Joint Inventory Research Articles

Technical Note—Joint Inventory and Pricing Control with General Additive Demand

This paper analyzes a periodic-review, joint inventory and pricing control problem for a firm that faces stochastic, price-sensitive demand under a nonstationary environment with fixed ordering costs. Any unsatisfied demand is backlogged. The objective is to maximize expected profit over a finite selling horizon by coordinating the inventory and pricing decisions in each period. We show that for an additive demand model, an (s, S, p) policy is optimal when the expected revenue is quasi-concave in price, the inventory cost (of holding and/or backlogging) is quasi-convex, and the nonnegative random demand has a Pólya or uniform density function. For the special case with no fixed ordering cost, the optimality of a base stock list price policy is demonstrated for more general demand distributions and convex inventory cost. These sets of sufficient conditions generalize the existing conditions in the literature that require, for example, the demand and/or revenue functions to be concave or the model parameters to be stationary in time. Our generalization makes the structural results applicable to models broadly supported by economic theory and empirical data. In addition, our proof uses a distinct sequential optimization technique for iteratively establishing the quasi-K-concavity of dynamic optimal value functions.

Technical Note-Joint Inventory and Pricing Control with General Additive Demand

This paper analyzes a periodic-review, joint inventory and pricing control problem for a firm that faces stochastic, price-sensitive demand under a nonstationary environment with fixed ordering cos...

Joint Pricing and Inventory Control for Seasonal and Substitutable Goods Mentioning

Joint Pricing and Inventory Control for Seasonal and Substitutable Goods Mentioning

Joint pricing and inventory control for additive demand models with reference effects

We study a periodic review joint inventory and pricing problem of a single item with stochastic demand subject to reference effects. The random demand is contingent on the current price and the reference price that acts a benchmark against which customers compare the price of a product. Randomness is introduced with an additive random term. The customers perceive the difference between the price and the reference price as a loss or a gain. Hence, they have different attitudes towards them, such as loss aversion, loss neutrality or loss seeking. We model the problem using safety stock as the decision variable and show that the problem can be decomposed into two subproblems for all demand models under mild conditions. Using the decomposition, we show that a steady state solution exists for the infinite horizon problem and we characterize the steady state solution. Defining the modified revenue as revenue less the production cost, we show that a state-dependent order-up-to policy is optimal for concave demand models with concave modified revenue functions and provide example demand models with absolute difference reference effects and loss-averse customers. We also show that the optimal inventory level increases with the reference price. All of our results hold for finite and infinite horizon problems.

Joint inventory and pricing decisions when customers are delay sensitive

We consider the joint pricing and inventory problem of a capacity constrained service facility with several classes of customers. The customers are differentiated with their sensitivity for waiting and their willingness to pay for the service. We model the problem using an M/M/1 queueing system with non-preemptive priorities. We give closed form solutions for the inventory decisions. We also show that the prices given by the first order conditions are also incentive compatible in the sense that they optimize the profit of the firm even if the firm does not know the type of an arriving customer and let the customer choose a price from the menu of prices. We approximate the problem and provide simple and explicit solutions when there is a single customer type. In numerical illustrations, we show that the customers, who are more sensitive to wait, do not enter the system until the base stock level is above a threshold. We provide extensions of our results for M/G/1 and M/M/m systems.

Joint location, inventory, and preservation decisions for non-instantaneous deterioration items under delay in payments

This study models a joint location, inventory and preservation decision-making problem for non-instantaneous deteriorating items under delay in payments. An outside supplier provides a credit period to the wholesaler which has a distribution system with distribution centres (DCs). The non-instantaneous deteriorating means no deterioration occurs in the earlier stage, which is very useful for items such as fresh food and fruits. This paper also considers that the deteriorating rate will decrease and the reservation cost will increase as the preservation effort increases. Therefore, how much preservation effort should be made is a crucial decision. The objective of this paper is to determine the optimal locations and number of DCs, the optimal replenishment cycle time at DCs, and the optimal preservation effort simultaneously such that the total network profit is maximised. The problem is formulated as piecewise nonlinear functions and has three different cases. Algorithms based on piecewise nonlinear optimisation are provided to solve the joint location and inventory problem for all cases. Computational analysis illustrates the solution procedures and the impacts of the related parameters on decisions and profits. The results of this study can serve as references for business managers or administrators.

