Periodic Review Inventory System Research Articles

A periodic review inventory system when received items are of imperfect quality under two supply mode

A periodic review inventory system when received items are of imperfect quality under two supply mode

A simple heuristic for computing non-stationary inventory policies based on function approximation

We consider a finite-horizon periodic-review inventory system with fixed replenishment costs that faces non-stationary demands. The structure of the optimal control policy for this system has long been known. However, finding optimal policy parameters requires solving a large-scale stochastic dynamic program. To circumvent this, we devise a recursion-free approximation for the cost function of the problem. This translates into an efficient and effective heuristic to compute policy parameters that significantly outperforms earlier heuristics. Our approach is easy-to-understand and easy-to-use as it follows by elementary methods of shortest paths and convex minimization.

Inventory Management of Saline using Forecasting Techniques in A Hospital Case Study

The purpose of this research is to efficiently manage the saline inventory system of the hospital by reducing storage and control problems according to patients' demands. First, all saline types in stock were grouped by value using the ABC technique which yielded an “A” cluster that accounted for 59.92% of the total saline stock value. Second, demand forecasting of group “A” saline by means of various forecasting techniques. In this study, the techniques applied were Moving Average, Weighted Moving Average, and Exponential Smoothing. The Mean Square Error (MSE) and the Mean Absolute Percentage Error (MAPE) were used to measure the forecast errors. And it was discovered that Exponential Smoothing is the most appropriate technique. Third, planning and analysis of the saline stock were fulfilled by implementing the periodic review inventory system at a 99 percent service level. With review policy, the maximum stock of group "A" saline was defined. Finally, inventory costs between "before" and "after" was compared, and found that 8.84% of costs can be reduced.

A periodic review inventory model facing different disruption profiles

We study a periodic review inventory system with alternations of periods with supply availability and unavailability. The system is controlled by a periodic review base stock policy (S,T). While periodic review inventory models have been studied assuming supply disruption, they mainly invoke the limiting disruption probabilities overlooking that these probabilities may correspond to different disruption profiles (ranging from rare-long disruptions to frequent-short ones). In this context, we use a continuous-time Markov chain (CTMC), in order to formulate a periodic review inventory model that can distinguish the different disruption profiles. Through theoretical results, we determine the policy variables (order-up-to level and review interval) that minimize the long-run average cost. We show that when the disruption profile is considered, the optimal order-up-to level, although Newsvendor-styled form, is not always linear in the review interval. We present analytical properties demonstrating the impact of the different disruption profiles (under the same limiting disruption probability) and the impact of the limiting probability on the optimal policy. Furthermore, we propose an approximation to obtain a closed-form (near-)optimal solution for the review interval. Finally, numerical comparisons highlight the impact on system's cost performance of deploying approaches that either use the above mentioned closed-form solution for the review interval or the limiting disruption probabilities instead of the time dependent ones in the cost formulation.

Closed-form (R,S) inventory policies for perishable inventory systems with supply chain disruptions

Hospital pharmacy managers make inventory decisions for thousands of different perishable drugs. Commonly, these managers do not have the resources to implement advanced mathematical models. Closed-form solutions are attractive because they provide the inventory policy quickly and are easy to implement. However, when deriving these solutions, one must consider that pharmaceutical supply chains experience disruptions. We first derive closed-form solutions for a non-perishable lost-sales (R,S) periodic review inventory system with supply chain disruptions. We then extend the solutions to incorporate perishability and apply the solutions to a hospital pharmacy inventory system. We find that (i) it is important to account for perishability and supply chain disruptions simultaneously as only accounting for supply chain disruptions increases both drug shortages [possible 65% increase] and waste [possible waste equivalent to 50% of the daily demand], (ii) it is critical to consider the duration of and time between supply chain disruptions, (iii) the expected number of shortages is insensitive to changes in the standard deviation when demand is normally distributed, but for short expiration lifetimes, the expected number wasted increases linearly as the standard deviation of demand increases, and (iv) not accurately depicting the supply chain disruption process can triple the number of shortages.

