International Journal of Inventory Research (14 papers in press)
Capacity planning on key work stations in a hybrid MTO-ETO production system: A case-study on Siemens AG
by Lars Zschorn, Steve Müller, Dmitry Ivanov
Abstract: The focus of this study is on tactical-level capacity management which refers to the determination of in-house workforce production capacity in an optimal cost-efficient manner in a multi-period mode. Two options for capacity planning are investigated for rapid prototyping with the help of a mixed-integer linear optimization model: smoothing the capacity utilization over time vs a higher level of capacity availability. A sensitivity analysis based on real empirical data in Siemens AG is used for the revealing the impact of workforce and capacity flexibility on operational performance. The results suggest that the number of workers decreases if production orders have not to be completed within only one week. On the contrary, if the binary restriction on the order fulfillment within one week is released, the production orders can be split into different weeks and this results in a higher smoothing rate and thus in a higher capacity utilization degree.
Keywords: production capacity; inventory; flexibility; adaptability; workforce; mixed-integer linear programming.
Replenishment policy in a Logistics System with Environmental Considerations
by Ata Allah Taleizadeh, Vahidreza Soleymanfar, Joaquín Sicilia
Abstract: One of the most applicable models in inventory and production planning is the Economic lot sizing model, which recently extended by environmental considerations and the sustainability concept. The theoretical sustainable lot sizing model is only a basic model that ignores many real-world conditions in the modern cloud manufacturing environments, for example, the possibility of shortage and stockout in the inventory system. In this work, we have presented new sustainable lot-sizing models in which different shortage conditions are considered. We developed a basic model for the time that shortage in not allowed, and full lost sale, full backordering and partial backordering models when shortages are allowed. We proposed an integrated procedure for determining the optimal values of the variables of the proposed models. The models and proposed procedure application are illustrated with numerical examples based on an Iranian petrochemical company's data. Finally, applying sensitivity analysis, the model's results have been analyzed and discussed. These results show that the partial backordering case is a general and more realistic model which can be used in many real cases.
Keywords: Partial Backordering; Inventory Management; Environmental Considerations.
An optimal policy for an integrated vendor-buyer model with two warehouses under vendor's capacity constraint
by Bibhas C. Giri, Ayan Chakraborty
Abstract: The paper considers an integrated single-vendor single-buyer supply chain model in which the vendor is assumed to be capacity constrained. The vendor can keep the excess units beyond the capacity of its own warehouse(OW) in a rented warehouse (RW) whose holding cost is higher than that of the own warehouse. The vendor delivers the buyer's order quantity in a number of equal shipments. The proposed integrated model is formulated and some of its characteristics are studied analytically. Considering the vendor's capacity as a control variable, the optimal decisions of the model are obtained for a numerical example. Sensitivity analysis is also carried out to measure the impact of key model-parameters on the outcome of the model.
Keywords: Supply chain; vendor-buyer integrated model; rented warehouse; capacity constraint.
On Inventory Control with Reference Prices
by Yigal Gerchak
Abstract: A retailer sets prices, as well as, simultaneously, selects quantities to order from a supplier. We consider a two periods setting where the second period\'s demand depends on the first period\'s (\"reference\") price, as well as on the second period price. We consider a linear-additive demand function as well as a novel iso-elastic multiplicative model.
Keywords: reference price; pricing newsvendor; additive noise; multiplicative noise.
Inventory model for non-instantaneous deteriorating item with random pre-deterioration period
by Manisha Pal
Abstract: The paper studies an inventory model for non-instantaneous deteriorating item where the deterioration of the item is initiated at a random time point. It is assumed that no shortages are allowed and demand occurs uniformly but at different rates during pre- and post- deterioration periods. The optimum order quantity and reorder intervals are determined so as to minimize the total expected cost per unit length of an inventory cycle. Numerical examples are cited and a sensitivity analysis is carried out to study the effect of model parameters on the optimum policy.
Keywords: Inventory control; periodic review model; non- instantaneous deteriorating item; random pre-deterioration period; deterioration dependent demand rate.
Coordinating replenishment and marketing policies for non-instantaneous deteriorating items with imprecise deterioration free time and general deterioration and holding cost rates
by Amirhosein Patoghi, Mostafa Setak
Abstract: In this paper an inventory system for non-instantaneous deteriorating items with imprecise deterioration free time is developed. We adopt a price and advertisement frequency dependent demand function, and in order to reach a general framework, arbitrary functions of deterioration and holding cost rates are hired. The major objective is to determine the optimal selling price, the optimal replenishment cycle and the optimal frequency of advertisement such that, the total profit is maximized. In order to determine the optimal solution several theoretical results are derived which indicate existence and uniqueness of the optimal solution. Thereafter, based on these theoretical results an iterative solution is developed. Finally, numerical examples are provided to demonstrate solution procedure, then sensitivity analysis is performed, it is shown that optimal policy under uncertain environment and crisp environment are identical and finally some managerial insights are proposed.
