Critical number ordering policy for LIFO perishable inventory systems

This paper considers a stochastic perishable product inventory system characterized by LIFO (Last-In-First-Out) issuing, critical number ordering and a two-period lifetime. Exact and approximate closed form expressions for expected outdates are derived. The approximation, which is straightforward to compute, is shown to be accurate over a wide range of model parameters. The paper concludes by comparing optimal policies and expected costs in the LIFO system with the corresponding policies and costs in a system controlled by FIFO (First-In-First-Out) issuing.     

An integrated vendor–buyer inventory model with backorder price discount and effective investment to reduce ordering cost

The single-vendor single-buyer integrated production inventory system has been an object of study for a long time, but little is known about the effect of investing in reducing ordering cost on the integrated inventory models with backorder price discount and variable lead time. The purpose of this article is to investigate in the continuous review model with backorder price discount and variable lead time to effectively increase investment and to reduce the joint expected annual total cost. The integrated strategy discussed here is one in which the buyer orders a quantity, then the vendor produces n times order quantity in each production cycle, in order to reduce setup cost. In addition, the buyer offers backorder price discounts to the customers that may motivate the customers’ desire for backorders, and buyer ordering cost can be reduced through effective investment. An integrated inventory model is established to find the optimal solutions of order quantity, ordering cost, backorder price discount, lead time, and the number of shipments from the vendor to the buyer in one production run, so that the joint expected annual total cost incurred has the minimum value. Furthermore, numerical examples are used to demonstrate the benefits of the model.     

Integrated inventory and transportation decision for ubiquitous supply chain management

We consider price-dependent demand and develop an integrated inventory and transportation policy with strategic pricing to maximize the total profit for a ubiquitous enterprise. The proposed policy provides the optimal ordering, shipment and pricing decision. We first assume that demand for a product is a linear function of the price. A mathematical model for the total profit under quantity based dispatch is developed in consideration of ordering, shipment and pricing variables. Optimality properties for the model are then obtained and an efficient algorithm is provided to compute the optimal parameters for ordering, shipment and pricing decision. Finally, we extend our results to a more general case where demand for the product is a convex or a concave function of the price.     

Single period stochastic inventory problems with ordering or returns policies

In recent years, there has been an increasing adoption of returns policies in the coordination of the supply chain, where market demand is always assumed to be satisfied by manufacturing or by ordering from suppliers. However, many industries face the important decision of how to balance their inventory level. This problem has long been studied in financial institutions such as banks. This study presents an optimal inventory policy under a given stochastic demand such as a uniformly distributed demand, single-item, and single period review inventory system. The optimal inventory control policy obtained in this study is called a four-point policy: that is, when the entity’s inventory level is below a reorder point, the entity must increase his stock level by ordering and order up-to a fixed level (second point); when the entity’s inventory level is over a return point (third point); the stock level must be decreased by returns and decreased to a fixed level (fourth point); otherwise, nothing should be done. We also analyze the (K, S)-convex properties of the inventory cost function.     

Mean-variance analysis and the single-period inventory problem

The classic single-period inventory problem, colloquially referred lo in the literature as the newsboy problem, is examined assuming the objective of maximizing a mean-variance utility function. This objective function is intended to reflect different attitudes of decision makers towards risk. The optimal order quantity is derived and it is shown that under risk aversion the amount that is ordered is less than the amount ordered under risk neutrality. On the other hand, it is shown that the optimal order quantity when the decision maker is a risk lover is greater than it would be were he risk neutral. The problem is also considered when the ordering cost includes a fixed cost component in addition to the purely variable quantity purchase cost. For this case, an optimal (s, Q) policy is derived (where s is the reorder point and Q is the order quantity).     

