assortment planning in fashion retailing methodology application and analysis abstract assortment planning is the process conducted by the retailer to determine the number and types of products in a line key questions that arise in this process include choosing the inventory depth and variety breadth and the mix between basic and fashion merchandise of the assortment to maximize expected profits we describe a method for resolving these questions using demand forecasts derived from historical sales patterns we use a nonlinear integer programming model to make the assortment choice efficient heuristics are developed to solve this problem we applied our method at a large catalog retailer specializing in women s apparel we compared our method to the existing rules used by this retailer and found that it could choose the assortment in a manner that reduces markdowns due to excessive inventory and lost margins due to stockouts by enough to increase profits by at least 40 insights are developed to better understand why products are included in an assortment and the implications of this choice on the realized profit we extend our model to include shelf space constraints and the effect of assortment choice on product demand

on the single resource capacity problem for multi item inventory systems in this paper we study multi item inventory systems under a single resource capacity constraint in contrast to most previous approaches we treat the capacity as a decision variable and not as given data this is consistent with many practical cases where additional capacities resources can be acquired rented at some cost profit two solution procedures are developed for deriving an optimal policy within the class of policies that has a fixed cycle for all items with phasing of orders within the cycle these solution procedures can be applied to various types of cost functions as illustrated by an example

optimal ordering for a probabilistic one time discount abstract we develop a model for a one time special purchasing opportunity where there is uncertainty with respect to the materialization of the discounted purchasing offer our model captures the phenomenon of an anticipated future event that may or may not lead to a discounted offer we analyze the model and show that the optimal solution results from a tradeoff between preparing for the special offer and staying with the regular ordering policy we quantify the tradeoff and find that the optimal solution is one of four intuitive policies we present numerical illustrations that provide additional insights on the relationship between the different ordering policies

lot sizing algorithm for a coordinated multi item multi source distribution problem abstract consider a distribution problem consisting of several warehouses or production facilities a production facility produces one or more items distributed to several retailers a retailer may receive supplies from any number of production facilities external demands for items are constant continuous and deterministic each facility has a fixed set up cost and incurs echelon holding cost for any unused stock a product nested replenishment policy whose cost is less than 2 above the cost of all feasible policies is determined the complexity of the solution algorithm is shown to be o w 4 d log d where w and d are the number of warehouses and items respectively

the cost allocation issue in joint replenishment abstract joint replenishment for several products to achieve a lower inventory logistics cost has been a topic of extensive studies less attention has been paid to the issue of deciding how the joint replenishment costs should be allocated across the individual products ideally when items are ordered together one would require a stable cost allocation such that no subset of products subsidizes another subset when part of each product s ordering cost is product specific and part can be shared with other products like in a 3pl setting of anily and haviv it has been shown that even when a stable allocation exists such an allocation might be difficult to compute in addition usually the components of ordering costs are partially determined using estimates and accounting discretion this paper provides two main insights for determining an appropriate cost allocation it provides the means to test how sensitive a stable cost allocation is to a range of cost parameter values then in a computational study it is shown how to obtain a stable cost allocation without excessive computation

capacitated two stage multi item production inventory model with joint setup costs we analyze a continuous time two stage production inventory system in the first stage a common intermediate product is produced in batches and possibly stored in the second phase the intermediate product is fabricated into n distinct finished products several finished products may be included in a single production batch of limited capacity to exploit economies of scale we propose a planning methodology to address the combined problem of joint setup costs and capacity limits per setup we restrict ourselves to a class of replenishment strategies with the following properties a replenishment strategy specifies a collection of families subsets of items covering all end items if an item belongs to several families a specific fraction of its sales is assigned to each family each time the inventory of one item in a family is replenished the inventories of all other items in the family are replenished as well we derive a simple roughly 0n log n algorithm that results in a strategy whose long run average cost comes within a few percentage points of a lower bound for the minimum achievable cost within the above class of strategies

