Inventory Position Research Articles

Styled Algorithmic Trading and the MV-MVP Style

Jackie Shen , Yingjie YuAbstractExcept for pre-trade assessment, algorithmic trading for optimal execution hasto be dynamically adapted to real-time market environments and inventory po-sitions. This makes dynamic programming (DP) the most natural approach.Due to the curse of dimensionality, however, it is highly challenging to designa rigorous DP strategy that invites a tractable solution procedure. Approxi-mate dynamic programming (ADP) has hence emerged as a practical solution,and the proposed framework of styled trading follows the ADP paradigm. Astyled model makes a particular choice for its state variables as well as the para-metric forms of its trading policies. Its calibration then becomes a nonlinear,constrained, but lower-dimensional optimization problem. The current frame-work also goes beyond the additive objectives normally required by a traditionalDP strategy and its associated Bellman solution procedure. It works with themean-variance utilities of Almgren and Chriss (J. Risk, 3, 2000) to e ectivelyexpress risk aversion of a typical trader. The new framework is demonstratedthrough building one particular style called MV-MVP, i.e., the mean-variance(MV) objective formulated upon the state variables of moneyness and volumeparticipation (MVP). The MV-MVP style generalizes the VWAP strategy by fa-cilitating dynamic reactions to moneyness and by embodying the popular streetpractice of trading aggressively or passively while in the money. Numericalcalibration based on stochastic gradient descent and binomial-tree gradient de-scent is discussed. Simulated dynamic trading paths help illustrate the generalbehavior of the MV-MVP style.Keywords: Dynamic programming, style, moneyness, aggressive, passive,participation, parametric, stochastic, gradient descent, binomial trees.

A real-time SPC inventory replenishment system to improve supply chain performances

Inventory replenishment rules contribute significantly to the bullwhip effect and inventory instability in supply chains. Smoothing replenishment rules have been suggested as a mitigation solution for the bullwhip effect but dampening the bullwhip effect might increase inventory instability. This paper evaluates a real-time inventory replenishment system denoted as SPC that utilizes a control chart approach to counteract the bullwhip effect whilst achieving competitive inventory stability. The SPC employs two control charts integrated with a set of decision rules to estimate the expected demand and adjust the inventory position, respectively. The first control chart works as a forecasting mechanism and the second control chart is devoted to control the inventory position variation whilst allowing order smoothing. A simulation analysis has been conducted to evaluate and compare SPC with a generalized (R, S) policy in a four-echelon supply chain, under various operational settings in terms of demand process, lead-time and information sharing. The results show that SPC is superior to the traditional (R, S) and comparable to the smoothing one in terms of bullwhip effect, inventory variance, and service level. Further managerial implications have been obtained from the results.

Optimal Inventory Control with Retail Pre‐Packs

A pre‐pack is a collection of items used in retail distribution. By grouping multiple units of one or more stock keeping units (SKU), distribution and handling costs can be reduced; however, ordering flexibility at the retail outlet is limited. This paper studies an inventory system at a retail level where both pre‐packs and individual items (at additional handling cost) can be ordered. For a single‐SKU, single‐period problem, we show that the optimal policy is to order into a “band” with as few individual units as possible. For the multi‐period problem with modular demand, the band policy is still optimal, and the steady‐state distribution of the target inventory position possesses a semi‐uniform structure, which greatly facilitates the computation of optimal policies and approximations under general demand. For the multi‐SKU case, the optimal policy has a generalized band structure. Our numerical results show that pre‐pack use is beneficial when facing stable and complementary demands, and substantial handling savings at the distribution center. The cost premium of using simple policies, such as strict base‐stock and batch‐ordering (pre‐packs only), can be substantial for medium parameter ranges.

Optimal inventory management with supply backordering

We study the inventory control problem of a retailer working under stochastic demand and stochastic limited supply. We assume that the unfilled part of the retailer׳s order is fully backordered at the supplier and replenished with certainty in the following period. As it may not always be optimal for the retailer to replenish the backordered supply, we also consider the setting in which the retailer has a right to either partially or fully cancel these backorders, if desired. We show the optimality of the base-stock policy and characterize the threshold inventory position above which it is optimal to fully cancel the replenishment of the backordered supply. We carry out a numerical analysis to quantify the benefits of supply backordering and the value of the cancelation option, and reveal several managerial insights.