Single-period inventory model with a delayed incentive option for selling excess inventory

The single‐period problem (SPP) is to find the order quantity which maximizes the expected profit in a single period probabilistic demand framework. We extend the SPP to a case where a retailer uses delayed incentives in the form of cash mail‐in rebates to sell remaining inventory that did not sell at the regular price. The advantage of cash mail‐in rebates is that not all consumers will redeem them. We address three cases: (1) rebate value is predetermined and the order quantity is a decision variable; (2) order quantity is a decision variable and rebate value is set to the value needed to sell all excess inventory, and (3) order quantity is a decision variable and the rebate may be used to sell part of or all excess inventory. In the third case, any inventory remaining after the rebate offer is salvaged at reduced price. We provide analytical solutions for uniform and exponential demand distributions. In all cases, rebates can lead to significant increases in expected profit. We first maximize the expected profit. We then maximize the probability of achieving a target profit and show that the use of rebates can lead to a substantial increase in that probability.     

Joint replenishment with imperfect items and price discount

A joint replenishment problem is presented to determine the ordering policy for multiple items having a certain percentage of defective units. The purpose of this paper is to study the impact of the percentage of defective units on the ordering policy. Two different scenarios are presented for joint replenishment problem: (1) without price discount and (2) with price discount. For each scenario, the total expected cost per unit time is derived and algorithms are presented to determine the family cycle length and the integer number of intervals that the replenishment quantity of each item will last. Numerical examples are presented and the results are discussed.     

Joint management of finished goods inventory and demand process for a make-to-stock product: a computational approach

In this paper, we consider the joint management of finished goods inventory and demand for a product in a make-to-stock production system. The production process is random with controllable mean rate, and the demand process is stochastic with changeable mean rate dependent on the sale price being high or low. The management issue is how to dynamically adjust the production rate and the sale price to maximize the long run total discounted profit. We show that: 1) the optimal management of the finished goods inventory follows a base stock policy: when the inventory is above certain base stock level, the production is halted; otherwise the maximum production rate is deployed to raise the inventory to the base stock level; and 2) the optimal management of the demand process follows a price switch threshold policy: when the inventory is above the threshold, the low sale price is chosen to sell the product; and below it the high price is chosen to reduce the demand. We provide an algorithm to compute the base stock level and price switch threshold. Extension to multiple price choices is given with proofs highlighted.     

A supplier-selection model with classification and joint replenishment of inventory items

Since inventory costs are closely related to suppliers, many models in the literature have selected the suppliers and also allocated orders, simultaneously. Such models usually consider either a single inventory item or multiple inventory items which have independent holding and ordering costs. However, in practice, ordering multiple items from the same supplier leads to a reduction in ordering costs. This paper presents a model in capacity-constrained supplier-selection and order-allocation problem, which considers the joint replenishment of inventory items with a direct grouping approach. In such supplier-selection problems, the following items are considered: a fixed major ordering cost to each supplier, which is independent from the items in the order; a minor ordering cost for each item ordered to each supplier; and the inventory holding and purchasing costs. To solve the developed NP-hard problem, a simulated annealing algorithm was proposed and then compared to a modified genetic algorithm of the literature. The numerical example represented that the number of groups and selected suppliers were reduced when the major ordering cost increased in comparison to other costs. There were also more savings when the number of groups was determined by the model in comparison to predetermined number of groups or no grouping scenarios.     

Optimal inventory control policy and supply chain coordination problem with carbon footprint constraints

Carbon footprint constraints exert pressure on supply chains to reexamine decisions. In this paper, we consider carbon transfer cost and carbon holding cost in a supply chain. A multiperiod dynamic programming model with carbon footprint constraints is presented to investigate the impact of carbon transfer cost and carbon holding cost on inventory control policy as well as the supply chain coordination problem. A two‐control limit inventory control policy is proved to be optimal and a contract with wholesale price, subsidy, and fixed setup cost is verified analytically to coordinate the supply chain. Finally, a numerical study is conducted to reveal managerial insights. We find that when the supply chain is coordinated, the chain's profit is more sensitive to carbon transfer cost while inventory level is more sensitive to carbon holding cost. Additionally, because of the complexity of the coordinated contract, when it is not easy to coordinate the supply chain, it is better to keep the values of wholesale price, subsidy, and fixed setup cost below the corresponding values for the coordinated supply chain.     