evaluating echelon stock r nq policies in serial production inventory systems with stochastic demand this paper studies echelon stock r nq policies in serial production inventory systems with stochastic demand we provide a recursive procedure to compute the steady state echelon inventory levels of the systems which can be used to evaluate the long run average holding and backorder costs as well as other performance measures the procedure is based upon an observation of a relationship between the inventory status of adjacent stages in a serial system we also device exact formulas for replenishment frequencies and setup costs our results apply to both continuous review systems with compound poisson demand and periodic review systems with independent identically distributed demands a preliminary numerical study was conducted to explore the cost effectiveness of echelon stock r nq policies for two stage systems with simple poisson demand we compared among the minimum costs of echelon stock r nq policies a lower bound on the minimum achievable costs and the minimum costs of installation stock r nq policies finally we present a modification of an existing approximate evaluation procedure

a hybrid algorithm for simultaneous scheduling of production and distribution in multi echelon structures this paper presents a dynamic programming algorithm for simultaneous determination of production batch sizes in an assembly network and distribution batch sizes in a conjoined distribution arborescent network the objective is to minimize average cost per period over an infinite horizon costs consist of processing costs at each node and linear holding costs for inventory final product demand rates may vary among the retail nodes but at each retail node the demand rate is assumed to be known constant and continuous all demand must be met backorders are not permitted the model can be used for a single product or for several products that are temporarily combined for distribution or for scheduling production in a system where several end products are produced from the same intermediate product as in some biochemical manufacturing processes

optimizing reorder intervals for two echelon distribution systems with stochastic demand we consider a periodic review inventory system in which n non identical retailers replenish from a warehouse which further replenishes from an outside vendor with ample supply each facility faces poisson demand and replenishes according to a base stock policy in a fixed time interval fixed costs are incurred for placing an order the warehouse fills the retailers orders in the same sequence as the occurrence of the demand at the retailers the objective is to minimize the average system cost per period this paper develops an evaluation scheme and provides a method to obtain the optimal base stock levels and reorder intervals specifically with fixed reorder intervals we show that the optimal base stock levels can be obtained by generalizing the result in the literature to find the optimal reorder intervals we first allocate the total system cost to each facility and then construct a lower bound to the allocated facility cost these lower bound functions which are separable functions of reorder i

optimal stationary policies in a 3 stage serial production distribution logistic chain facing constant and continuous demand in this paper we study a 3 stage production distribution system that faces constant and continuous demand the system is made up of three storing sites a production facility a warehouse and a retailer this system was constructed to study the need for coordinating distribution and production in the decision of lot sizes hence the production capacity is limited our objective is to compute lot sizes that leads to the lowest possible cost in such a system we consider stationary inventory management policies in such a policy a fixed lot size is supplied from one stage to the next with a constant time interval we introduce the concept of multiple policies and give a solution to find the best one we then prove that multiple policies are guaranteed to cost less than 1 51 more than the best stationary policy we improve this guarantee to 0 51 by adding some simple but non multiple policies to our candidate policies

single resource multi item inventory systems we consider two economic order quantity models where multiple items use a common resource in the tactical model the objective is to establish and coordinate order quantities to minimize total inventory ordering and carrying costs without ever exceeding a capacity constraint on the resource in the strategic model the objective is to establish and coordinate order quantities to minimize the average cost which includes in addition to the ordering and inventory costs a cost proportional to the peak usage of the resource the common resource may be space in an automated warehouse or total capital invested in inventory we show that a lower bound on the peak resource usage known for certain subsets of policies is valid for any feasible policy we use this to derive lower bounds on the optimum average cost for both models and show that simple heuristics for either model have bounded worst case performance ratios more sophisticated heuristics require an effort to solve the embedded staggering problem of time phasing the arrival of the orders to minimize the maximum use of the resource we develop a heuristic for the staggering problem and use it to obtain efficient heuristics for the strategic and tactical models