Keywords: Inventory; imprecise deterioration free time; arbitrary deterioration and holding cost rates; price and advertisement dependent demand.
Special Issue on: Advances in Inventory Management under Uncertainty
Optimal Replenishment Policy for Price Dependent Demand in different Financial Scenario under Fuzzy Environment
by Anuj Sharma, Chandra Jaggi, Sunil Tiwari
Abstract: In present business culture, usually supplier offers a permissible delay in payments to retailer in order to stimulate his demand. However, while developing the inventory model under permissible delay in payments in the existing literatures, authors generally assumed that retailers have to settle their accounts at the end of credit period i.e. supplier accept only full amount at the end of the credit period. However in reality, supplier may accept the partial amount at the end of the credit period with unpaid balance settled in due course or he may also accept the full amount at a fix point after the expiry of the credit period instead of accepting the partial payment, if the retailer finances the inventory from the supplier itself. Hence in this direction, this paper establishes an inventory model which incorporates the above discussed realistic approach for settling the accounts when supplier offers permissible delay in payments under fuzzy environment. Further, demand has been assumed to be price dependent i.e. a bp, where and are treated as trapezoidal fuzzy numbers. Graded Mean Representation has been used to defuzzify the total cost function and expression for the optimal order quantity and optimal cycle length under different scenario has been derived. An appropriate algorithm is proposed to solve the model. In order to obtain the validity of the model, two hypothetical examples were considered. Also a comprehensive sensitivity analyses has been performed to measure the robustness of model for different key parameters.
Keywords: Inventory; Fuzzy Variable; Trapezoidal Fuzzy Number and Graded Mean Integration Representation Method.
An Economic Production Quantity Inventory Model with a Defective Production System and Uncertain Uptime
by Amirhossein Nobil, Amir Hosein Afshar Sedigh
Abstract: In this study, a fuzzy mathematical programming for an inventory control problem with defective items is considered. In this system, some unacceptable items are produced that should be disposed at a constant cost. The production system under study consists of a single machine that requires maintenance to enhance its efficiency, performance, and lifespan. In real-world scenarios estimation of machine uptime is hard and faces environmental uncertainties. As a result of uptime estimation based on the linguistic variables, i.e. experts ideas; the inherited uptime would be a fuzzy parameter itself. This fuzzy variable has a trapezoid form, i.e. it works certainly up to a time then it stops working at a time this time has an optimistic and pessimistic estimation. Based on the maintenance policy the machinery should be stopped to go through a preventive procedure during downtime. The proposed model helps production managers to reduce system costs and defective items by improving machine efficiency and performance employing appropriate maintenance policies. To solve the proposed problem, we optimised system costs, i.e. production costs, setup costs, disposal costs, holding costs, and maintenance costs, by calculating optimum production cycle. To do so, an algorithm is proposed to calculate optimum solution by calculating upper and lower bounds of inherited crisp problem. Finally, a numerical example is represented to investigate the effectiveness of the proposed algorithm.
Keywords: Fuzzy programming model; Economic batch quantity; Defective production system; Maintenance policy.
OPTIMAL CONSIGNMENT STOCKING POLICY FOR A VENDOR-BUYER SUPPLY CHAIN SYSTEM WITH PERIODIC INVENTORY AUDIT AND IN-TRANSIT HOLDING COST
by Mohamed Ohaiba, Md. Shahriar Hossain, Bhaba Sarker
Abstract: The research presents an integrated inventory model for a single-vendor-single-buyer consignment stock policy where demand rate and lead-time are constant. The vendor controls the buyers warehouse, whereas the stock of all finished goods is owned by the vendor. The vendor delivers finished goods to the buyer at a fixed lot size. Shortage is not allowed by controlling the production rate greater than the demand rate. The problem is formulated as a nonlinear cost model which is minimized to arrive at an optimal policy to cooperatively operate the joint contract. An iterative search approach is followed to obtain an optimal value of order quantity and number of shipments. Computational results are presented for a practical example and some empirical studies. The model presented here are applicable in numerous supply chain systems including retail business, assembly and production houses, where two parties are tied together for achieving their common goal.
Keywords: Consignment stocking policy; two stage supply chain; single vendor-buyer cooperation.