Joint inventory and pricing decisions with reference effects

This article considers a periodic review joint replenishment and pricing problem of a single item with reference effects. The demand is random and is contingent on the price history as well as the current price. Randomness is introduced with both an additive and a multiplicative random term. Price history is captured by a reference price, which is developed by consumers that are frequent buyers of a product or a service. The common reference price acts as a benchmark against which the consumers compare the price of a product. They perceive the difference between the price and the reference price as a loss or a gain and have different attitudes to these perceptions, such as loss aversion, loss neutrality, or loss seeking. A general way to handle the nonconvexity of the holding cost for nonlinear demand models is to make a transformation and use the inverse demand function. However, in reference price-dependent demand models, this brings the problem of a nonconvex action space. This problem is circumvented by defining an action space that preserves the convexity after a transformation. For the transformed problem, it is shown that a state-dependent order-up-to policy is optimal for concave demand models and concave transformed expected revenue functions that are not necessarily differentiable. It is shown that there are demand models with relative difference reference effects and loss-averse customers that satisfy the considered concavity assumptions. A computational study is performed to highlight the effects of joint inventory and pricing decisions under reference effects.

Joint shipment consolidation and inventory decisions in a two-stage distribution system

This study is motivated by a problem that an industrial distributorship faced while distributing automotive spare parts to service and repair centers. Considering the problem encountered, we present an analytical model for joint inventory and shipment consolidation decisions in a two-stage distribution system with a single distribution center, multiple non-identical retailers, and an outside supplier. The retailers face stochastic end-customer demand and use continuous review to replenish inventories. On the other hand, the distribution center uses a periodic review policy and employs a time-based shipment consolidation policy to dispatch retailers’ accumulated orders at the end of each consolidation cycle. We present an exact optimization technique to compute the optimal replenishment quantity at the distribution center, order-up-to level at retailers, and a shipment consolidation cycle length to measure the effects of inventory at retailers on the overall performance. Finally, we perform numerical experiments to measure the impact of various parameters on the overall distribution system.

Clinical results of 40 years of paediatric keratoplasty in a single university eye clinic

To evaluate indications for paediatric keratoplasty in recipients aged ≤16 years and assess long-term clinical outcome. Recipients were identified from records of the Danish Cornea Bank. Data were collected from patient journals, clinical follow-up examinations and questionnaires and stratified into pre-, peri- and postoperative variables. Diagnoses were classified into acquired traumatic, acquired nontraumatic and congenital groups. Recipients were divided into groups of <8 and ≥8 years. Data were analyzed using relative percentages and Kaplan-Meier survival plots. Thirty-three out of sixty identified recipients (73 keratoplasties in 63 eyes) were invited. Twenty-four accepted, seven still attended follow-up in our clinic. Follow-up data reached 95% of the eligible recipients (median follow-up 11 years). Twenty-three per cent were <8 years and 77%≤8 years. Diagnoses were mainly acquired nontraumatic (69%), acquired traumatic (12%) and congenital (7%). Indications were primarily optical (52%) or tectonic (41%). Graft survival was best in the acquired nontraumatic group (except regrafts) (median survival 15-20 years) and poorest in the regraft subgroup as well as the acquired traumatic and congenital groups (median survival 1-2 years). Graft failure was higher in the youngest with predisposing risk factors and in combined procedures. In terms of indications, visual improvement and eye preservation was achieved in 70%. Paediatric keratoplasty was successful regarding indication. Graft survival was best in the acquired nontraumatic group and poorest in the congenital group. Vascularization and/or combined risk factors, additional surgeries and young recipient age influenced negatively on graft survival.

The Effect of Supply Uncertainty in Price-Setting Newsvendor Models

We consider a price-setting newsvendor model in which a firm needs to make joint inventory and pricing decisions before the selling season. The supply process is uncertain such that the received quantity is the product of the order quantity and a random yield rate. Two cost structures are investigated, the in-house production case in which the firm pays for the order quantity and the procurement case in which the firm pays for the quantity received only. Our objective is to investigate the effect of yield randomness on optimal decisions and expected profit. By using the theory of stochastic comparisons, we find that under both cost structures, a less variable yield rate leads to a lower optimal price and a higher expected profit. Moreover, we show that in the in-house production case, a stochastically larger yield rate also results in a lower optimal price and a higher profit, but this is not true in the procurement case. Examples show that the effect of supply uncertainty on optimal order quantity is not universal.