multi item replenishment and storage problem mirsp heuristics and bounds automated warehouses are often faced with the problem of smoothing their stock volume over time in order to minimize the cost due to space acquisition in this paper we consider an infinite horizon multi item replenishment problem in addition to the usual setup and holding costs incurred by each item an extra charge proportional to the peak stock volume at the warehouse is due this last cost raises the need for careful coordination while making decisions on the individual item order policies we restrict ourselves to the class of policies that follows a stationary rule for each item separately we derive a lower bound on the optimal average cost over all policies in this class then we investigate the worst case of the rotation cycle policy we show that depending on the problem s parameters the rotation cycle policy may yield an extremely good solution but in other settings this heuristic may generate an extremely poor policy we also develop a new heuristic whose performance is at least as good as that of the rotation cycle procedure and moreover it is guaranteed to come independently of the problem s parameters within no more than 41 of the optimal solution

near optimal r q policies for a two stage serial inventory system with poisson demand we consider a two stage serial inventory system whose cost structure exhibits economies of scale in both stages in the system stage 1 faces poisson demand and replenishes its inventory from stage 2 and the latter stage in turn orders from an outside supplier with unlimited stock each shipment either to stage 2 or to stage 1 incurs a fixed setup cost we derive important properties for a given echelon stock r q policy for an approximation of the problem where all states are continuous based on these properties we design a simple heuristic algorithm that can be used to find a near optimal r q policy for the original problem numerical examples are given to demonstrate the effectiveness of the algorithm

94 effective policies for a two stage serial inventory system with stochastic demand a two stage inventory system is considered where poisson demand occurs at stage 1 and stage 1 replenishes its inventory from stage 2 which in turn orders from an outside supplier with unlimited stock each shipment either to stage 2 or to stage 1 incurs a fixed setup cost under the assumption that the supply leadtime at stage 2 is zero we characterize a simple heuristic policy whose long run average cost is guaranteed to be within 6 of optimality i e a 94 effective policy the paper also provides heuristic policies for more general inventory systems and reports computational results

lower bounds for multi echelon stochastic inventory systems we establish lower bounds on the minimum cost of managing certain production distribution networks with setup costs at all stages and stochastic demands these networks include serial assembly and one warehouse multi retailer systems we obtain the bounds through novel cost allocation schemes we evaluate the bounds performance for one warehouse multi retailer systems by comparing them with simple heuristic policies the bounds are quite tight for systems with a small number of retailers we also present simplified proof of known optimality results for serial and assembly systems

coordination mechanisms of supply chain systems supply chain management scm has become an important management paradigm as supply chain members are often separate and independent economic entities a key issue in scm is to develop mechanisms that can align their objectives and coordinate their activities so as to optimize system performance in this paper we provide a review of coordination mechanisms of supply chain systems in a framework that is based on supply chain decision structure and nature of demand this framework highlights the behavioral aspects and information need in the coordination of a supply chain the identification of these issues points out several directions of future research in this area

the investment opportunity set and accounting procedure choice abstract this paper provides evidence on the cross sectional relation between firms investment opportunities their debt and compensation contracts their size and financial leverage and their accounting procedure choices this evidence is important because previous studies hypothesize that the link between firms investment opportunities and their accounting choices helps explain extant results on the size debt equity and bonus plan hypotheses however while i find that firms investment opportunities do affect the nature of their contracts i also find that the traditional explanations for accounting choice are important after controlling for the effects of the investment opportunity set

note an acquisition policy for a single item multi supplier system in this paper we consider the problem of developing an acquisition policy specifically given a set of potential qualified suppliers from whom should the firm buy the product in what quantities and how often we provide properties of the optimal solution and relate them to the approach of using a single source as advocated by jit the solution procedure provides the periodic order quantity from each supplier the order size and the firm cycle time as well as how many times per cycle we should order from each supplier we show that the maximum error of our solution can be made as small as desired

multi item one warehouse multi retailer distribution systems in this paper we study the problem of coordinating the purchase and shipment of i items in a one warehouse n retailer inventory system the model includes positive echelon holding costs fixed costs for ordering and shipping each item and a fixed joint item order cost at each retailer demand for each item at each retailer is assumed to occur at a constant and continuous rate a mathematical model is developed based on these assumptions and the assumption that a stationary nested policy is followed an efficient algorithm is presented based on the problem s structure that involves only sorting and runs in oni log ni time the cost of the policy computed is proven to be within 6 of the cost of an optimal nested policy an example is presented to illustrate the problem structure and the proposed algorithm