Supply Chain Network Design Under Uncertain Demand: Robust and Stable Optimization Approaches
by Simone Zanoni, Ivan Ferretti, Laura Mazzoldi
Abstract: Efficient design of distribution and delivery of products to customers in globally extended supply chain networks is a crucial issue. This paper is focused on the design of a supply chain taking into account the variability of the final customer demand: the traditional strategy for the network configurations so as to face such uncertainty, named robust approach, is to seek the minimum expected total cost over the planning horizon. The novelty of this contribution resides in the investigation of an alternative way to face the uncertainty, named stable approach, which aim is to determine the minimum variability of transport and handling cost in the considered time horizon. In particular, we study the design of a one-to-many distribution system, considering the product flows from the producers to the different distribution centres and to retailers, as well as the reverse flows from the retailers to the producers. The optimization procedure consists of two main steps: the first step is the definition of the number of producers and distribution centres to include in the network, jointly with their location; the second step is the definition of the products flows from producers and distribution centres to retailers, in order to satisfy their specific demand. The fluctuating demand of the products over the different regions, represented by the demand of retailers that serve such regions, influences the optimal solution for the different periods considered. The goal is the definition of the network configuration that can efficiently operate under the uncertainty of the customer demand, to this extent the solutions of the robust and the stable approaches have been compared. A numerical analysis has been performed over a realistic case study data, and results of robust and stable and hybrid solutions have been reported.
Keywords: Supply chain networks; robustness; flexibility; demand uncertainty.
Coordination with No Risk Sharing and Risk Sharing Discount Contracts in Two Echelon Supply Chains
by Marjan Zarea
Abstract: Production and procurement management in a supply chain are considerably affected by random yield. This paper considers a supply chain that includes a supplier who is faced with random yield production and two retailers who are faced with uncertain demand. Using Stackelberg game, two models are presented regarding discount coordination retailers with respect to the risk sharing and no risk sharing contracts. The supplier specifies quantity discount percentage and a wholesale price. Then, retailers determine their optimal order quantity in which their profit is maximized. Finally, the supplier determines the production quantity. Moreover, comparing the contracts shows that how the supply chain's performance enhances under certain conditions in risk sharing contract. Furthermore, numerical examples are presented to illustrate the presented models.
Keywords: Random yield; Uncertain demand; Supply chain; Discount coordination.
Special Issue on: Sustainable Inventory Management
Closed-loop supply chain simulation with disruption considerations: A case-study on Tesla
by Pietro Gianesello, Dmitry Ivanov, Daria Battini
Abstract: Performance impact of severe disruptions in the reverse part of an automotive closed-loop supply chain is studied with the use of a discrete-event simulation model implemented in anyLogistix software. A hybrid case study-simulation methodology is applied in this research to analyze the six-echelon closed-loop supply chain of Tesla from positions of resilience. Based on the secondary data, an example for the German market has been created and investigated. More specifically, the results help to show how a disruption in the reverse supply chain may affect the financial and operational performances of the company. Different recovery policies have been simulated in order to analyse how each might recover the supply chain from disruption and restore its operation and performance.
Keywords: closed-loop supply chain; resilience; simulation; anyLogistix; disruption; case-study; performance; e-mobility; reverse logistics.
Dynamic Pricing and Profit Maximization: A Simulation based approach for Agri-fresh Products Retailing in India
by Lamay Bin Sabir, Jamal Ahmad Farooquie
Abstract: Fresh agri-food products, like fruits and vegetables (F&V), are perishable products having a very short shelf life. They are different from non-perishables in managing their inventories as customers are more concerned about the nutritious value and shelf life. Customers are becoming strategic and planning their purchase based on the markdown and other promotional activities. Retailers are finding it difficult to a trade-off between the prices and remaining shelf life for offering markdown. Therefore decisions depending upon the value and timing of such markdowns for not so fresh F&V are important. This paper attempts to address these issues based on previously published studies which suggested a simple procedure to identify the quantum and time of markdowns for perishable products inside a retail store. Extending the approach, monte-carlo simulation is applied in order to generate randomness in the probability of sales and demand for F&V. A questionnaire is used in order to get the primary data from 89 retailers from Delhi/NCR, India. Organized retail of F&V is still at starting stage in India and no such study has been attempted before.
Keywords: Perishable; Inventory; Profit; Simulation; Retail; Agri-fresh; Dynamic Pricing.
DETERMINISTIC INVENTORY MODEL FOR ITEMS WITH LINEAR DEMAND, VARIABLE DETERIORATION AND PARTIAL BACKLOGGING
by SAURABH SRIVASTAVA
Abstract: A deterministic inventory model is developed for a deteriorating item having linear demand and variable deterioration rate. Shortages are allowed and partially backlogged. In developing the model we have assumed that the rate of backlogging is variable and dependent on the waiting time for the next replenishment. The objective of the model is to develop an optimal policy that minimizes the total average cost. Suitable numerical example has been discussed to understand the problem. Sensitivity analysis has been carried out to show the effect of changes in the parameter on the optimum total average cost.
Keywords: Inventory; Deteriorating Item; Linear Demand; Shortages; Partial Backlogging; Variable Deteriorating Rate.