Periodic review inventory models with multiclass demands and fixed order costs

We consider a periodic review inventory system with multiclass demands and fixed setup cost. Demand arrivals of each class are assumed to be a Poisson process, and a lost-sales setting is adopted. The demand classes are classified by the cost of their unsatisfied demands. We consider two cases: the leftover inventory at the end of a restocking interval is entirely discarded or entirely carried over to the next period. We obtain the optimal rationing policy, the optimal ordering policy and the optimal duration of the periodic review interval that minimize the average cost per unit time. We derive the differential equations satisfied by the value function characterized by the on-hand inventory level and the residual restocking time. This value function does not have the traditional modularity and convexity properties. Hence, the optimal policy is derived directly based on the ordinary differential equations satisfied by the value function. Moreover, some structural properties of the optimal policy such as the monotone property of the optimal rationing policy are obtained.

Determining (s, S) Inventory Policy for Healthcare System

In this paper, an (s, S) policy is determined by using a simulation-optimization approach for a periodic review inventory system at a pharmacy department of a major hospital in Thailand. The simulation, which imitates the inventory system behavior, is constructed on a spreadsheet, while the cyclic coordinate method with a golden section search is adopted as the optimization algorithm. Solutions for the policy's parameters from the search algorithm are evaluated using the simulation, which features randomly generated demand and lead time data from empirical distributions of actual datasets. The objective is to minimize the total inventory cost, including ordering, holding, and shortage costs. This model is applied for 10 medicine items, selected as representatives of the entire item range in the pharmacy department. According to the simulation results, a minimal cost inventory policy for each item is obtained within a short amount of run time. This indicates the effectiveness and efficiency of the proposed approach for this type of problem.

Inventory control under corporate income tax and accrual accounting

Corporate income tax constitutes a significant portion of financial costs in business operations. A typical tax system is characterized by the tax structure, accounting method, and loss carryover rule. In this article, we study the optimal inventory policies under taxation and accrual accounting. We consider a lost-sales periodic-review inventory system under a proportional tax with loss carryforward. We formulate the problem as a cyclic stochastic dynamic program with multiple accounting periods, each of which consists of multiple review periods. We show that an income-dependent basestock policy is optimal. We find that tax function convexity and loss carryforward may introduce conflicting incentives into inventory decisions: the former drives risk-averse decisions whereas the latter induces risk-seeking behavior. We identify two intertemporal effects of taxation, the intra-accounting-period effect and the inter-accounting-period effect, both inducing smaller basestock levels. We further extend the analysis to the progressive tax, backordering system, and cash accounting method. Our numerical study examines the effects of various characteristics of taxation on the optimal policies. Our results demonstrate that ignoring taxation in inventory decisions may lead to significant losses especially when the tax rate and demand uncertainty are sufficiently high, which reveals the value of tax considerations in inventory management.

Optimal strategy for a periodic review inventory system with discounted variable cost and finite ordering capacity

We study a periodic review inventory system with finite ordering capacity, and assume the variable ordering cost would be discounted when the ordering quantity is the full capacity. Applying the concept of strong CK-concavity, we show that the optimal pricing and ordering strategy could be partially characterized by an (S, S′, p) strategy in four regions depending on the starting inventory level per period. Numerical experiments verify the proposed strategy.

Dual sourcing: Creating and utilizing flexible capacities with a second supply source

We study a finite horizon, single product, periodic review inventory system with two supply sources and a salvage option. These supply sources are typically capacitated and capacity levels often need to be reserved or installed in advance of the operational planning horizon. The supply sources may thus be differentiated by their lead times, capacities, and fixed and variable order costs. Salvage options allow for inventory reductions and incur fixed cost and variable revenues. We first analyze the tactical problem of determining an optimal procurement strategy under given capacity profiles at the two suppliers. We then address the strategic model in which optimal capacity profiles, both static and dynamically adjusted, are obtained based on two‐part capacity contracts. We characterize the structure of optimal procurement strategies when the lead times of the two suppliers differ by a single period and the lead time for salvage opportunities matches that of one of the suppliers. For general lead time combinations, we show that the optimal procurement strategies satisfy monotonicity and limited sensitivity properties, and construct effective heuristics and upper and lower bounds based on our structural results.