98 effective integer ratio lot sizing for one warehouse multi retailer systems a warehouse supplies n retailers constant external demand occurs at each retailer and shortages are not allowed there are linear holding costs and fixed costs for ordering at the warehouse and at each retailer the goal is to minimize the long run average cost over an infinite time horizon we define a new class of policies for this problem whose simple structure facilitates both computation and implementation the cost of a policy that is optimal within this class is shown to be within 2 of the cost of an optimal policy for the original problem in the worst case such a policy can be computed in on log n time

an integrated supply chain problem with environmental considerations in this paper a novel formulation for a multiple product capacitated inventory location supply chain model with risk pooling and carbon emission considerations is proposed various products are shipped from a single plant to retailers with stochastic demand via a network of capacitated warehouses in the presence of environmental regulations the locations and inventory policies of the warehouses are chosen so as to minimize the sum of fixed facility location transportation inventory carrying costs and emissions related costs the warehouses retain safety stock so as to maintain appropriate service levels in the face of uncertain demand at the retailers for multiple products computational results are also presented

including sustainability criteria into inventory models research on sustainability performance has considerably enriched operations management literature in recent years however work with quantitative models is still scarce this paper contributes by revisiting classical inventory methods taking sustainability concerns into account we believe that reducing all aspects of sustainable development to a single objective is not desirable we thus reformulate the classical economic order quantity model as a multiobjective problem we refer to this model as the sustainable order quantity model then a multi echelon extension of the sustainable order quantity model is studied for both models the set of efficient solutions pareto optimal solutions is analytically characterized these results are used to provide some insights about the effectiveness of different regulatory policies to control carbon emissions we also use an interactive procedure that allows the decision maker to quickly identify the best option among these solutions the proposed interactive procedure is a new combination of multi criteria decision analysis techniques

a century of evolution from harris s basic lot size model survey and research agenda abstract determining the economic lot size has always represented one of the most important issues in production planning this problem has long attracted the attention of researchers and several models have been developed to meet requirements at minimum cost in this paper we explore and discuss the evolution of these models during one hundred years of history starting from the basic model developed by harris in 1913 up to today following harris s work a number of researchers have devised extensions that incorporate additional considerations the evolution of eoq theory strongly reflects the development of industrial systems over the past century here we outline all the research areas faced in the past by conducting a holistic analysis of 219 selected journal papers and trying to give a comprehensive view of past work on the eoq problem finally a new research agenda is proposed and discussed

modified echelon r q policies with guaranteed performance bounds for stochastic serial inventory systems we consider the classic continuous review nstage 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 lead time the optimal policy for this system under the long run average cost criterion is unknown finding a good worst case performance guarantee remains an open problem we tackle this problem by introducing a class of modified echelon r q policies that do not require qi 1 qi 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 ri and stage i 1 has positive on hand inventory then a shipment is sent to stage i to raise its echelon inventory position to ri qias 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 k1 k2 times the optimal cost where k1 is the downstream fixed cost and k2 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 it is efficiently computable and it performs well numerically it is even likely to outperform the optimal integer ratio echelon r q policies when k1 is dominated by k2 third the heuristic is asymptotically optimal when we take some dominant relationships between the setup or holding cost primitives at an upstream stage and its immediate downstream stage to the extreme for example when h2 h1 0 where h1 is the downstream holding cost parameter and h2 is the upstream holding cost parameter

offsetting inventory cycles of items sharing storage abstract the ability to determine the optimal frequencies and offsets for independent and unrestricted ordering cycles for multiple items can be very valuable for managing storage capacity constrained facilities in a supply chain the complexity of this problem has resulted in researchers focusing on more tractable surrogate problems that are special cases of the base problem this research has focused on developing fundamental properties of the original problem we exploit the problem structure and present a heuristic for offsetting independent and unrestricted ordering cycles for items to minimize their joint storage requirements heuristics of this type may prove useful in solving the more general problem of selecting order quantities to minimize combined holding ordering and storage costs

