A heuristic to manage perishable inventory with batch ordering,positive lead-times,and time-varying demand

So far the literature on inventory control for perishable products has mainly focused on (near-) optimal replenishment policies for a stylized environment, assuming no lead-time, no lot-sizing, stationary demand, a first in first out withdrawal policy and/or product life time equal to two periods. This literature has given fundamental insight in the behavior and the complexity of inventory systems for perishable products. In practice, many grocery retailers have recently automated the inventory replenishment for non-perishable products. They recognize they may need a different replenishment logic for perishable products, which takes into account e.g. the age of the inventory in the system. Due to new information technologies like RFID, it now also becomes more economically feasible to register this type of information. This paper suggests a replenishment policy for perishable products which takes into account the age of inventories and which requires only very simple calculations. It will be shown that in an environment, which contains important features of the real-life retail environment, this new policy leads to substantial cost reductions compared with a base policy that does not take into account the age of inventories.     

A genetic algorithm approach for multi-product multi-period continuous review inventory models

This paper formulates an approach for multi-product multi-period (Q, r) inventory models that calculates the optimal order quantity and optimal reorder point under the constraints of shelf life, budget, storage capacity, and “extra number of products” promotions according to the ordered quantity. Detailed literature reviews conducted in both fields have uncovered no other study proposing such a multi-product (Q, r) policy that also has a multi-period aspect and which takes all the aforementioned constraints into consideration. A real case study of a pharmaceutical distributor in Turkey dealing with large quantities of perishable products, for whom the demand structure varies from product to product and shows deterministic and variable characteristics, is presented and an easily-applicable (Q, r) model for distributors operating in this manner proposed. First, the problem is modeled as an integer linear programming (ILP) model. Next, a genetic algorithm (GA) solution approach with an embedded local search is proposed to solve larger scale problems. The results indicate that the proposed approach yields high-quality solutions within reasonable computation times.     

A numerical solution for a two-stage production and inventory system with random demand arrivals

This paper is about the study of a production lot sizing problem consisting of customers, one retailer, and one manufacturer. Demand from customers arrives randomly at a retailer one unit at a time. The retailer replenishes inventory from the manufacturer upon receiving a customer's order after its inventory depleted to zero. The manufacturer's production rate is assumed to be a finite constant. A production cycle starts when the manufacturer's inventory falls to or below zero and stops when its on-hand inventory reaches its optimal level. During the uptime in a production cycle, inventory is being built while randomly arriving orders from retailer are being fulfilled. The order arrival times from customers are independently and identically distributed, hence the inventory processes at both the manufacturer and the retailer become a renewal process that is difficult to solve analytically for a general distribution of order arrival time. Therefore, a numerical approach is used in developing a search procedure to obtain the optimal solution to the problem. Employing such a numerical approach, we also investigate how optimal solutions in different cases will change over the spectrum of some key parameters of the problem.     

A two‐warehouse inventory model for items with three‐parameter Weibull distribution deterioration,shortages and linear trend in demand

Depending on the type of goods and storage facilities available, perishable goods decay in different manners in terms of the initial point and rate of deterioration. The three‐parameter Weibull distribution is an excellent generalization of exponential decay, with the flexibility of modeling various types of deteriorations. Since inventory management of perishable goods involves expensive storage facilities, the retailer with small storage may have to rent a warehouse. In this paper, we discuss a two‐warehouse inventory model where deteriorations in the two warehouses follow independent three‐parameter Weibull distributions. Transfer of units is from the rented warehouse to the own warehouse, and incurs a positive cost per unit. Demand is a non‐decreasing linear function of time, shortages are backlogged and replenishment is instantaneous. A solution procedure for obtaining optimal values of initial inventory level and cycle time is presented. Sensitivity analysis is carried out. The effect of using other related deterioration distributions is illustrated.     

A multi-warehouse inventory model for items with time-varying demand and shortages