Multi-objective optimization of hybrid backorder inventory model

This paper addresses inventory problem for the products that are sold in monopolistic and captive markets experiencing hybrid backorder (i.e., fixed backorder and time-weighted backorder). The problem with stochastic demand is studied first by developing single objective (cost) inventory model. Computational results of a numerical problem show the effectiveness of hybrid backorder inventory model over fixed backorder inventory model. The model is later extended to multi-objective inventory model. Three objectives of multi-objective inventory model are the minimization of total cost, minimization of stockout units and minimization of the frequency of stockout. A multi-objective particle swarm optimization (MOPSO) algorithm is used to solve the inventory model and generate Pareto curves. The Pareto curves obtained for hybrid backorder inventory model are compared with the existing Pareto curves that are based on fixed backorder. The results show a substantial reduction in stockout units and frequency of stockout with a marginal rise in cost with proposed hybrid backorder inventory system in comparison to existing fixed backorder inventory system. Sensitivity analysis is done to study the robustness of total cost, order quantity, and safety stock factor with the change in holding cost. In the end, the performance of the MOPSO algorithm is compared with the multi-objective genetic algorithm (MOGA). The metrics that are used for the performance measurement of the algorithms are error ratio, spacing and maximum spread.     

A fixed interval ordering policy for joint optimization of age replacement and spare part provisioning

A new policy is presented for the joint optimization of age replacement and spare provisioning. The policy, referred to as a fixed interval ordering policy, is formulated by combining an age replacement policy with a periodic review ( t₀,q) type inventory policy, where t0 is the order interval and q is the order quantity. It is generally applicable to any operating system with either a single item or a number of identical items. A SLAM based simulation model has been developed to determine the optimal values of the decision variables by minimizing the total cost of replacement and inventory. The behaviour of the policy has been studied for a number of case problems specifically constructed by five-factor second-order rotatory design and the effects of different cost elements and item failure characterisics have been highlighted. The performance of the proposed policy has also been compared with that of the stocking policy which incorporates a continuous review ( s, S) type of inventory policy, where s is the stock reorder level and S is the maximum stock level. Simulation results clearly indicate that the optimal fixed interval ordering policy is less expensive than the optimal stocking policy when the system consists of a large number of operating units.     

Inventory models for multi-warehouse systems under fixed and flexible space leasing contracts

In this paper, we analyze a practical situation in which an inventory manager is faced with several options to store excess stocks whenever the storage capacity of his/her warehouse is insufficient. The manager can choose from either storage space providers through fixed long term or flexible leasing contracts, or the manager can acquire the extra required space from the spot market. We formulate this inventory problem with multiple storage facilities as a nonlinear program and show that it has a global optimal solution. We then provide closed-form solutions for the optimal ordering quantity and leased spot market space depending on the value of the unconstrained economic order quantity. In addition, we develop some structural properties for the optimal ordering policy and include several examples to illustrate the formulated models.     

Supplier selection and procurement decisions with uncertain demand,fixed selection costs and quantity discounts

In this paper, we study the supplier selection and procurement decision problem with uncertain demand, quantity discounts and fixed selection costs. In addition, a holding cost is incurred for the excess inventory if the buyer orders more than the realized demand and the shortage must be satisfied by an emergent purchase at a higher price otherwise. The objective is to select the suppliers and to allocate the ordering quantity among them to minimize the total cost (including selecting, procurement, holding and shortage costs, etc.). The problem is modeled as a Mixed Integer Programming (MIP) and is shown to be NP-hard. Some properties of the optimal policy are provided and an optimal algorithm is proposed based on the generalized Bender's decomposition. Numerical experiments are conducted to show the efficiency of the algorithm and to obtain some managerial insights.     

