Optimal Order Cycle Research Articles

Improving solid waste management in remote First Nations communities through inventory-theory-based optimization

Solid waste management (SWM) is crucially important for sustainable development and the environmental management system in First Nations (FN) communities and reserves. This research developed an inventory-theory-based optimization model under uncertainty for SWM to support FN communities. The model can be used to pick the most appropriate facilities and the most optimal waste destination for achieving minimum system cost. The opening conditions of SWM facilities depend on the situation to satisfy the demand for solid waste treatment. The economic order quantity model is combined with the developed model to determine the optimal batch size and order cycle to minimize inventory costs. The facility selection and waste allocation in the normal and winter seasons under different risk levels can all be obtained from the developed model. These solutions can guide professionals in analyzing the trade-offs between system cost and constraint-violation risks in management and operation.

Optimal investment in preservation technology for non-instantaneous deteriorating items under carbon emissions consideration

Freshly, many countries have imposed carbon taxes on businesses in an effort to reduce emissions and regulate carbon pollution. As carbon emission is a principal contributor to climate change and is unavoidable, policymakers must work out a way to tax carbon emissions to lessen its impact and adapt themselves to the change. Carbon taxes are typically levied on a company that produces large amounts of carbon dioxide, and the tax is calculated based on the amount of emissions generated. As a source of carbon emissions, a metric is devised in our study to determine the optimal investment in preservation technology for non-instantaneous deteriorating inventory. The goal of preservation is not only to extend an item’s life span but also to limit the need for future intervention. In light of the above, an Economic Order Quantity (EOQ) model is more comprehensive if the preservation technology and carbon emissions are taken into account. Our proposed model caters to all these elements and aims to identify the optimal order quantity, cycle period, and preservation level for profit maximisation. The key point is that the preservation we focus on is not particularly for ongoing deterioration but also for a non-fixed delay interval before the deterioration process begins. The findings and sensitivity analysis reveal that investing in preservation technology has a profitable impact on a company, but an excessive level of preservation technology may have an adverse effect. The influences of some significant parameters are demonstrated through their applicability to managerial implications.

Fuzzy EOQ Model for Time Varying Deterioration and Exponential Time Dependent Demand Rate under Inflation

In this study we have discussed a fuzzy eoq model for deteriorating products with time varying deterioration under inflation and exponential time dependent demand rate. Shortages are not allowed in this fuzzy eoq model and the impact of inflation is investigated. An inventory model is used to determine whether the order quantity is more than or equal to a predetermined quantity for declining items.The optimal solution for the existing model is derived by taking truncated taylor’s series approximation for finding closed form optimal solution. The cost of deterioration, cost of ordering, cost of holding and the time taken to settle the delay in account are considered using triangular fuzzy numbers. In this study the fuzzy triangular numbers are used to estimate the optimal order quantity and cycle duration. Furthermore we have used graded mean integration method and signed distance approach to defuzzify these values. To validate our model numerical examples are discussed for all cases with the help of sensitivity analysis for different parameters. Finally, a higher decay rate results in a shorter ideal cycle time as well as higher overall relevant cost is established. The presented model can be used to predict demand as a quadratic function of time,stock level time dependent demand, selling price, and other variables.

Impacts of expiration date on optimal ordering policy for deteriorating items under two-level trade credit: Quantity loss and quality loss

Practically, two-level trade credit is usually applied to stimulate the retailer’s order incentive for deteriorating items with expiration date. Nevertheless, previous studies ignore to identify both quantity loss and quality loss derived from expiration date, and lack of examining whether these joint losses impact effectiveness of two-level trade credit. Thus, this paper firstly builds an inventory model for deteriorating items with expiration date, which accurately determines the retailer’s optimal response when involving both quantity and quality losses. (1) For given expiration date, this paper identifies the phenomenon of limit effect and its occurred conditions, referring that the retailer’s optimal order cycle for deteriorating items equals its expiration date; (2) this paper validates the scope of limit effect, below which deteriorating items should be optimally replenished with its expiration date. In addition, two-level trade credit is further incorporated into deteriorating items, resulting in two types of expiration date scenarios including lower and higher. Specifically, for the given expiration date, upstream credit period can affect the retailer’s selection of operational policies, and the occurrence of limit effect. And along with the increase of expiration date, more operational policies can be assumed by the retailer.

