Generalized spare ordering policies with allowable inventory time

In this paper, a generalized ordering policy of a one-unit system with age-dependent minimal repair and random lead time is considered. We treat the general order-replacement model with two decision variables: ordering time and allowable inventory time. The allowable inventory period is measured from the time instant that the ordered spare is delivered. By introducing costs due to ordering, repairs, shortage, and holding, we derive the expected cost per unit time in the long run as a criterion of optimality, and seek the optimum policy by minimizing that cost. And we can prove under some mild conditions that there exists a finite and unique optimum policy. Various special cases are discussed.     

Optimal maintenance policies with lead times and repair

Maintenance policies with lead times and repair are discussed. We first discuss ordering policy with repair and refer to inspection-ordering policy. In each policy, as a criterion of optimality, we apply cost effectiveness which balances system effectiveness and cost, and obtain the optimal policies. It is shown that, under certain conditions, there exists a finite and unique optimal policy.     

Supply disruptions with time-dependent parameters

We consider a firm that faces random demand and receives shipments from a single supplier who faces random supply. The supplier's availability may be affected by events such as storms, strikes, machine breakdowns, and congestion due to orders from its other customers. In our model, we consider a dynamic environment: the probability of disruption, as well as the demand intensity, can be time dependent. We model this problem as a two-dimensional non-homogeneous continuous-time Markov chain (CTMC), which we solve numerically to obtain the total cost under various ordering policies. We propose several such policies, some of which are time dependent while others are not. The key question we address is: How much improvement in cost is gained by using time-varying ordering policies rather than stationary ones?     

A generalized model for jointly determining the optimal ordering point and the optimal number of minimal repairs before replacement

Many maintenance policies have assumed that whenever a unit is to he replaced, a new unit is immediately available. However, if the procurement lead time is not negligible, an ordering policy should be considered that determines when to order a spare and when to replace the operating unit after it has begun operating. A generalized model is presented to jointly determine the optimal ordering point and the optimal number of minimal repairs before replacement. By introducing costs due to ordering, repairs, shortage and holding, the expected cost per unit time in the long run is derived as a criterion of optimality, and the optimal ordering point and the optimal number of minimal repairs before replacement are sought by minimizing that cost. Various special cases are discussed. Finally, a numerical example is given.     

The governing dynamics of supply chains: The impact of altruistic behaviour

This paper analyses an infinite horizon two-echelon supply chain inventory problem and shows that a sequence of the optimum ordering policies does not yield globally optimal solutions for the overall supply chain. First-order autoregressive demand pattern is assumed and each participant adopts the order-up-to (OUT) policy with a minimum mean square error forecasting scheme to generate replenishment orders. To control the dynamics of the supply chain, a proportional controller is incorporated into the OUT policy, which we call a generalised OUT policy. A two-echelon supply chain with this generalised OUT policy achieves over 10% inventory related cost reduction. To enjoy this cost saving, the attitude of first echelon player to cost increases is an essential factor. This attitude also reduces the bullwhip effect. An important insight revealed herein is that a significant amount of benefit comes from the player doing what is the best for the overall supply chain, rather than what is the best for local cost minimisation.     

An ordering policy with lead time

An ordering policy in which a working item can be replaced by an item supplied by order with load time is considered. We discuss the optimum ordering policy minimizing the expected cost per unit time for an infinite time span. It is shown in n, theorem that there exists a finite and unique optimum policy under suitable conditions. A sub-optimum policy is also presented.     

Modified age replacement policies

Modified age replacement policies, where a system is not always as good as new after each maintenance, are discussed. The expected total discounted cost for an infinite time-span, introducing some costs and a continuous type discount rate is applied as a criterion of optimality, and the optimum policies minimizing this cost are obtained. It is shown that, under certain conditions, there exists a finite and unique optimum policy. Relations to the existing publications are also shown.     

Bullwhip reduction for ARMA demand: The proportional order-up-to policy versus the full-state-feedback policy

A ‘proportional’ order-up-to policy reacting to ARMA demand is analyzed using stochastic optimal control theory. This policy is compared with a full-state-feedback order-up-to policy. Necessary conditions for an optimum of a weighted sum of the inventory and the ordering variances for both policies are formulated. Based on this a relatively simple expression for the ‘full-state’ policy is derived. The comparison between the two policies demonstrates that the ‘intuitively’ designed proportional policy does not fulfill the objective of controlling both the inventory and ordering variance for all parameter values of the demand model as well as the full-state-feedback policy. The full-state-feedback policy outperforms the proportional policy in several aspects.     