Inventory Control System Based on Control Charts to Improve Supply Chain Performances

Inventory replenishment rules have been recognized as a major cause of the bullwhip effect and inventory instability in multi-echelon supply chains. There is a trade-off between bullwhip effect and inventory stability where mitigating the bullwhip effect through order smoothing might increase inventory instability. Therefore, there is a substantial need for inventory control policies that can cope with supply chains dynamics. This paper attempts to formulate an inventory control system based on a statistical control chart approach to handle the trade-off between order variability amplification and inventory stability. The proposed replenishment system, namely IR-SPC, incorporates individual control charts to control both the inventory position and the placed orders. A simulation study has been conducted to evaluate and compare the IR-SPC with a generalized order-up-to that has order smoothing mechanism. The comparisons showed that the IR-SPC outperforms both the smoothing order-up-to policy and the Min-Max inventory policy in terms of bullwhip effect and inventory performances. (Received in June 2013, accepted in January 2014. This paper was with the authors 1 month for 2 revisions.)

Optimal Policies for Assembly Systems: Completing Rosling's Characterization

We study an assembly system with stochastic demand. This is the model studied in Rosling (1989), one of the classic papers in inventory theory, where the optimal policy is characterized as a balanced echelon base-stock policy, assuming that the initial state of the system possesses a certain property referred to as 'long-run balance.' We characterize the optimal policy starting with any arbitrary initial state, thereby completing the optimal policy description of Rosling (1989). The optimal policy is essentially a balanced echelon base-stock policy again, but with dynamically evolving echelon base-stock levels. We also show that the policy prescribed by Rosling (1989) is still optimal, if the initial echelon inventory positions are non-decreasing in item index, which is a milder condition than the long-run balance assumption and is easy to state and to check.

Supply Chain Performance Evaluation Using Spreadsheet Simulation

The objective of this paper is to develop a spreadsheet-based simulation methodology to evaluate the performance of a serial supply chain under different inventory position based ((r, Q) and (r, S)) and non-inventory position based (Fixed Order Quantity (FOQ) and Demand Flow Strategy (DFS)) periodic review inventory policies. The performance measures comprises of Fill Rate, Risk of Shortage, Bullwhip Effect and Total Cost of Supply Chain. An experimental study with four scenarios are carried out for two customer demand distributions under information sharing and no information sharing scenarios to determine performance measures in lost sales environment. The best performing inventory control policy for each scenario is found by conducting Grey Relational Analysis and the analysis show that one of non-inventory position based policy, FOQ is the better policy compared to other three policies.

Decentralized and centralized model predictive control to reduce the bullwhip effect in supply chain management

Mitigating the bullwhip effect is one of crucial problems in supply chain management. In this research, centralized and decentralized model predictive control strategies are applied to control inventory positions and to reduce the bullwhip effect in a benchmark four-echelon supply chain. The supply chain under consideration is described by discrete dynamic models characterized by balance equations on product and information flows with an ordering policy serving as the control schemes. In the decentralized control strategy, a MPC-EPSAC (Extended Prediction Self-Adaptive Control) approach is used to predict the changes in the inventory position levels. A closed-form solution of an optimal ordering decision for each echelon is obtained by locally minimizing a cost function, which consists of the errors between predicted inventory position levels and their setpoints, and a weighting function that penalizes orders. The single model predictive controller used in centralized control strategy optimizes globally and finds an optimal ordering policy for each echelon. The controller relies on a linear discrete-time state-space model to predict system outputs. But the predictions are approached by either of two multi-step predictors depending on whether the states of the controller model are directly observed or not. The objective function takes a quadratic form and thus the resulting optimization problem can be solved via standard quadratic programming method. The comparisons on performances of the two MPC strategies are illustrated with a numerical example.