Retailer’s Operational Decision Based on EOQ Model with Upstream Flexible Two-Part Trade Credit and Downstream Partial Trade Credit

Flexible two-part trade credit is widely used in supply chain, however, there is scant research about inventory management engaged in flexible two-part trade credit strategy. This paper bridges this gap and studies a new two-level trade credit based on an EOQ model in which the supplier provides flexible two-part trade credit to the retailer and the retailer provides partial trade credit to its customer. We adopt a convex optimization method to obtain retailer’s optimal operational decision (i.e., the optimal ordering cycle, the optimal fraction of purchase cost that paid in advance, and the optimal credit period for its downstream customer). Moreover, we design a numerical algorithm to solve this model computationally. We find that: (1) the retailer is not sensitive to small cash discount provided by the supplier; (2) the length of credit period in flexible two-part trade credit strategy will affect the customer and retailer: the shorter one influences the retailer’s behavior, but not the customer’s; the longer one influences the customer’s behavior, but not the retailer’s; (3) the retailer can control its risk through partial trade credit.

Optimal Machine Stopping Time and Ordering Cycle for Parts to Minimize the Total Cost of a Supply Chain

Many parts or components in a facility are sometime vulnerable to failure causing downtime and production loss. So, in order to decrease the downtime, parts of the same type that follow the same lifespan distribution need to be replaced at least once to minimize the cost of unscheduled labor and the damages to the products. A decision on replacing all such vulnerable parts decreases the total cost including penalty cost, purchasing cost and holding cost. Different preempt times of a machine result in different purchasing quantity, procurement cost and carrying costs. So, a rational decision of allowable stopping time of a machine and order cycle for vulnerable parts jointly minimizes the total cost of supply chain. This study proposes a novel model to minimize the total cost for the vulnerable parts which have joint influence on machine performance. An integrated nonlinear cost model developed here is optimally solved and tested with several different distributions. Strong results are propounded to support the proposed model in terms of manufacturing time and system cost.

Endorsement of Optimal ordering cycle implementing Quick Switching System with Single Sampling Plan with Permissible delay in Payments involving non-destructive testing

Endorsement of Optimal ordering cycle implementing Quick Switching System with Single Sampling Plan with Permissible delay in Payments involving non-destructive testing

Avoiding the capacity cost trap: Three means of smoothing under cyclical production planning

Companies tend to set their master production schedule weekly, even when producing and shipping on a daily basis—the term for this is staggered deliveries. This practice is common even when there is no marginal cost of setting a new schedule. We argue that the practice is sound for companies that use the ubiquitous order-up-to (OUT) policy to control production of products with a significant capacity cost. Under these conditions, the length of the order cycle (time between schedule updates) has a damping effect on production, while a unit (daily) order cycle can cause significant capacity costs. We call this the capacity cost trap.Developing an analytical model based on industrial evidence, we derive capacity and inventory costs under the staggered OUT policy, showing that for this policy there is an optimal order cycle possibly greater than unity. To improve on this solution, we consider three approaches to smoothing: either levelling within the cycle, deferring excess production or idling to future cycles via a proportional OUT policy, or increasing the length of the cycle. By deriving exact cost expressions we compare these approaches, finding that smoothing by employing the proportional OUT policy is sufficient to avoid the capacity cost trap.

An Imprecise EOQ Model for Non-instantaneous Deteriorating Item with Imprecise Inventory Parameters Using Interval Number

In this paper, an imprecise EOQ model for non-instantaneous deteriorating item with different demand rate, shortages and salvage value is formulated and solved with inventory parameters like demand rate, holding cost, deteriorating cost, shortage cost and salvage value which are considered to be imprecise. The rate of deterioration here is assumed to be constant but imprecise. Here the impreciseness of the above inventory parameters are assumed as interval numbers which are made crisp representations them in parametric forms. For the first time, total average cost of the system is presented by introducing parametric functional form of interval number. The optimal order cycle, the optimal shortage period and the optimal order quantity of the proposed imprecise model are derived by minimizing the total average cost. A numerical example is presented to illustrate the solution of the proposed imprecise model. Finally a graphical representation of the optimal solution is provided to demonstrate the proposed approach. It is seen that at the lower ends of the intervals, the average total cost is maximum where as at the corresponding upper ends, the said cost is lowest.

Research on Ordering Strategy of Perishable Products with Variable Demand

This paper mainly considers the influence of price on demand for perishable products. According to the characteristics of products and the condition of demand, demand is a function of price elasticity. Under the premise of allowing the shortage, this study constructs optimal inventory control model of perishable products by introducing the lost order coefficient and solves the model, improves the traditional inventory model. Using optimization method, which deduces the optimal ordering cycle, the optimal order quantity and the total inventory cost, etc. Through the example for the deterioration rate and service level to sensitivity analysis, the results show that as deterioration rate increases, the total inventory cost and sale price are on the rise, while the unit profit is decreasing; The service level is directly proportional to the selling price, inversely proportional to the total inventory cost and unit profit. This research provides a theoretical basis for firms in the efficient inventory management.