On ordering adjustment policy under rolling forecast in supply chain planning

Rolling forecast is a useful tool for lowering total cost with regard to practical inventory management. The details regarding a rolling forecast are obtained from a customer’s projected ordering data. The customer estimation of a rolling forecast may deviate from actual orders because of unstable conditions or customer’s deliberation. This study investigates what measures a customer might apply in responding to a situation where the rolling forecast deviates from the actual order. In addition, an appropriate ordering adjustment policy is proposed for better monitoring the supply chain performance with regard to a variant level of error concerning rolling forecast data. This study also considers the influence of lead time and inventory cost structure. We adopted a simulation approach, employing a model developed and examined in several different settings. The proposed ordering adjustment policies are determined by AVG, SD, and RMSE calculated from differences existing between historical forecasts and realized data. Levels of estimate error and estimate bias in a rolling forecast are included in the experimental procedure. Results reveal that the RMSE ordering adjustment policy is the most effective in situations of normal and downside estimation bias, whereas the AVG policy is more appropriate in the case of upside estimation bias. The level of estimation error is irrelevant to the selection of ordering adjustment policies, but it is positively associated with inventory costs. Stock-out costs and lead time are positively associated with inventory costs. Accuracy of the rolling forecast is therefore deemed to be essential in a situation involving a long lead time with high stock-out costs.     

A generalized age replacement policy with random delivery time and inspection

This paper is concerned with an age replacement policy that is more general because spare part random delivery time, age-dependent minimal repair and inspection are considered. Introducing the cost due to ordering, repairs, shortage, holding and inspection, we derive the expected cost per unit time in the long run as a criterion of optimality and seek the optimum age replacement policy by minimizing that cost. Various special cases are discussed and a numerical example is finally given to illustrate the method.     

Controlling lead times and minor ordering costs in the joint replenishment problem with stochastic demands under the class of cyclic policies

In this paper, we consider the periodic review joint replenishment problem under the class of cyclic policies. For each item, the demand in the protection interval is assumed stochastic. Moreover, a fraction of shortage is lost, while the other quota is backordered. We suppose that lead times and minor ordering costs are controllable. The problem concerns determining the cyclic replenishment policy, the lead times, and the minor ordering costs in order to minimize the long‐run expected total cost per time unit. We established several properties of the cost function, which permit us to derive a heuristic algorithm. A lower bound on the minimum cost is obtained, which helps us to evaluate the effectiveness of the proposed heuristic. The heuristic is also compared with a hybrid genetic algorithm that is specifically developed for benchmarking purposes. Numerical experiments have been carried out to investigate the performance of the heuristic.     

Optimum repair limit policies with a time constraint

In this paper, we discuss the optimum repair limit policies with a time constraint. We apply the expected total discounted cost as a criterion and obtain the optimum policies which minimize it. We show that, under certain conditions, there exists a finite and unique optimum policy. Finally, we present a numerical example using a mixed Weibull distribution.     

An optimal batch size under a periodic delivery policy

This paper addresses the problem of a manufacturing system that procures raw materials from suppliers in a lot and processes them to convert to finished products. It proposes an ordering policy for raw materials to meet the requirements of a production facility. In turn, this facility must deliver finished products demanded by outside buyers at fixed interval points in time. First, a general cost model is developed considering both raw materials and finished products. Then this model is used to develop a simple procedure to determine an optimal ordering policy for procurement of raw materials and also the manufacturing batch size to minimize the total cost for meeting the customer demand on time. The proposed procedure provides better results than the traditional separate policies. Numerical examples are also presented.     

A combined age‐and‐stock‐based policy for ordering blood units in hospital blood banks

This paper analyses the performance of an ordering policy for hospital blood banks (HBBs) that takes into account the information regarding the on‐hand stock along with the remaining life of blood products. The blood items are assumed to start aging as soon as they have been collected. We develop a simulation model to show that the combined age‐and‐stock‐based policy would outperform some of the popular periodic reviews and continuous review policies in controlling total costs by about 5% on an average basis. Our results show that the suggested policy will reduce the total operational cost of managing platelets, which have a very short shelf life, by about 27% at a real‐life HBB. The policy will also lead to about 7% reduction in the total cost of the negative blood groups, which are characterized by extremely erratic demand patterns. The implementation of the ordering policy will help HBBs to reduce their operational costs while ensuring a minimum desirable level of the availability of critical blood products.     

Non-clairvoyant Scheduling Games

In a scheduling game, each player owns a job and chooses a machine to execute it. While the social cost is the maximal load over all machines (makespan), the cost (disutility) of each player is the completion time of its own job. In the game, players may follow selfish strategies to optimize their cost and therefore their behaviors do not necessarily lead the game to an equilibrium. Even in the case there is an equilibrium, its makespan might be much larger than the social optimum, and this inefficiency is measured by the price of anarchy—the worst ratio between the makespan of an equilibrium and the optimum. Coordination mechanisms aim to reduce the price of anarchy by designing scheduling policies that specify how jobs assigned to a same machine are to be scheduled. Typically these policies define the schedule according to the processing times as announced by the jobs. One could wonder if there are policies that do not require this knowledge, and still provide a good price of anarchy. This would make the processing times be private information and avoid the problem of truthfulness. In this paper we study these so-called non-clairvoyant policies. In particular, we study the RANDOM policy that schedules the jobs in a random order without preemption, and the EQUI policy that schedules the jobs in parallel using time-multiplexing, assigning each job an equal fraction of CPU time.     