Joint inventory and pricing decisions for perishable products with two‐period lifetime

AbstractWe consider a periodic review model over a finite horizon for a perishable product with fixed lifetime equal to two review periods. The excess demand in a period is backlogged. The optimal replenishment and demand management (using price) decisions for such a product depend on the relative order of consumption of fresh and old units. We obtain insights on the structure of these decisions when the order of consumption is first‐in, first‐out and last‐in, first‐out. For the FIFO system, we also obtain bounds on both the optimal replenishment quantity as well as expected demand. We compare the FIFO system to two widely analyzed inventory systems that correspond to nonperishable and one‐period lifetime products to understand if demand management would modify our understanding of the relationship among the three systems. In a counterintuitive result, we find that it is more likely that bigger orders are placed in the FIFO system than for a nonperishable product when demand is managed. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013

Joint Inventory and Cash Management for Multi-Divisional Supply Chains

Cash pooling is a powerful tool to consolidate intragroup liquidity for multi-divisional corporations. This paper develops a centralized supply chain model that aims to assess the value of cash pooling. The supply chain is owned by a single corporation with two divisions, where the downstream division (headquarter), facing random customer demand, replenishes materials from the upstream one. The downstream division receives cash payments from customers and determines a system-wide inventory replenishment and cash retention policy. We consider two cash management systems that represent different levels of cash concentration. For cash pooling, the supply chain adopts a financial services platform which allows the headquarter to create a corporate master account that aggregates the divisions' cash. For transfer pricing, on the other hand, each division owns its cash and pays for the ordered material according to a fixed price. Comparing both systems yields the value of adopting such financial services. We prove that the optimal policy for the cash pooling model has a surprisingly simple structure -- both divisions implement a base-stock policy for material control; the headquarter monitors the corporate working capital and implements a two-threshold policy for cash retention. Solving the transfer pricing model is more involved. We derive a lower bound on the optimal cost by connecting the model to an assembly system. Our results show that the value of cash pooling can be very significant when demand is increasing (stationary) and the markup for the upstream division is small (high). Nevertheless, a big portion of the pooling benefit may be recovered if the headquarter can decide the optimal transfer price and the lead time is short.

Two-stage optimal ordering policy of joint inventory with backlogging for seasonal commodity

This paper proposed a two-stage inventory model for seasonal commodity,in which the market and manufacturing channels were combined.This model can be used to solve the production policy and the order policies of the raw materials for the manufacturer.By assuming that the retailers' demand obeys normal distribution and that the retailer makes orders according to the newsboy model,the necessary and sufficient conditions were given for the optimal solution of production size,wholesale price,and replenishment cycle of raw materials for the manufacturer.Finally,the necessary condition was explored in order to obtain managerial insights and economic implications based on numerical examples and sensitivity analysis.

The effect of supply uncertainty in price-setting newsvendor models

We consider a price-setting newsvendor model in which a firm needs to make joint inventory and pricing decisions before the selling season. The supply process is uncertain such that the received quantity is the product of the order quantity and a random yield rate. Two cost structures are investigated, the in-house production case in which the firm pays for the input quantity and the procurement case in which the firm pays for the quantity received only. Our objective is to investigate the effect of yield randomness on optimal decisions and expected profit. By using the theory of stochastic comparisons, we find that under both cost structures, a less variable yield rate leads to a lower optimal price and a higher expected profit. Moreover, we show that in the in-house production case, a stochastically larger yield rate also results in a lower optimal price and a higher profit, but this is not true in the procurement case. Examples show that the effect of supply uncertainty on optimal order quantity is not universal.

