete pooling, no pooling) and a recently proposed heuristic. It points to the possibility of substantial cost savings over current practice.     

A single-period inventory placement problem for a supply system with the satisficing objective

Consider the inventory placement problem in an N-stage supply system facing a stochastic demand for a single planning period. Each stage is a stocking point holding some form of inventory (e.g., raw materials, subassemblies, product returns or finished products) that after a suitable transformation can satisfy demand. Stocking decisions are made before demand occurs. Unsatisfied demands are lost. The revenue, salvage value, ordering, transformation, and lost sales costs are proportional. There are fixed costs for utilizing stages for stock storage. The objective is to maximize the probability of achieving a given target profit level.     

Coordinated maintenance in a multi-component system with compound Poisson deterioration

This paper proposes a coordinated maintenance model in a multi-component system with compound Poisson deterioration. The main contribution is a policy-iteration approach for Semi-Markov processes that optimizes the threshold at which the component is eligible for preventive maintenance if another component requires corrective maintenance. The methodology is novel as we develop explicit expressions for the policy evaluation and prove these expressions to satisfy the set of linear equations which characterize traditional policy evaluation. By doing so, long-run average cost savings are achieved, since setup costs can be shared.     

A comparison of outbound dispatch policies for integrated inventory and transportation decisions

This paper investigates the impact of alternative outbound dispatch policies on integrated stock replenishment and transportation decisions. The logistics literature reports that two different types of such policies are popular in current practice. These are time-based and quantity-based dispatch policies. Considering the case of stochastic demand, the paper presents analytical and numerical results showing that the cost savings obtained through quantity-based policies can be substantial. However, under a quantity-based policy, a specific delivery time cannot be quoted when the customer places an order. Hence, the paper also investigates the cost and customer waiting time implications of hybrid policies and demonstrates that hybrid policies are superior to time-based policies in terms of the resulting costs. Furthermore, although hybrid policies are not superior to quantity-based policies in terms of the resulting costs, they are superior in terms of a service measure which is quantified by the long-run average cumulative waiting time.     

Production lot sizing with process deterioration and machine breakdown

The paper presents a generalized economic manufacturing quantity model for an unreliable production system in which the production facility may shift from an ‘in-control’ state to an ‘out-of-control’ state at any random time (when it starts producing defective items) and may ultimately break down afterwards. If a machine breakdown occurs during a production run, then corrective repair is done; otherwise, preventive repair is performed at the end of the production run to enhance the system reliability. The proposed model is formulated assuming that the time to machine breakdown, corrective and preventive repair times follow arbitrary probability distributions. However, the criteria for the existence and uniqueness of the optimal production time are derived under general breakdown and uniform repair time (corrective and preventive) distributions. The optimal production run time is determined numerically and the joint effect of process deterioration, machine breakdowns and repairs (corrective and preventive) on the optimal decisions is investigated for a numerical example.     

FISHERY BENEFITS OF FULLY PROTECTED MARINE RESERVES: WHY HABITAT AND BEHAVIOR ARE IMPORTANT

ABSTRACT. Fully protected marine reserves, areas that are closed to all fishing, have attracted great interest for their potential to benefit fisheries. A wide range of models suggest reserves will be most effective for species that are relatively sedentary as adults but produce offspring that disperse widely. Adult spawning stocks will be secure from capture in reserves, while their offspring disperse freely into fishing grounds. Such species include animals like reef fish, mollusks and echino‐derms, and models typically indicate that when they are over‐fished, catches will be higher with reserves than without. By contrast, the same models suggest that reserves will be ineffective for animals that are mobile as adults species like cod, tuna or sharks. They remain vulnerable to fishing whenever they move outside reserves. Unfortunately, most models lack sufficient realism to effectively gauge reserve effects on migratory species. They usually assume that individuals are homogeneously distributed in a uniform sea and move randomly. They also assume that fishers hunt at random. Neither is true. For centuries, fishers have targeted places and times when their quarry are most vulnerable to capture. Protecting these sites could have disproportionately large effects on stocks. Furthermore, models rarely take into account possible benefits from improvements in habitat within reserves. Such changes, like increased biomass and complexity of bottom‐living organisms, could alter fish movement patterns and reduce natural mortality rates in ways that enhance reserve benefits. We present a simple model of reserve effects on a migratory fish species. The model incorporates spatial variation in vulnerability to capture and shows that strategically placed reserves can offer benefits in the form of increased spawning stock and catch, especially when fishing intensities are high. We need to develop a new generation of models that incorporate habitat and behaviour to better explore the utility of reserves for mobile species. Migratory behavior does not preclude reserves from benefiting a species, but it demands that we apply different principles in designing them. We must identify critical sites to species and develop reserve networks that focus protection on those places.     

Supply chain model for a deteriorating product with time-varying demand and production rate

The paper develops a two-echelon supply chain model with a single-buyer and a single-vendor. The buyer sells a seasonal product over a short selling period and its inventory is subject to deterioration at a constant rate over time. The vendor's production rate is dependent on the buyer's demand rate, which is a linear function of time. Also, the vendor's production process is not perfectly reliable; it may shift from an in-control state to an out-of-control state at any time during a production run and produce some defective (non-conforming) items. Assuming that the vendor follows a lot-for-lot policy for replenishment made to the buyer, the average total cost of the supply chain is derived and an algorithm for finding the optimal solution is developed. The numerical study shows that the supply chain coordination policy is more beneficial than those policies obtained separately from the buyer's and the vendor's perspectives.     

Comparison among three pull control policies: kanban, base stock, and generalized kanban

This paper is concerned with maketostock pull control policies. A classical policy is the kanban policy. Another policy, very easy to implement, is the base stock policy. These two policies contain one design parameter per stage. A general control policy, known as the generalized kanban policy, can also be used to implement the pull mechanism. The generalized kanban policy includes, as special cases, the kanban and the base stock policies. This policy uses two parameters for each stage of the production system. The aim of this paper is to provide qualitative and quantitative comparisons of these three policies. The results of our study will help to choose the policy to implement in order to control a production system. We give practical rules. We also show that if there is no delay in filling orders, all three policies have similar costs. However, for the systems studied, we show that, if there is a delay in filling orders, generalized kanban systems and base stock systems yield close to optimal costs, which are lower than costs of kanban systems for the same service quality.     

A preventive maintenance policy for a continuously monitored system with correlated wear indicators

A continuously monitored system is considered, that gradually and stochastically deteriorates according to a bivariate non-decreasing Lévy process. The system is considered as failed as soon as its bivariate deterioration level enters a failure zone, assumed to be an upper set. A preventive maintenance policy is proposed, which involves a delayed replacement, triggered by the reaching of some preventive zone for the system deterioration level. The preventive maintenance policy is assessed through a cost function on an infinite horizon time. The cost function is provided in full form, and tools are provided for its numerical computation. The influence of different parameters on the cost function is studied, both from a theoretical and/or numerical point of view.