Optimal Buyer’s Replenishment Policy in the Integrated Inventory Model for Imperfect Items

In the classical economic order quantity (EOQ) models, a common unrealistic assumption is that all the items received are of good quality. However, in realistic environment, a received shipment usually contains a fraction of imperfect quality items. These imperfect items may be scrapped, reworked at a cost, or salvaged at a discounted price. While the percentage of imperfect items is random, the optimal ordering cycle is rarely considered in current literatures. This paper revisits the model (Maddah and Jaber, 2008) and extends it by assuming that the ordering cycle is determined by the demand rate, delivery quantity per shipment, and the mathematical expectation of the defective rate. The possibility of stockout or residue in the end of a cycle will be considered, and the loss of stockout and the salvage of the residue are counted into the cost. Besides, we consider consolidating the shipments of imperfect items over multiple deliveries. Thus, an integrated vendor-buyer inventory model for imperfect quality items with equal-size shipment policy is established to derive the optimal ordering cycle, ordering quantity, and number of deliveries. The computational method of the optimal delivery quantity per shipment and number of deliveries is given through theoretical results. Finally, sensitivity of main parameters is analyzed through simulation experiments and shown by some figures.

EOQ model with linear time dependent demand and different holding cost functions

In real life observation demand rate depends on time. In this paper demand rate is considered as linearly time dependent and holding cost is exponentially time dependent for case I and time dependent for case II. Previous models considered that demand rate as well as holding cost both being constant. To stimulate more sales the demand rate is not constant but it is time-dependent, stock dependent, inflation dependent, cash discount etc. Differential calculus is used for finding optimal order cycle, optimal cycle time, optimal total inventory cost for both cases (i.e., case I and case II). Sensitivity analysis is given for the variation of various parameters for both cases.

An Order Size Dependent Trade Credit Integrated Inventory Model with Capacity Constraint

Trade credit has many forms in today’s business practice. The most common form of trade creditpolicy that is used to encourage retailers to buy largerquantities is order-size dependent. This study attempts to determine economic order quantity for deteriorating items with two-storage facilities (one is an owned warehouse and the other is a rented warehouse) where trade credit is linked to order quantity. When the number of ordered units exceeds the capacity of the own warehouse, an additional rented warehouse is required to store the excess units. Therefore, to incorporate the concept of order-size dependent trade credit and limited storage capacity, we proposed an integrated inventory model that the retailer receives an arriving lot containing some defective items with capacity constraint and a permissible delay payment period that is order-size dependent. In addition, the unit production cost, which is a function of the production rate, is considered. Our objective is to determine the retailer’s optimal order cycle length, the order quantity, and the optimal number of shipments per production runs from the supplier to the retailer so that the entire supply system has maximum profit. Finally, numerical examples are presented to illustrate the solution procedure.

Optimal Replenishment Policy for Deteriorating Items with Time Sensitive Demand Under Trade Credit Financing

SYNOPTIC ABSTRACTIn this study, we have formulated an inventory model for deteriorating items with trade credit financing under profit maximization criteria, considering the demand as a linear function of time. Optimal solution procedures to find the optimal order quantity and cycle time are discussed. Several numerical examples are provided for the proposed model in order to illustrate the solution procedure. Sensitivity analysis of the optimal solution with respect to various parameters of the system is carried out, and the managerial implications are discussed in detail.

An Optimal Ordering Cycle at Interactions of Fuzzy Parameters and High Disposal Fees of Food or Drug Supply Systems

In many cities the food and drug waste is invading their districts, and disposal fees are high. In this paper we investigate how to determine an optimal ordering cycle when the demand for products and the price are fuzzy variables, and lead time is constant, in the case of perishable food or drugs of unknown deteriorating ratio, and at high disposal fees. The parameters required for the solution are trapezoidal membership functions for the fuzzy demand, the fuzzy purchase cost for each item, the fixed cost to place the order, and the cost of disposal (i.e. disposal fee), the fuzzy deterioration rate, and the fixed storage cost specified for each item per period. The three fuzzy parameters in the total cost function are described as trapezoidal fuzzy variables so that the influence of volatility of these variables on the criterion function could be calculated. In the paper, the safety stock decays at the same rate as the rest of the inventory. Credibility distributions are given for such cases. Here, we demonstrated that the expected value of total costs in the ordering cycle is equal to the signed distance to the origin. The kurtosis of variables when appearing simultaneously, and their influence on the disposal fee are under investigation, therefore the trapezoidal membership functions are investigated. Through an extensive analytical study and the numerical example, we concluded the following: (1) for the items having a trapezoidal demand membership function, increasing the volatility of demand generates a membership function with a flatter shape, thus shortening the optimal ordering cycle, and (2) an increment of fuzziness reduces the optimal cycle length more gradually than the crisp values, when the sum of the purchase price plus the disposal fee of the product, or the demand, or the deterioration rate are increasing. This means that a high fuzziness reduces the sensitivity of the optimal cycle duration.

