Optimal Inventory Strategy Research Articles

The Impact of Operational Decisions on the Design of Salesforce Incentives

When facing high levels of overstock inventories, firms often push their salesforce to work harder than usual to attract more demand, and one way to achieve that is to offer attractive incentives. However, most research on the optimal design of salesforce incentives ignores this dependency and assumes that operational decisions of production/inventory management are separable from design of salesforce incentives. We investigate this dependency in the problem of joint salesforce incentive design and inventory/production control. We develop a dynamic Principal-Agent model with both Moral Hazard and Adverse Selection in which the principal is strategic and risk-neutral but the agent is myopic and risk-averse. We find the optimal joint incentive design and inventory control strategy, and demonstrate the impact of operational decisions on the design of a compensation package. The optimal strategy is characterized by a menu of inventory-dependent salesforce compensation contracts. We show that the optimal compensation package depends highly on the operational decisions; when inventory levels are high, (a) the firm offers a more attractive contract, and (b) the contract is effective in inducing the salesforce to work harder than usual. In contrast, when inventory levels are low, the firm can offer a less attractive compensation package, but still expect the salesforce to work hard enough. In addition, we show that although the inventory/production management and the design of salesforce compensation package are highly correlated, information acquisition through contract design allows the firm to implement traditional inventory control policies: a market based state-dependent policy (with a constant base-stock level when the inventory is low) that makes use of the extracted market condition from the agent is optimal. This work appears to be the first paper on operations that addresses the important interplay between inventory/production control and salesforce compensation decisions in a dynamic nature. Our findings shed light on the effective integration of these two significant aspects for the successful operation of a firm.

An integrated vendor-buyer inventory model with defective items and partial backlogging

This paper investigates the integrated vendor-buyer inventory model in which each buyer's arrival order lot contains a random proportion of defective items and the lead-time demand in the market has a normal distribution. The inspection strategy adopted here is that the buyer inspects all the items before selling, allowing defective items to be discovered and returned to the vendor. We formulated an integrated vendor-buyer inventory model with partial backlogging, in which the order quantity, reorder point and the number of shipments from the vendor to the buyer are decision variables. An algorithm was developed to obtain the optimal production and inventory strategy. Furthermore, the affect of parameters on the optimal solution is also discussed.

A multi-period pricing and inventory control model

The authors analyze a finite horizon, single product, period review model in which pricing and inventory decisions are made simultaneously. Demands in different periods are random variables that are independent of each other and their distributions depend on the product price. Pricing and ordering decisions are made at the beginning of each period and all shortage are backlogged. Ordering cost is a convex function of the amount ordered. The objective is to find an inventory and pricing policy maximizing expected discounted profit over the finite horizon. The authors characterize the structure of the optimal combined pricing and inventory strategy for this model. Moreover, the authors demonstrate how the profit-to-go function, order up to level, reorder point and optimal price change with respect to state and time.

Inventory and pricing strategies for deteriorating items with limited capacity and time-proportional backlogging rate

In the present study, a two-warehouse deterministic inventory model for deteriorating items with price-sensitive demand is developed. A rented warehouse (RW) is used to store the excess units over the fixed capacity of the own warehouse (OW). In addition, shortages are allowed in the OW and it is assumed that the backlogging demand rate is dependent on the duration of the stock-out. The objective is to find the optimal inventory and pricing strategies maximising the total average profit over the infinite planning horizon. For any given selling price, we first prove that the optimal replenishment schedule not only exists but is unique. Next, we show that the total average profit is a concave function of price when the replenishment schedule is given. The optimal selling price and replenishment schedule is also calculated for the proposed model. Finally, the results have been validated with the help of a numerical example.

An inventory model for ameliorating and deteriorating items taking account of time value of money and finite planning horizon

The objective of this study is to develop an optimal replenishment inventory strategy to consider both ameliorating and deteriorating effects taking account of time value of money and finite planning horizon. The amelioration rate and the deterioration rate are assumed to follow a Weibull distribution. The inventory system is particularly useful for young livestock whose utility increase over time. The discounted cash flow and optimisation technique are used to derive an optimal solution. A numerical example and sensitivity analysis are given to illustrate the theory of the inventory system.

Inventory competition and allocation in a multi-channel distribution system

Consider a supply chain involving one manufacturer and one independent retailer. The manufacturer distributes her product to the end consumer through the independent retailer as well as through her direct channel. Each of the two channels faces a stochastic demand. If one channel is out of stock, a fraction of the unsatisfied customers visit the other channel, which induces inventory competition between the channels. Under the scenario described above, will the manufacturer ever undercut the retailer’s order when the capacity is infinite? What are the equilibria of the game? How does a capacity constraint affect the equilibrium outcome? What is the optimal inventory allocation strategy for the manufacturer? Using a game theoretic model we seek answers to the above questions. Both the capacitated and the infinite capacity games are considered. We establish the necessary condition for a manufacturer to undercut a retailer’s order and show that a manufacturer may deny the retailer of inventory even when the capacity is ample. We show that there can be an equilibrium in the capacitated game where a manufacturer might not use the entire capacity and still deny a retailer inventory. We also show that a mild capacity constraint may make both parties better off and thereby increase the total supply chain profit. We develop a simple yet practical contract called the reverse revenue sharing contract and show that along with a fixed franchise fee this contract can coordinates our decentralized supply chain.