Optimal Inventory Control with Retail Pre-Packs

A pre-pack is a collection of items used in retail distribution. By grouping multiple units of one or more stock keeping units (SKU), distribution and handling costs can be reduced; however, ordering flexibility at the retail outlet is limited. This paper studies an inventory system at a retail level where both pre-packs and individual items (at additional handling cost) can be ordered. For a single-SKU, single-period problem, we show that the optimal policy is to order into a �band� with as few individual units as possible. For the multi-period problem with modular demand, the band policy is still optimal, and the steady-state distribution of the target inventory position possesses a semi-uniform structure, which greatly facilitates the computation of optimal policies and approximations under general demand. For the multi-SKU case, the optimal policy has a generalized band structure. Our numerical results show that pre-pack use is beneficial when facing stable and complementary demands, and substantial handling savings at the distribution center. The cost premium of using simple policies, such as strict base-stock and batch-ordering (pre-packs only), can be substantial for medium parameter ranges.

A Genetic Algorithm on Inventory Routing Problem

Inventory routing problem can be defined as forming the routes to serve to the retailers from the manufacturer, deciding on the quantity of the shipment to the retailers and deciding on the timing of the replenishments. The difference of inventory routing problems from vehicle routing problems is the consideration of the inventory positions of retailers and supplier, and making the decision accordingly. Inventory routing problems are complex in nature and they can be solved either theoretically or using a heuristics method. Metaheuristics is an emerging class of heuristics that can be applied to combinatorial optimization problems. In this paper, we provide the relationship between vendor-managed inventory and inventory routing problem. The proposed genetic for solving vehicle routing problem is described in detail.

A model predictive control framework for centralised management of a supply chain dynamical system

In this paper, a centralised model predictive control (MPC) strategy is applied to control inventories in a four-echelon supply chain. The single MPC controller used in this strategy optimises globally and finds an optimal ordering policy for each node. The controller relies on a linear discrete-time state-space model to predict system outputs and the prediction can be approached by either of the two multi-step predictors depending on the measurability of the controller states. The objective function has a quadratic form and thus the resulting optimisation problem can be solved via standard quadratic programming. Simulation results show that a centralised MPC strategy is preferred because it can track customer demand and, in the meantime, maintain a proper inventory position level with reduced bullwhip effect.

Discrete inventory control in systems with perishable goods – a time‐delay system perspective

This study considers the problem of providing efficient control of periodic-review production–inventory systems with perishable goods. The stock storage and replenishment is modelled as a first-order process with delay subject to external perturbations. The study investigates formally the classical delay compensation mechanisms used in inventory control and shows deficiencies of inventory position and Smith predictor-based concepts in the context of systems with deteriorating stock. Then, a new dead-time compensation mechanism is developed and non-linear control law synthesised. The proposed control scheme is proved robust with respect to arbitrary demand and delay variations.

Optimal Control of a Make-to-Stock System with Outsourced Production and Price-Sensitive Demand

We consider a make-to-stock system with controllable demand rate (by varying product selling price) and adjustable service rate (by outsourcing production). With one outsourcing alternative and a choice of either high or low price, the system decides at any point in time whether to produce or even outsource for additional capacity as well as which price to sell the product at. We show in the paper that the optimal control policy is of dynamic threshold type: all decisions are based on the product inventory position which represents the state of the system; there is a state dependent base stock level to decide on production and a higher level on outsourcing; and there is a state dependent threshold which divides the choice of high and low prices.

An Inventory Model for Deteriorating Items with Stochastic Demand, Variable Lead Time, Shortages Considering Inflation and Time Value of Money