Inventory model with stock dependent demand and different holding cost functions

This study develops inventory models in which demand rate is stock level dependent and three different holding cost functions: 1) constant holding cost; 2) exponential time dependent; 3) stock level dependent. Mathematical models have been developed for these three different situations to determine optimal order quantities, cycle time and optimal total inventory cost. Truncated Taylor's series expansion is used for exponential terms for finding closed form numerical solutions. The results are illustrated with the help of numerical examples. The sensitivity analysis of the optimal solution with respect to the variation of the parameters of the model is also discussed.

Optimal Decisions and Coordination Mechanisms for a Fresh Agricultural Product Supply Chain System

For a one-supplier-one-retailer agricultural product supply chain, quantity and quality of the agricultural products often reduce because their own perishable and anthropogenic factors in the process from the supplier via the retailer to final consumers. This paper takes shortage and deterioration factors into account, establishes related profit functions of the supplier and the retailer, obtains the optimal ordering cycle and quantity decisions, and analyzes the impact of deterioration on decision makers under the decentralized system. To maximize the total profit of supply chain, we explore coordination mechanisms for the supply chain when considering shortage and deterioration factors, such as revenue sharing contract, quantity discount contract and buy-back contract. By comparing these different contracts, the coordination effect is analyzed in details. Finally, through series of numerical analysis, some managerial insights are provided.

The Optimal Replenishment Policy under Trade Credit Financing with Ramp Type Demand and Demand Dependent Production Rate

This paper investigates the optimal replenishment policy for the retailer with the ramp type demand and demand dependent production rate involving the trade credit financing, which is not reported in the literatures. First, the two inventory models are developed under the above situation. Second, the algorithms are given to optimize the replenishment cycle time and the order quantity for the retailer. Finally, the numerical examples are carried out to illustrate the optimal solutions and the sensitivity analysis is performed. The results show that if the value of production rate is small, the retailer will lower the frequency of putting the orders to cut down the order cost; if the production rate is high, the demand dependent production rate has no effect on the optimal decisions. When the trade credit is less than the growth stage time, the retailer will shorten the replenishment cycle; when it is larger than the breakpoint of the demand, within the maturity stage of the products, the trade credit has no effect on the optimal order cycle and the optimal order quantity.

Optimising a Model of Minimum Stock Level Control and a Model of Standing Order Cycle in Selected Foundry Plant

Abstract It has been found that the area where one can look for significant reserves in the procurement logistics is a rational management of the stock of raw materials. Currently, the main purpose of projects which increase the efficiency of inventory management is to rationalise all the activities in this area, taking into account and minimising at the same time the total inventory costs. The paper presents a method for optimising the inventory level of raw materials under a foundry plant conditions using two different control models. The first model is based on the estimate of an optimal level of the minimum emergency stock of raw materials, giving information about the need for an order to be placed immediately and about the optimal size of consignments ordered after the minimum emergency level has occurred. The second model is based on the estimate of a maximum inventory level of raw materials and an optimal order cycle. Optimisation of the presented models has been based on the previously done selection and use of rational methods for forecasting the time series of the delivery of a chosen auxiliary material (ceramic filters) to a casting plant, including forecasting a mean size of the delivered batch of products and its standard deviation.

Modeling and Optimization of Inventory-Distribution Routing Problem for Agriculture Products Supply Chain

Mathematical models of inventory-distribution routing problem for two-echelon agriculture products distribution network are established, which are based on two management modes, franchise chain and regular chain, one-to-many, interval periodic order, demand depending on inventory, deteriorating treatment cost of agriculture products, start-up costs of vehicles and so forth. Then, a heuristic adaptive genetic algorithm is presented for the model of franchise chain. For the regular chain model, a two-layer genetic algorithm based on oddment modification is proposed, in which the upper layer is to determine the distribution period and quantity and the lower layer is to seek the optimal order cycle, quantity, distribution routes, and the rational oddment modification number for the distributor. By simulation experiments, the validity of the algorithms is demonstrated, and the two management modes are compared.