Optimal production and inventory policies of priority and price-differentiated customers

Many firms are exploring production and supply chain strategies when customers may be segmented into different classes based on service level or priority. Such segmentation can result in a more efficient production system as well as a better match between supply and demand. In this research, we analyze a system with customer classes 1 and 2, where customer class 1 has a higher priority of fulfillment than customer class 2 in the same period. We develop an optimal production and inventory strategy that rations current and future limited capacity between customer classes 1 and 2, through reserving inventory for the future and accepting orders now for future delivery when demand and production are general stochastic functions. We show that a modified order-up-to policy (S*, R i*, B i*) is optimal in each period. S* is the targeted inventory level after production at the beginning of the period; R 1* represents the optimal inventory to be protected from being sold to both classes, and R 2* is the additional amount of inventory to protect from class 2. B 2* is the optimal amount of future capacity to make available to both classes through backlogging, and B 1* is the additional backlogging amount for class 1. Computational analysis shows that the differentiation strategy can result in a significant profit improvement over a traditional inventory policy.

Inventory and pricing strategies for deteriorating items with shortages: A discounted cash flow approach

In this article, we consider an infinite horizon, single product economic order quantity where demand and deterioration rate are continuous and differentiable function of price and time, respectively. In addition, we allow for shortages and completely backlogged. The objective is to find the optimal inventory and pricing strategies maximizing the net present value of total profit over the infinite horizon. For any given selling price, we first prove that the optimal replenishment schedule not only exists but is unique. Next, we show that the total profit per unit time is a concave function of price when the replenishment schedule is given. We then provide a simple algorithm to find the optimal selling price and replenishment schedule for the proposed model. Finally, we use a couple of numerical examples to illustrate the algorithm.

Joint inventory-and-pricing strategy for a stochastic continuous-review system

We analyze an infinite-horizon continuous-review stochastic inventory system in which the selling price and inventory replenishment are determined simultaneously. The demand process is Poisson with a price-dependent arrival rate. The ordering cost includes a fixed setup cost and a variable cost proportional to the order quantity. We obtain closed-form solutions for the optimal inventory control strategy and optimal pricing strategy, which provide managerial insights as well as quantitative and qualitative relationships between decision rules and system parameters. We show that the optimal price is a unimodal function of the inventory level. We also develop efficient algorithms to compute the optimal strategies and present numerical examples.

An investigation of fuzzy lost sales on the periodic review inventory model with variable lead time

For inventory systems in which shortages are allowed, the amount of backorders (or lost sales) often incurs disturbance due to various uncertainties. This article extends the variable lead time, periodic review inventory models to include this situation, specifically, the lost sales rate is fuzzified to be a fuzzy number. We investigate the optimal inventory strategy in the fuzzy sense for the cases where information of the demand distribution during the protection interval (i.e., lead time plus review period) is complete and incomplete.

Joint Optimal Buffer Inventory and Preventive Maintenance Strategy for a Randomly Failing Production Unit

This paper presents an analytical model to determine both the buffer stock size and the preventive maintenance period for a production unit whose lifetime is random and which is submitted to regular preventive maintenance of random duration. The production unit must supply, at a constant rate β, an assembly line operating on a just-in-time basis. The proposed model integrates maintenance, storage and shortage costs. It allows to determine the values of operating parameters which minimize the total average cost per time unit.

A minimax distribution free procedure for mixed inventory models involving variable lead time with fuzzy lost sales

Recently, the continuous review inventory models with allowable shortages have been extended to include variable lead time, where a fixed fraction of the demand during the stockout period is backordered. However, in practice, the backorder (or lost sales) rate may change slightly due to some uncertainties. To incorporate this reality, this article attempts to apply the fuzzy set concepts to deal with the uncertain lost sales rate. For a situation where information about the lead time demand distribution is partial, we utilize the minimax distribution free procedure to find the optimal inventory strategy in the fuzzy sense. Two numerical examples are given to illustrate the results.

A reverse logistics valuation method for inventory control

We propose a method for valuing new, recoverable, and recovered assemblies (products, components, parts, etc.) in production systems with reverse logistics. Values of assemblies influence their opportunity holding cost rates and are hence essential for comparing inventory strategies in average cost models. We argue that the proposed method is 'correct' from a discounted cash flow (DCF) point of view. We refer to some previous results on valuing assemblies in systems without disassembly of returned products that seem to confirm this. Furthermore, we test the method for a specific example with disassembly of returned products. The simulation results indicate that the method indeed leads to (nearly) DCF optimal inventory strategies.

Combined Pricing and Inventory Control Under Uncertainty

This paper addresses the simultaneous determination of pricing and inventory replenishment strategies in the face of demand uncertainty. More specifically, we analyze the following single item, periodic review model. Demands in consecutive periods are independent, but their distributions depend on the item's price in accordance with general stochastic demand functions. The price charged in any given period can be specified dynamically as a function of the state of the system. A replenishment order may be placed at the beginning of some or all of the periods. Stockouts are fully backlogged. We address both finite and infinite horizon models, with the objective of maximizing total expected discounted profit or its time average value, assuming that prices can either be adjusted arbitrarily (upward or downward) or that they can only be decreased. We characterize the structure of an optimal combined pricing and inventory strategy for all of the above types of models. We also develop an efficient value iteration method to compute these optimal strategies. Finally, we report on an extensive numerical study that characterizes various qualitative properties of the optimal strategies and corresponding optimal profit values.

Inventory management under random supply disruptions and partial backorders

We explore the management of inventory for stochastic-demand systems, where the product's supply is randomly disrupted for periods of random duration, and demands that arrive when the inventory system is temporarily out of stock become a mix of backorders and lost sales. The stock is managed according to the following modified (s, S) policy: If the inventory level is at or below s and the supply is available, place an order to bring the inventory level up to S. Our analysis yields the optimal values of the policy parameters, and provides insight into the optimal inventory strategy when there are changes in the severity of supply disruptions or in the behavior of unfilled demands. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 687–703, 1998