the optimal and heuristic solutions of a distribution network abstract competitive environment of global networking and customization call for cost reduction in arborescent tree like inventory system one of the keys to cost reduction is the integration of the supply chain much practical research has been done in the area of integrating the inventory system in recent years integration involves the joint decision making among the producer the distributors and the retailers in the supply chain by revising goyal s model an optimal solution is derived in this paper a heuristic solution model is also developed for a producer distributors retailers inventory system using the principle of strategic partnership numerical results indicate the heuristic solution is a good estimation of the optimal solution

one warehouse multiretailer systems with centralized stock information we consider a distribution system with a central warehouse and multiple retailers the warehouse orders from an outside supplier and replenishes the retailers which in turn satisfy customer demand the retailers are nonidentical and their demand processes are independent compound poisson there are economies of scale in inventory replenishment which is controlled by an echelon stock batch transfer policy for the special case with simple poisson demand we develop an exact method for computing the long run average holding and backorder costs of the system based on this exact method we provide approximations for compound poisson demand numerical examples are used to illustrate the accuracy of the approximations we also present a numerical comparison between the average costs of a heuristic echelon stock policy and an existing lower bound on the average costs of all feasible policies

single supplier multiple buyer supply chain coordination incorporating buyers expectations under vertical information sharing abstract we address the coordination problem in a single supplier multiple buyer supply chain the supplier wishes to coordinate the supply chain by offering quantity discounts to obtain their complete cost information the supplier exchanges his own cost parameters with buyers leading to vertical information sharing the supplier thinks that the buyers as they have access to supplier s setup and holding cost information may demand a portion of the anticipated coordination savings based on the partial information they hold about the cost structure of the entire supply chain we model each buyer s expectations based on her limited view of the entire supply chain which consists of herself and the supplier only these expectations are then incorporated into the modeling of the supply chain which results in a generalization of the traditional stackelberg type models we discuss alternative efficiency sharing mechanisms and propose methods to design the associated discount schemes that take buyers expectations into account in designing the discount schemes we consider both price discriminatory and non price discriminatory approaches the study adds to the existing body of work by incorporating buyers expectations into a constrained stackelberg structure and by achieving coordination without forcing buyers to explicitly comply with the supplier s replenishment period in choosing their order quantities the numerical analysis of the coordination efficiency and allocation of the net savings of the proposed discount schemes shows that the supplier is still able to coordinate the supply chain with high efficiency levels and retain a significant portion of the net savings

production and inventory model using net present value using the net present value is the standard methodology in theoretical analysis and the most frequently used method for making financial decisions however net present value is rarely used in production and inventory decisions the main reasons appear to be the complexity of the formulae and the robustness of the eoq model we investigate the general multiproduct multistage production and inventory model using the net present value of its total cost as the objective function a power of two heuristic gives us a near optimal solution to this problem if the base period is fixed or varied the solution based on the best power of two heuristic will be within 6 2 or 2 1 of the optimal this result is surprisingly similar to models using the long term average cost the average cost does not reflect the time value of money does this mean that decisions based on average cost are significantly inferior to those based on net present value the answer is quite surprising if we include discounted production cost in the holding cost it turns out that the decision based on average cost is only 9 6 in terms of the net present value of the total cost worse than the decision based on the net present value however the reorder interval based on the average cost could be much longer than that derived using net present value this result shows that average cost is a good approximation to the net present value when the demands are deterministic

designing two echelon supply networks a modern distribution network design model needs to deal with the trade offs between a variety of factors including 1 location and associated fixed operating cost of distribution centers dcs 2 total transportation costs and 3 storage holding and replenishment costs at dcs and retail outlets in addition network design models should account for factors such as 4 stockouts by setting appropriate levels of safety stocks or 5 capacity concerns which may affect operating costs in the form of congestion costs the difficulty of making such trade offs is compounded by the fact that even finding the optimal two echelon inventory policy in a fixed and uncapacitated distribution network is already a hard problem in this paper we propose a generic modeling framework to address these issues that continues and extends a recent stream of research aimed at integrating insights from modern inventory theory into the supply chain network design domain our approach is flexible and general enough to incorporate a variety of important side constraints into the problem