This paper develops a deterministic replenishment model with multiple warehouses (one is an owned warehouse and others are rented warehouses) possessing limited storage capacity. In this model, the replenishment rate is infinite. The demand rate is a function of time and increases at a decreasing rate. The stocks of rented warehouses are transported to owned warehouse in continuous release pattern. The model allows shortages in owned warehouse and permits part of the backlogged shortages to turn into lost sales—which is assumed to be a function of the currently backlogged amount. The solution procedure for finding the optimal replenishment policy is shown. As a special case of the model, the corresponding models with completely backlogged shortages and without shortages are also presented. The models are illustrated with the help of numerical examples. Sensitivity analysis of parameters is given in graphical form.Scope and purposeIn practical inventory management, there exist many factors like an attracted price discount for bulk purchase, etc. to make retailers buy goods more than the capacity of their owned warehouse. In this case, retailers will need to rent other warehouses or to rebuild a new warehouse. However, from economical point of views, they usually choose to rent other warehouses. If there are multiple warehouses available, an important problem faced by the retailers is which warehouses to be selected to hold items replenished, when to replenish as well as what size to replenish. For such a problem, the existing two-warehouse models, based on an unrealistic assumption that the rented warehouse has unlimited storage capacity, presented some procedures for determining the optimal replenishment policy. This paper extends the existing two-warehouse models in three directions. Firstly, the traditional two-warehouse models assumed the storage capacity of the rented warehouse unlimited. The present paper relaxes this impractical assumption and considers the situation with multiple rented warehouses having a limited capacity. Secondly, the traditional two-warehouse models considered a constant demand rate or a linearly increasing demand rate. In this model, the demand rate varies over time and increases at a decreasing rate, which implies an increasing market going to saturation. Thirdly, we extend the two-warehouse models to the case with partially backlogged shortages. The purpose of this paper is to build a multi-warehouse replenishment model to help decision-makers solve the problem of which warehouses to be chosen to store items replenished and how to replenish.     

Multi-product multi-chance-constraint stochastic inventory control problem with dynamic demand and partial back-ordering: A harmony search algorithm

In this paper, a multiproduct inventory control problem is considered in which the periods between two replenishments of the products are assumed independent random variables, and increasing and decreasing functions are assumed to model the dynamic demands of each product. Furthermore, the quantities of the orders are assumed integer-type, space and budget are constraints, the service-level is a chance-constraint, and that the partial back-ordering policy is taken into account for the shortages. The costs of the problem are holding, purchasing, and shortage. We show the model of this problem is an integer nonlinear programming type and to solve it, a harmony search approach is used. At the end, three numerical examples of different sizes are given to demonstrate the applicability of the proposed methodology in real world inventory control problems, to validate the results obtained, and to compare its performances with the ones of both a genetic and a particle swarm optimization algorithms.     

Optimization of variable demand fuzzy economic order quantity inventory models without and with backordering

A variable demand inventory model was developed for minimizing inventory cost, treating the holding and ordering costs and demand as independent fuzzy variables. Thereafter, backordering cost was also considered as an independent fuzzy variable. Fuzzy expected value model and fuzzy dependent chance programming model were constructed to find the optimal economic order quantity, which would minimize the fuzzy expected value of the total cost, so that the credibility of the total cost not exceeding a certain budget level was maximized. Optimization was carried out using genetic algorithms and particle swarm optimization algorithm, and their performances were compared. The developed model was found to be efficient not only in one artificial case study but also in two data sets collected from the industries. Therefore, this model could solve real-world problems, too.     

A heuristic for rationing inventory in two demand classes with backlog costs and a service constraint

We study the rationing policy in an inventory system with two demand classes and different service criteria for backorders. Due to the difference of customer values, system performance sometimes has to be measured with a mixture of penalty cost and service level in managing inventory. With a continuous review (r,Q) system, we develop a critical level rationing policy in which a threshold mechanism is adopted to allocate backorders when multiple outstanding orders exist. Due to the complexity of the problem, a heuristic is developed based on the principle that both demand classes are served with respective target service levels. We also introduce bounds so that the search ranges of decision variables become restrictive. The numerical examples indicate an excellent performance of our heuristic. In addition, when ordering cost is medium or high, the threshold clearing mechanism has the same results as the optimal one. When ordering cost is small (set to zero), different clearing mechanisms should be used depending on the priorities of demand classes. Further analysis indicates that transforming the service constraint into a cost parameter and then applying the existing algorithm will not be a good approach for this problem with mixed performance criteria. It either increases the costs or violates the service constraint. This study also shows the importance of applying rationing policy when high priority class has a low demand volume, target service levels between two classes have a large gap, or replenishment lead time is long. The results of this study should enhance our understanding of how to implement rationing policies in practice.     

An optimization approach for joint pricing and ordering problem in an integrated inventory system with order-size dependent trade credit

Under a business trading environment, it is common for the trade credit to depend on the order size. Therefore, it is important to discuss the single-supplier and single-buyer supply chain problem which includes order-size dependent trade credit. In this study, an integrated inventory model with a price sensitive demand rate, determining jointly economic lot size of the buyer’s ordering and the supplier’s production batch, are developed to maximize the total profit per unit time. An efficient algorithm is provided to obtain the optimal solution, and then numerical examples are presented to illustrate the theoretical results. Finally, the comparison between whether an optimal solution is jointly or independently determined is also provided.     