Pricing, rebate, advertising and ordering policies of a retailer facing price-dependent stochastic demand in newsvendor framework under different risk preferences

This paper evaluates the pricing and ordering policies of risk‐neutral, risk‐averse and risk‐seeking newsvendor‐type retailers facing price‐dependent stochastic demand and several sales‐promotion policies, namely pricing, rebates and advertising. Optimal pricing and ordering policies are obtained for the iso‐elastic demand function and for additive and multiplicative demand‐error structures. Performance is measured by the risk‐adjusted expected profit and evaluated across risk preferences. Pricing, rebate and advertising, in that order, are the most profitable sales‐promotion policies. The more risk averse the retailer, the lower its profit and the more it favors multiple promotion policies.     

Solving the multi-buyer joint replenishment problem with the RAND method

The multi-buyer joint replenishment problem (MJRP) is the multi-item inventory problem of coordinating the replenishment of a group of items that are jointly ordered from a single supplier. Joint replenishment of a group of items reduces cost by decreasing the number of times that the major ordering cost is charged. The objective of MJRP is to develop inventory policies minimizing the total costs over the planning horizon. The single buyer joint replenishment problem may be solved by techniques using the collectively described as the best available heuristics (e.g. Simulated Annealing, Genetic Procedures, Tabu Search, and others), collectively discussed as the RAND method. In this paper, we propose a new efficient RAND method to solve MJRP.     

A decision rule for coordination of inventory and transportation in a two-stage supply chain with alternative supply sources

This paper deals with a two-stage supply chain that consists of two distribution centers and two retailers. Each member of the supply chain uses a (Q,R) inventory policy, and incurs standard inventory holding and backlog costs, as well as ordering and transportation costs. The distribution centers replenish their inventory from an outside supplier, and the retailers replenish inventory from one of the two distribution centers. When a retailer is ready to replenish its inventory that retailer must decide whether it should replenish from the first or second distribution center. We develop a decision rule that minimizes the total expected cost associated with all outstanding orders at the time of order placement; the retailers then repeatedly use this decision rule as a heuristic. A simulation study which compares the proposed policy to three traditional ordering policies illustrates how the proposed policy performs under different conditions. The numerical analysis shows that, over a large set of scenarios, the proposed policy outperforms the other three policies on average.     

Optimal maintenance policies for several imperfect repair models

Three new maintenance models, two imperfect preventive maintenance models and a cost limit (imperfect) repair model are proposed. In these models the imperfect maintenance is treated in such a way that after maintenance the lifetime of a unit will be decreased to a fraction of the one immediately preceding it, and the imperfect repair time as well as cost increases as the number of imperfect repairs increases. The long-run expected maintenance cost rates and corresponding asymptotic average availabilities for these three models are derived. The optimum maintenance policies subject to maintenance time are discussed. Some constraint optimization problems related to maintenance cost rate and availability are presented. Finally, numerical examples are given.     

Optimal reorder decision utilizing centralized stock information in a two-echelon distribution system

The objective of this paper is to develop an optimal reorder policy for a two-echelon distribution system with one central warehouse and multiple retailers. We assume the warehouse has centralized stock information and each facility uses continuous-review batch ordering policy. Since echelon stock policies may show poor performance for distribution systems, we propose a new type of policy that utilizes the centralized stock information more effectively. We define the order risk policy, which decides reorder time based on the order risk which represents the relative cost increase due to immediate order compared to delayed order. We formulate the order risk and prove the optimality of the order risk policy under the system assumption that the warehouse guarantees delivery within the fixed lead time. The order risk is derived from the marginal analysis. Since exact calculation of the order risk is complex, an approximation method is provided. Computational experiment that compares our policy with existing policies shows that a significant cost savings is obtained. The concept of the order risk can be extended to the other models.Scope and purposeDue to the improvement of modern information technologies, many companies start tracking the real-time stock information of the supply chain members. Thus, the reorder policy based on the real-time centralized stock information becomes very important. In this paper, we consider the reorder policy for a continuous-review batch-ordering two-echelon distribution system, utilizing the centralized stock information. Existing reorder policies are classified into installation stock policies and echelon stock policies. Since installation stock policies consider only local stock information, echelon stock policies have been used when the centralized stock information is available. For serial and assembly systems, it has been known that the echelon stock policies are superior to the installation stock policies. However, for distribution systems, both policies may outperform each other in different situations. The purpose of this study is to develop the optimal reorder policy for a distribution system with one-warehouse and multiple retailers, where the real-time stock information is centralized at the warehouse. We define a new type of reorder policy of which the reorder decision is based on the ‘order risk’. The order risk is defined as the relative cost increase due to immediate order compared to delayed order. We formulate the order risk and prove the optimality. For computational simplicity, we provide an approximation method to calculate the order risk. Computational experiment shows that a significant cost savings is obtained.