Coping with Demand Uncertainty: The Interplay between Dual Sourcing and Endogenous Partial Backordering

In some stockout situations, a retailer may be better off declining to fulfill some demand even though it could have been backordered. We study the conditions under which endogenous (retailer‐driven) partial backordering is the cost‐minimizing strategy in an infinite horizon periodic review inventory system with dual sourcing. At the beginning of each period, the retailer can place two orders. The first order (with higher unit purchase cost) is delivered immediately from the fast supplier and brings the inventory level up to a target level Z. The second order (with lower unit purchase cost) is delivered one period later from the slow supplier (or the same supplier using a slower delivery mode) and brings the inventory position up to the base‐stock R. In each period, the realized demand can be accepted up to the maximum of inventory on‐hand and R – k, implying that some excess demand requests may be backordered while the rest is rejected. The on‐order quantity k denotes the reservation quantity held back for use in subsequent periods. Each of k, Z, and R is a decision variable in our model with dual sourcing. The case k = R – Z yields the full lost sales model while the case k = –∞ yields the full backorder model. We determine structural properties of the optimal ( k, Z, R) policy and discuss how to find the optimal base‐stock and reservation quantities. In a complementary numerical investigation, we find that a suitably designed single supplier partial backorder policy can be nearly as cost‐effective as the optimal dual source policy.

Improving inventory system performance by selective purchasing of buyers’ willingness to wait

We develop a demand postponement mechanism to improve the performance of a single item, periodic review inventory system with advance demand. The focus in the literature has been on how to stimulate customers towards advance demand. Predicting how demand will shift can be problematic, however, and backorders may still occur. We focus on how a firm can address backorders under a given advance demand pattern by a mechanism of compensation from which both the firm and the customers will benefit: the firm may offer a discount to customers for accepting later deliveries at a promised delivery date. Delivery postponement offers are made selectively, i.e. in some periods and to some customers only when there is a benefit for the firm to do so. Customers may decline the offer, but then face the probability of a backorder. In each period, the firm has to decide whether to make delivery postponement offers and for how long, and whether to order from its supplier and how much. We formulate the problem as a Markov Decision Process and solve it by backward induction. Numerical examples illustrate the properties of the state-dependent policies obtained for both uncapacitated and capacitated inventory systems. The postponement mechanism in capacitated systems leads to policies that differ from the threshold policy identified as optimal in the literature. Overall, the approach shows promise to improve system performance more efficiently compared to strategies aiming to increase advance demand in the system.

An analysis of optimal ordering policies for a two-supplier system with disruption risk

We study a single-product, periodic-review inventory system with the presence of fixed ordering cost. There are two suppliers: One is perfectly reliable while the other offers a cost advantage but is subject to possible supply interruptions. We present a theoretical framework with mathematical proofs for the optimal ordering policy in the finite-horizon setting, which exhibits an (s,S) structure, but with multiple, sometimes overlapping, reorder points and order-up-to levels. Then, we analyze the limiting behavior of our (s,S) policy and show that both the optimal cost and ordering policy parameters converge over time. This steady-state (s,S) policy characterizes the optimal sourcing strategy for the infinite-horizon setting. Through computational studies, we investigate the effects of parameter changes on the optimal policy and demonstrate that our two-supplier (s,S) ordering policy is optimal under a wide range of system parameters beyond the conditions required in the optimality proof.

Socially concerned periodic review replenishment system with customer service level and supply chain contracting

This study contributes to the periodic review inventory system literature by: (1) investigating customer service level (CSL) as a social responsibility in pharmaceutical supply chains (PSCs) and (2) proposing supply chain contracting to achieve win–win coordination and guarantee a satisfied CSL. Specifically, considering the demand uncertainty as one of the main challenges faced by pharmacies, we analyze how applying contracts to coordinate the inventory policy of a pharmacy with that of its supplier can affect their profits and the CSL offered to society. Having shown the advantages of the centralization compared to the decentralization, we design a coordination scheme based on the quantity discount contract to encourage the players move towards centralization. Under the proposed scheme, we first obtain the minimum and maximum acceptable amounts of discount from each actor’s viewpoint. Then, we propose a benefit-sharing strategy in order to make the plan interesting to both sides. The proposed discount contract and benefit-sharing strategy distribute the extra profits equitably between the two participants according to their bargaining power, which can make a win–win condition for two actors. Our results suggest that coordinating review period and order-up-to-level of the retailer and replenishment multiplier of the supplier will be of benefit in terms of both economic profitability and social responsibility.