Supplier–retailer inventory coordination with credit term for inventory‐dependent and linear‐trend demand

In this paper, a nonintegrated and collaborative replenishment policy is considered, respectively, which incorporates varying demand depending on both inventory level and time during the finite planning horizon. For additional cost savings realized from coordination, the paper adopts trade credit as a cost‐saving shift means and introduces a brand new parameter, that is, credit period rate. Then, the equitable credit period rate is determined, and different values of the credit period rate reflect the allocation of additional cost savings between the supplier and retailer. Furthermore, the conditions for the existence and uniqueness of an optimal solution are proved for the nonintegrated and collaborative replenishment policy, and an efficient solution procedure is developed to determine the optimal results and coordination of the inventory model. Finally, several numerical examples are provided to illustrate the proposed strategy and algorithm, and the sensitivity analysis of the optimal solution with respect to each parameter is presented. The sensitivity analysis suggests that the size of the credit period rate has a strong relationship with the supplier's and retailer's inventory cost (including capital cost) and setup cost. In real‐life situations, this proposed strategy may be applied to some consumer products in the growth phase or best‐selling consumer goods, etc.     

Production and allocation policies in a two-class inventory system with time and quantity dependent waiting costs

This paper presents an integrated production and inventory allocation model in a two-echelon supply chain system. The higher echelon is a manufacturer, who produces a single commodity. The lower echelon consists of two types of major commodity distributors who might face stochastic or deterministic demands from multiple retailers. Our analytical model provides optimal decision policies that minimize total production and customer waiting costs from the manufacturer's perspective when there are time and quantity dependent customer waiting costs. We identify the value of the integrated policy and compare it with typical approximations such as aggregating the multiple demands or applying the single demand multiple times.     

Centralized and decentralized inventory policies for a single-vendor two-buyer system with permissible delay in payments

In today's business transactions, vendors usually offer their buyers a delay period in payment. This strategy has benefits to the vendor since it attracts new buyers who consider the delay period as a type of price reduction. In addition, permissible delay in payments also is advantageous for the buyers since they do not have to pay the vendor immediately after they receive the items. In contrast, the buyers can delay the payment until the end of the allowed period and during the credit period they can earn interest on the accumulated revenues. However, if the payment is not settled by the end of the credit period, a higher interest is charged. Under this scenario, an inventory model consisting of a single vendor which supplies an item to two different buyers is analyzed. First, we address the problem assuming that buyers and vendor are willing to cooperate and the integrated model is derived in terms of single-cycle policies. Next, we analyze a decentralized model where the buyers and the vendor make decisions independently. A numerical example is solved to illustrate both strategies. We carry out a computational study to compare integrated and decentralized policies. A sensitivity analysis is also performed to examine the effects of each parameter on both total costs. According to the computational results and the statistical analysis, in most scenarios the integrated policies outperform the decentralized strategies.     

Policy measurement for the dynamic linear model with expectations variables: A multiplier approach

To estimate the economic policy effects of per unit policy change, the conventional policy multipliers, as a measure of policy effects, can be easily calculated from the traditional dynamic econometric model without expectations variables. However, the past decade has witnessed much research and debate on the rational expectations hypothesis. In a model with expectations variables, the complexity of measuring policy effects arises not only from its dynamic properties, but also from its treatment of expectations variables.In this paper, we present a method of deriving the policy multipliers for the dynamic linear model with expectations variables and a backward recursive substitution algorithm to calculate these multipliers. The development of our methodology is basically along the traditional theory of the policy multiplier, with a substantial modification to distinguish unanticipated from anticipated policy effects.     

Variable neighborhood search for the inventory routing and scheduling problem in a supply chain

The inventory, routing and scheduling decisions are three major driving factors for supply chain performance. Since they are related to one another in a supply chain, they should be determined simultaneously to improve the decision quality. In the past, the inventory policy, vehicle routing and vehicle scheduling are determined sequentially and separately. Hence, the total cost (inventory, routing and vehicle costs) would increase. In this paper, an integrated model for the inventory routing and scheduling problem (IRSP) is proposed. Since searching for the optimal solution for this model is a non-polynomial (NP) problem, a metaheuristic, variable neighborhood search (VNS), is proposed. The proposed method was compared with other existing methods. The experimental results indicate that the proposed method is better than other methods in terms of average cost per day.     