(ProQuest: ... denotes formulae omitted.)1. IntroductionMonk (1987) defined inventory as idle resources that possess economic value. In a broad sense, everyone keeps inventory such as food, clothes, domestic items, paper, pens and many other goods. Inventory applies to all types of work systems. Some types of inventory are raw materials inventory, in-process inventory, finished goods inventory, spare parts inventory, and so on.There are three basic reasons for keeping an inventory:a. Time - The time lags present in the supply chain, from supplier to user at every stage, requires that you maintain certain amounts of inventory to use during the lead time.b. Uncertainty - Inventories are maintained as buffers to address the problems of uncertainties in demand, supply and movements of goods.c. Economies of scale - Ideal condition of one unit at a time at a place where a user needs it, when he needs principle tends to incur lots of costs in terms of logistics. So bulk buying, movement and storing brings in economies of scale, thus inventory (Wikipedia, 2010).The total cost of inventory is calculated as the sum of the purchasing cost, setup cost, holding cost, and shortage cost (Taha, 2007).Economic order quantity is the level of inventory that minimizes the total inventory holding costs and ordering costs.Several models exist depending on the assumptions taken in efforts to describe real life situations. Some considerations used are:a. Demand: the classical inventory model assumed demand to be known with certainty (deterministic). Chaudhuri (2003) considered a scenario where the demand varies with time, while Teng et. al. (2005) considered demand as deterministic but as an exponential function. Kar et. al. (2001) also considered demand as stochastic and price-dependent.b. Shortages: The classical model assumes that shortages are not allowed. Many works have been carried out under this assumption in times past and even recent times (e.g. Covert & Phillip (1973), Teng. et. al. (2005)). However, some works have also been done in which shortage-costs component is added to the inventory model (e.g. Kar et. Al,.2001; Mirzazadeh, 2010).c. Ordering pattern: Sharma (1987) identified five ordering policies namely:i. (s ,Q) policy: Place order for a fixed quantity, Q whenever the inventory position drops to a given level s or below.ii. (s ,S) Policy: Place order for a quantity that would bring the inventory to a given maximum stock level, S whenever the inventory position drops to a given level s or below.iii. (T, S) Policy: Place order for a quantity that would bring the inventory to a given maximum stock level, S at regular interval of time T, spaced at time intervals of equal length.iv. (T, s, S) Policy: Place order for a quantity that would bring the inventory to a given maximum stock level, S at regular interval of time T, spaced at time intervals of equal length if the inventory level is at level s or below.v. (T, Q) Policy: Place order for quantity Q at every ordering interval, T.Researchers (Sivakumar, 2009; Kalpakam & Sapna, 1995; Kalpakam & Sapna, 1994) have considered ordering policy in their studies.d. Inflation: Inflation can simply be defined as an increase in the supply of currency or credit relative to the availability of goods and services, resulting in higher prices and a decrease in the purchasing power of money. Buzacott (1975) stated that while classical EOQ formula assumes all costs are constant, it would be unreasonable to use the EOQ formula without investigating how it is modified when inflation causes cost to increase with time. The Buzacott model (1975) led to the consideration of inflation as an important factor in the determination of economic order quantity by many researchers and thus led to the development of many other models with inflation considerations (Mirzazadeh, 2010; Mirzazadeh et al. …

Supply Streams

A supply stream is a continuous version of a supply chain. It is like a series inventory system, but stock can be held at any point along a continuum, not just at discrete stages. We assume stationary parameters and aim to minimize the long-run average total cost. We show that a stationary continuous-stage echelon base-stock policy is optimal. That is, at each geographic point along the supply stream, there is a target echelon inventory level, and the optimal policy at all times is to order and dispatch material so as to move the echelon inventory position as close as possible to this target. We establish this result by showing that the solutions to certain discrete-stage systems converge monotonically to a limit, as the distances between the stages become small, and this limit solves the continuous-stage system. With demand approximated by a Brownian motion, we show that, in the continuous-stage limit, the supply stream model is equivalent to one describing first-passage times. This linkage leads to some interesting and useful results. Specifically, we obtain a partial differential equation that characterizes the optimal cost function, and we find a closed-form expression for the optimal echelon base-stock levels in a certain special case, the first in the inventory literature. These expressions demonstrate that the well-known square-root law for safety stock does not apply in this context.

Hedging costs, liquidity, and inventory management: The evidence from option market makers

Hedging the risk of holding undesired inventory is very important for market makers. However, prior studies seldom capture the role of inventory positions in measuring hedging costs. This study measures hedging costs directly using data on inventory positions of market makers in the Taiwan Index Options market. We break down rebalancing costs into two sources: rebalancing costs due to inventory changes and rebalancing costs due to delta changes. Contrary to prior studies on stock options, we find rebalancing costs are more important than initial hedging costs in explaining option spreads. Our findings underscore the importance of inventory management.