a two echelon inventory distribution system with power demand pattern and backorders abstract this paper addresses the implications of considering power demand pattern and backorders in the one warehouse n retailer problem specifically we assume that items at the retailers are withdrawn from the inventory following a power pattern the objective function consists of the sum of ordering holding and backordering costs at all installations this objective function depends on the class of inventory policies that we choose for the formulation of the problem in general obtaining the cost function is an arduous task since the average inventory at the warehouse could be difficult to determine however if we apply single cycle policies the computation of the total average cost becomes possible under these assumptions we show that the one warehouse n retailer system with power demand pattern and backorders can be formulated as a mixed non linear programming problem

lot sizing in a serial distribution system with capacitated in system production flow abstract in this paper we focus on an n stage serial production distribution system with limited production capacity at the first stage our objective in such a system is to find inventory management policies that minimize the global logistic cost including transportation and holding costs we use myopic heuristics based on the breakdown of the system into local systems one of these systems is a 2 stage system and the second is a 3 stage system they both can be solved with a very good performance guarantee the successive optimizations of such systems provide quite good policies for the global system as asserted by the experimental results at the end of the paper

dynamic version of the economic lot size model this article originally appeared in management science october 1958 volume 5 number 1 pp 89 96 published by the institute of management sciences a forward algorithm for a solution to the following dynamic version of the economic lot size model is given allowing the possibility of demands for a single item inventory holding charges and setup costs to vary over n periods we desire a minimum total cost inventory management scheme which satisfies known demand in every period disjoint planning horizons are shown to be possible which eliminate the necessity of having data for the full n periods

supplier pricing and lot sizing when demand is price sensitive abstract the problem of co ordination between a vendor and a buyer is formulated as a two person fixed threat bargaining game the vendor decides on his lot size and the price schedule he is to offer to the buyer the buyer decides upon his lot size and the selling price in the market we have characterized pareto efficient solutions and the nash bargaining solution for the problem we have also proposed two pricing schedules for the vendor who is supplying to a large population of buyers the first one is based upon profit sharing the second one resembles the classical all unit quantity discount schedule we have thus provided for the supplier a procedure for setting all unit quantity discount schedule

a serial supply chain of newsvendor problem with safety stocks under complete and partial information sharing abstract we consider a supply chain where multiple members are serially connected the decision is to determine the ordering quantity of a member to the next upstream member in the supply chain the basic cost model is similar to the newsvendor problem with additional consideration to safety stock this paper presents optimal approaches for coordination of the supply chain under both complete and partial information sharing in order to maximize the total expected benefit for complete information sharing we develop an optimal coordination algorithm for partial information sharing we propose an optimal coordination algorithm based on the alternating direction method and the diagonal quadratic approximation method a numerical example is discussed to show the optimal convergence of ordering quantities and discuss the properties of the proposed algorithms

a continuous approximation approach for the integrated facility inventory allocation problem abstract in today s retail business many companies have a complex distribution network with several national and regional distribution centers this article studies an integrated facility location and inventory allocation problem for designing a distribution network with multiple distribution centers and retailers the key decisions are where to locate the regional distribution centers rdcs how to assign retail stores to rdcs and what should be the inventory policy at the different locations such that the total network cost is minimized due to the complexity of the problem a continuous approximation ca model is used to represent the network nonlinear programming techniques are developed to solve the optimization problems the main contribution of this work lies in developing a new ca modeling technique when the discrete data cannot be modeled by a continuous function and applying this technique to solve an integrated facility location allocation and inventory management problem our methodology is illustrated with the network from a leading us retailer numerical analysis suggests that the total cost is significantly lower in the case of the integrated model as compared with the non integrated model where the location allocation and inventory management problems are considered separately this paper also studies the effects of changing parameter values on the optimal solutions and to point out some management implications