Pricing and inventory policies for Hi-tech products under replacement warranty

Companies, especially in the Hi-tech (high-technology) industry (such as computer, communication and consumer electronic products), often provide a replacement warranty period for purchased items. In reality, simultaneously determining the price and inventory decisions under warranty policy is an important issue. The objective of this paper is to develop a joint pricing and inventory model for Hi-tech products under replacement warranty policy. In the first model, we consider a Hi-tech product feature in which the selling price is declining in a trend. We determine the optimal inventory level for each period and retail price for the first period while maximising the total profit. In the second model, we further determine the optimal retail price and inventory level for each period in the dynamic demand market. This study develops solution approaches to solve the problems described above. Numerical analysis discusses the influence of system parameters on the company's decisions and behaviours. The results of this study could serve as a reference for business managers or administrators.     

A vendor managed inventory model under contractual storage agreement

Vendor managed inventory (VMI) is a supply chain partnership strategy that allows a supplier to place orders on behalf of its customers. This paper considers a supply chain composed of a single vendor and multiple retailers operating under a VMI contract that specifies limits on retailers' stock levels. We address the problem of synchronizing the vendor's cycle time with the buyers' unequal ordering cycles by developing a mixed integer non-linear program that minimizes the joint relevant inventory costs under storage restrictions. We also propose a cost efficient heuristic to solve the developed optimization problem. We conducted computational experiments to assess the reduction in the total supply chain costs resulting from relaxing the restriction of equal ordering cycles. It is found that the heuristic generates greater cost savings in cases of increased variability in retailers' demand and cost parameters.     

The optimal integrated inventory policy with price-and-credit-linked demand under two-level trade credit

In this paper, we proposed a generalized, integrated, supplier–retailer inventory model using a trade credit policy. The trade credit policy adopted here is a two-level trade credit policy in which the supplier offers the retailer a permissible delay period M, and the retailer in turn provides customers a permissible delay period N. Cases where M > N and M ? N are explored thoroughly. In addition, the demand rate is assumed to be a function of both retail price and the customers’ credit period. Consequently, this paper deals with the problem of determining the optimal retail price, economic order quantity, and the number of shipments from the supplier to the retailer in one production run for an integrated inventory system under both two-level trade credit and price-and-credit-linked demand rate. Algorithms are developed in order to determine the joint optimal policies. Numerical examples are presented to illustrate the proposed models, as well as sensitivity analysis of key parameters.     

Optimal dynamic pricing and replenishment policy for perishable items with inventory-level-dependent demand

An inventory system for perishable items with limited replenishment capacity is introduced in this paper. The demand rate depends on the stock quantity displayed in the store as well as the sales price. With the goal to realise profit maximisation, an optimisation problem is addressed to seek for the optimal joint dynamic pricing and replenishment policy which is obtained by solving the optimisation problem with Pontryagin’s maximum principle. A joint mixed policy, in which the sales price is a static decision variable and the replenishment rate remains to be a dynamic decision variable, is presented to compare with the joint dynamic policy. Numerical results demonstrate the advantages of the joint dynamic one, and further show the effects of different system parameters on the optimal joint dynamic policy and the maximal total profit.     

A mathematical model for order splitting in a multiple supplier single-item inventory system

In this paper we develop a mathematical model which considers multiple-supplier single-item inventory systems. The lead times of the suppliers and demand arrival rate are random variables. All shortages are backordered. Continuous review (s, Q) policy has been assumed. When the inventory level hits the reorder level, the total order is split among n suppliers. The problem is to determine the reorder level and order quantity for each supplier so that the expected total cost per time unit, including ordering cost, procurement cost, inventory holding cost and shortage cost is minimized. We also conduct extensive numerical experiments to show the advantages of our model compared to the relevant models in the literature. In addition, some managerial insights are observed.     

The joint replenishment problem involving multiple suppliers offering quantity discounts

In this article, we deal with the problem of determining the economic operating policy when a number of items are to be procured from a number of suppliers offering different quantity discounts schedules. In such inventory problems, a fixed cost is incurred with each replenishment order, independent of the suppliers as well as the items involved in the order. Further, the item involves a minor fixed cost. In such a system, it includes the supplier selection problem when considering the quantity discounts as well as the general joint replenishment problem. We develop a hybrid genetic algorithm for this NP-hard decision problem and extend it to systems with resource restrictions.