Cooperation and game-theoretic cost allocation in stochastic inventory models with continuous review

We study cooperation strategies for companies that continuously review their inventories and face Poisson demand. Our main goal is to analyze stable cost allocations of the joint costs. These are such that any group of companies has lower costs than the individual companies. If such allocations exist they provide an incentive for the companies to cooperate.We consider two natural cooperation strategies: (i) the companies jointly place an order for replenishment if their joint inventory position reaches a certain reorder level, and (ii) the companies reorder as soon as one of them reaches its reorder level. Numerical experiments for two companies show that the second strategy has the lowest joint costs. Under this strategy, the game-theoretical Shapley value and the distribution rule—a cost allocation in which the companies share the procurement cost and each pays its own holding cost—are shown to be stable cost allocations. These results also hold for situations with three companies.

A periodic-review inventory control policy for a two-level supply chain with multiple retailers and stochastic demand

We consider a time-based inventory control policy for a two-level supply chain with one warehouse and multiple retailers in this paper. Let the warehouse order in a fixed base replenishment interval. The retailers are required to order in intervals that are integer-ratio multiples of the base replenishment interval at the warehouse. The warehouse and the retailers each adopt an order-up-to policy, i.e. order the needed stock at a review point to raise the inventory position to a fixed order-up-to level. It is assumed that the retailers face independent Poisson demand processes and no transshipments between them are allowed. The contribution of the study is threefold. First, we assume that when facing a shortage the warehouse allocates the remaining stock to the retailers optimally to minimize system cost in the last minute before delivery and provide an approach to evaluate the exact system cost. Second, we characterize the structural properties and develop an exact optimal solution for the inventory control system. Finally, we demonstrate that the last minute optimal warehouse stock allocation rule we adopt dominates the virtual allocation rule in which warehouse stock is allocated to meet retailer demand on a first-come first-served basis with significant cost benefits. Moreover, the proposed time-based inventory control policy can perform equally well or better than the commonly used stock-based batch-ordering policy for distribution systems with multiple retailers.

Two-Commodity Markovian Inventory System with Compliment and Retrial Demand

are assumed to form a independent Poisson processes. The second commodity is supplied as a gift whenever the demand occurs for the first commodity, but no major item is provided as a gift for demanding a second commodity. ) , ( 1 1 Q s type control policy for the first commodity, with random lead time but instantaneous replenishment for the second commodity are considered. If the inventory position of first commodity (major item) is zero then any arriving primary demand for the first commodity enters into an orbit of finite size N . These orbiting customers compete for service by sending out signals that are exponentially distributed. The joint probability distribution for both commodities and the number of demands in the orbit, is obtained in the steady state case. Various system performance measures in the steady state are derived. The results are illustrated with numerical examples.

Performance Evaluation of Modified Echelon <i>(r, Q)</I> Policies for Stochastic Serial Inventory Systems

We consider the classic continuous-review N-stage serial inventory system with a homogeneous Poisson demand arrival process at the most downstream stage (Stage 1). Any shipment to each stage, regardless of its size, incurs a positive fixed setup cost and takes a positive constant leadtime. The optimal policy for this system under the long-run average cost criterion is unknown. Finding a good worst-case performance guarantee for this problem remains an open problem. We tackle this problem by introducing a class of modified echelon (r, Q) policies that do not require Q_{i 1}/Q_i to be a positive integer: Stage i 1 ships to Stage i based on its observation of the echelon inventory position at Stage i; if it is at or below r_i and Stage i 1 has positive on-hand inventory, then a shipment is sent to Stage i to raise its echelon inventory position to r_i Q_i as close as possible. We construct a heuristic policy within this class of policies, which has the following features: First, it has provably primitive-dependent performance bounds. In a two-stage system, the performance of the heuristic policy is guaranteed to be within (1 K_1/K_2) times of the optimal cost, where K_1 is the downstream fixed cost and K_2 is the upstream fixed cost. We also provide an alternative performance bound, which depends on efficiently-computable optimal (r, Q) solutions to N single-stage systems, but tends to be tighter. Second, the heuristic is simple, efficiently computable and numerically performs well, likely to even outperform the optimal integer-ratio echelon (r,Q) policies when K_1 is dominated by K_2. Third, the heuristic is asymptotically optimal, as we take some dominant relationships, between the setup or holding cost primitives at an upstream stage and its immediate downstream stage, to the extreme, e.g., when h_2/h_1\rightarrow0, where h_1 is the downstream holding cost parameter and h_2 is the upstream holding cost parameter.