The window fill rate in a periodic review inventory system with order crossover

Many periodic review inventory studies make the simplifying assumption that orders do not crossover, that is, that they are delivered in the same sequence as they were issued. In many real-life situations, however, long international shipping routes result with frequent crossovers. Accordingly, we investigate a periodic review inventory system with backlogged compound Poisson demand in which order may crossover. We develop an exact formula for the window fill rate, i.e. the probability for customers to receive service within their tolerable wait. Evaluating the window fill rate using the exact formula is very time consuming and therefore an efficient approximation formula that assumes that orders do not crossover is considered. Lead times of actual global supply lines demonstrate that this approximation results in considerable overstocking when customers' tolerable wait is high, or understocking when the tolerable wait is low. Replacing the actual lead times distribution with the effective lead times distribution improves the approximation formula's accuracy considerably. This result allows us to show how the window fill rate depends on the model parameters and make practical observations about the trade-off between the tolerable wait and stock levels needed to maintain a required level of window fill rate.

Effects of government’s policy on supply chain coordination with a periodic review inventory system to reduce greenhouse gas emissions

In many countries, the governments and statesmen set various regulations to reduce Greenhouse Gas (GHG) emissions and entities must also comply with these rules to maintain their profitability. This paper aimed to reduce GHG emissions in the two-echelon Supply Chain (SC) with one supplier and one retailer under the government’s policies. Emissions from the intended SC are results of using trucks to deliver orders from the supplier to the retailer to replenish his/her inventory. Furthermore, the demand of market is stochastic and a periodic review inventory system is used by the retailer in which, the supplier determines the visit interval. Since the retailer has direct interaction with the end customer, he/she should select the best SC service level. In this regard, because the supplier as a leader has full authority for the retailer’s inventory replenishment and he/she leads to GHG emissions in the SC, the government is trying to control environmental pollution by applying the subsidy and penalty to the supplier. Therefore, the proposed model has an environmental objective to minimize the GHG emissions and an economical objective to maximize the profitability of the SC. In this study, firstly the decentralized and centralized SCs are analyzed, and then, due to the government’s regulations, the Revenue Sharing (RS) contract and Delay in Payments (DP) contract are used to coordinate SC members. It should be noted that the proposed model is solved by the method of augmented epsilon constraint. Finally, sensitivity analyses of numerical examples show that the government’s policies, with a slight reduction in profitability of the whole SC, can reduce GHG emissions significantly.

A periodic review inventory system under stochastic demand with controllable safety stock, lead time, and price discount under partially backlogged shortages

A periodic review inventory system under stochastic demand with controllable safety stock, lead time, and price discount under partially backlogged shortages

A simulation-optimization approach to determine optimal order-up-to level for inventory system with long lead time

This paper proposes a simulation-optimisation technique to determine an optimal order-up-to level for a single product in a periodic review inventory system. A vital aspect of the problem is that the replenishment lead time is much longer than the review period. Customer demands are stochastic, discrete, and intermittent, and the lead times are stochastic and discrete. With these demand and lead time characteristics, an empirical distribution is used to fit the distribution of demand during the lead time. A simulation-optimisation approach is developed with the objective to minimise the total annual inventory management cost, which consists of the holding cost and backlog cost, while maintaining an acceptable service level. Real data from a warehouse of an international trading company are used to test the performance of the proposed method. Results from a computational test show the method effectiveness.

A periodic review inventory system under stochastic demand with controllable safety stock, lead time, and price discount under partially backlogged shortages

The stochastic inventory system analysed in this paper explores the problem of the backorder price discount, safety stock, lead time, and review period as control variables to widen applications for a periodic review inventory model. In many practical situations, the variable lead time can be divided into some components which have a crashing cost for the reduced lead time. Moreover, the firm may offer a price discount to the obliged and loyal customers to pay off the uncomfortableness of backordering. Furthermore, the protection interval demand (i.e., review period plus lead time) is assumed to follows a normal distribution. The aim is to develop an algorithm to determine the optimal solutions, so that the total expected annual cost reaches at a minimum value. A numerical example is given to illustrate the application of the system.

Periodic review integrated inventory model with controllable lead time and setup cost in the presence of a service level constraint

The impact of lead time reduction on an integrated periodic review inventory system comprising a single vendor and multiple buyers with a step crashing cost function and service level constraints is explored in this study. Distribution free and normal distribution procedure with Lagrange multipliers is applied to determining the lead time, the common shipment cycle time, the target levels of replenishments and the number of shipments per production cycle so that the expected total system cost is minimised. The efficient algorithm is constructed to find the optimal lead time, the common shipment cycle time, the target levels of replenishments and the number of shipments per production cycle simultaneously. Moreover, the numerical example is introduced to illustrate the proposed model. Through sensitivity analysis, some observations and managerial implications are provided.