Combined Sales Effort and Inventory Control under Demand Uncertainty

We study the joint inventory and sales effort management problems of a retailer in a broad context and investigate the optimal policies for a single item, periodic-review system. In each period, the demand is uncertain depending on the sales effort level exerted by the retailer, which incurs an associated cost. The retailer’s objective is to find a joint optimal inventory replenishment and sales effort policy to maximize the discounted profit over a finite horizon. We first consider a basic setting with zero setup cost and no batch ordering, under which the base stock list sales effort policy is optimal. Two extensions are then investigated: (1) the case with nonzero setup cost, under which we show that(s,S,e)policy is optimal; and (2) the case with batch ordering, under which we prove the optimality of the(r,Nq,e)policy. Finally, we conduct numerical studies to provide additional managerial insights.

Multi-Echelon Integrated Inventory Control Strategy of Equipment Spare Parts

Inventory control strategy of spare parts is an effective way to improve equipment support efficiency and scientific and reasonable inventory policy can make spare parts availability reach the upper limit. Multi-echelon integrated inventory control strategy of equipment spare parts is studied. Three-level integrated inventory control model consisting of rear warehouse, equipment using units and spare parts supplier is established according to the architecture and control program of multi-echelon joint inventory. The algorithm of solving the proposed model is analyzed and a numerical example is provided. The proposed equipment spare parts inventory model can improve inventory quality to a certain degree and decrease the contradictions between inventory and maintenance. The correctness and effectiveness of the proposed model are verified by the example, which provides an effective model for equipment spare parts inventory.

Joint inventory and transshipment control for perishable products of a two-period lifetime

We analyze the impact of transshipments among retailers on their inventory replenishment decisions when products are perishable. Previous studies have shown that transshipments improve their operational efficiencies through inventory reallocation. However, these studies have not investigated transshipments for perishable products having a limited lifetime. In this paper, we consider a centrally managed firm owning several retail stores, which coordinates their replenishment policies along with the utilization of transshipments for perishable goods of a two-period lifetime. For this, the single-period planning horizon is analyzed, with a general solution approach for the optimal replenishment and transshipment decisions. We further present a designated solution approach for a two-location system as a special case and illustrate numerical examples in order to highlight the potential value of implementing transshipments for perishable products.

Joint pricing and inventory management with deterministic demand and costly price adjustment

We analyze a joint inventory and pricing model of a single product over a finite planning horizon with deterministic demand. In this model, an ordering quantity and a price are decided simultaneously at the beginning of each period, demand of the period depends on the price, and a price adjustment cost is incurred if the price is changed from the previous period. We develop polynomial time algorithms to maximize the total profit and discuss their computational complexity.

Joint inventory and constant price decisions for a continuous review system

PurposeThe purpose of this paper is to study joint inventory and pricing strategy for a continuous inventory review system. While dynamic pricing decisions are often studied in the literature along with inventory management, the authors' aim in this study is to obtain a single long‐run optimal price; also to gain insight about how to obtain the optimal price and inventory control variables simultaneously and then the benefits of joint optimization of the inventory and pricing decisions over the sequential optimization policy often followed in practice.Design/methodology/approachA general (R;Q) policy system with fixed cost of ordering is modelled and then the case where unsatisfied demand is lost is studied. General forms of both the additive and multiplicative demand models are used to obtain structural results.FindingsBy showing optimality conditions on the price and inventory decision variables, two algorithms on how to obtain optimal decision variables, one for additive and another for multiplicative demand‐price model are provided. Through extensive numerical analyses, the potential profit increases are reported if the price and inventory problem are solved simultaneously instead of sequentially. In addition, the sensitivities of optimal decision variables to system parameters are revealed.Practical implicationsAlthough there are several studies in the literature investigating emergency price change models, they use arbitrary exogenous prices menus. However, the value of a price change can be better appreciated if the long‐run price is optimal for the system.Originality/valueVery few researchers have investigated constant price and inventory optimization, and while there are several past studies demonstrating the benefits of dynamic pricing over a static one, there still are not many findings on the benefit of joint price and inventory optimization.

Optimal Structural Policies for Ambiguity and Risk Averse Inventory and Pricing Models

This paper discusses multiperiod stochastic joint inventory and pricing models when the decision maker is risk and ambiguity averse. We study infinite horizon models with discounted and long run average optimization criteria. The main result of this paper is establishing the optimality of stationary $(s,S,p)$ policies for the infinite horizon inventory and pricing models.