A joint model for cash and inventory management for a retailer under delay in payments

As retail companies continue to navigate through the economy downturn, it becomes critical to find innovative cost reduction methods. Cash management is a cost-intensive process for retailers, who are currently focusing on effective cash management, such as deciding on the maximum cash level to keep in their business accounts and how much to borrow to finance inventories and pay suppliers. In this paper, we consider the problem of finding the optimal operational (how much to order and when to pay the supplier) and financial decisions (maximum cash level and loan amount) by integrating the cash management and inventory lot sizing problems. We consider a supplier offering a retailer an interest-free credit period for settling the payment. Beyond this period, the supplier charges interest on the outstanding balance. Whenever the cash exceeds a certain limit, it will be invested in purchasing financial securities. At the time when the retailer pays the supplier for the received order, cash is withdrawn from the account, incuring various financial costs. If the cash level becomes zero or not sufficient, the retailer obtains an asset-based loan at interest. We model this problem as a nonlinear program and propose a solution procedure for finding the optimal solution. We perform a numerical study to analyze the impact of optimal cash management on the inventory decisions. The results indicate that the optimal order quantity decreases as the retailer’s return on cash increases. We compare our model to a model that ignores financial considerations of cash management, and show numerically that our model lowers the retailer’s cost. Also, we illustrate the effect of changing various model parameters on the optimal solution and obtain managerial insights.     

A case-deletion diagnostic for penalized calibration estimators and BLUP under linear mixed models in survey sampling

The penalized calibration technique in survey sampling combines usual calibration and soft calibration by introducing a penalty term. Certain relevant estimates in survey sampling can be considered as penalized calibration estimates obtained as particular cases from an optimization problem with a common basic structure. In this framework, a case deletion diagnostic is proposed for a class of penalized calibration estimators including both design-based and model-based estimators. The diagnostic compares finite population parameter estimates and can be calculated from quantities related to the full data set. The resulting diagnostic is a function of the residual and leverage, as other diagnostics in regression models, and of the calibration weight, a singular feature in survey sampling. Moreover, a particular case, which includes the basic unit level model for small area estimation, is considered. Both a real and an artificial example are included to illustrate the diagnostic proposed. The results obtained clearly show that the proposed diagnostic depends on the calibration and soft-calibration variables, on the penalization term, as well as on the parameter to estimate.     

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.     

A model for integrating process planning and production planning and control in machining processes

The goal of process planning is to propose the routing of a previously designed part and results in a sequence of operations and their parameters. It concerns and requires detailed information about the process. The goal of production planning, on the other hand, is to schedule, sequence and launch the orders introduced on the routing sheet into the job-shop according to the enterprise's strategic goal and the actual conditions of the production plant. The goals, information and decisions taken in process planning and production planning and control are often very different and, because of that, it is very difficult to integrate them.

The objective of this work is to develop a model that can be applied in the future to the development of an integrated process planning and scheduling tool using an integrated definition (IDEF) methodology to design an activity model, which integrates process and production planning in metal removal processes. An activity model will be used to develop a system that allows the user to plan the process and the production at the same time in collaborative engineering work. To design the activity model, a wide range of parts were evaluated and processed in an actual job-shop factory. Several activities were developed in detail to be tested in real cases, and an example of one of them is introduced in this article.     

A parallel approach for determining confidence intervals of variable statistics in large and sparse linear equations with RHS ranges

This study proposes an algorithm capable of working in parallel for solving variable statistics with large and sparse linear equations under given right hand side ranges. A comparative study to the direct linear programming method is conducted under a main central processor and up to four parallel processors. The studied results are reported computationally and discussed. Moreover, the approach can be adapted for the system under domain decompositions structure leading to a better efficiency experimentally in a case example.     

GA-PARSIMONY: A GA-SVR approach with feature selection and parameter optimization to obtain parsimonious solutions for predicting temperature settings in a continuous annealing furnace

This article proposes a new genetic algorithm (GA) methodology to obtain parsimonious support vector regression (SVR) models capable of predicting highly precise setpoints in a continuous annealing furnace (GA-PARSIMONY). The proposal combines feature selection, model tuning, and parsimonious model selection in order to achieve robust SVR models. To this end, a novel GA selection procedure is introduced based on separate cost and complexity evaluations. The best individuals are initially sorted by an error fitness function, and afterwards, models with similar costs are rearranged according to model complexity measurement so as to foster models of lesser complexity. Therefore, the user-supplied penalty parameter, utilized to balance cost and complexity in other fitness functions, is rendered unnecessary. GA-PARSIMONY performed similarly to classical GA on twenty benchmark datasets from public repositories, but used a lower number of features in a striking 65% of models. Moreover, the performance of our proposal also proved useful in a real industrial process for predicting three temperature setpoints for a continuous annealing furnace. The results demonstrated that GA-PARSIMONY was able to generate more robust SVR models with less input features, as compared to classical GA.