Sandra Transchel

Periodic review inventory-control for perishable products under service-level constraints

Food retail inventory management faces major challenges by uncertain demand, perishability, and high customer service level requirements. In this paper, we present a method to determine dynamic order quantities for perishable products with limited shelf-life, positive lead time, FIFO or LIFO issuing policy, and multiple service level constraints. In a numerical study, we illustrate the superiority of the proposed method over commonly suggested order-up-to-policies. We show that a constant-order policy might provide good results under stationary demand, short shelf-life, and LIFO inventory depletion.

The impact of dynamic pricing on the economic order decision

This paper analyzes the impact of dynamic pricing on the single product economic order decision of a monopolist retailer. Items are procured from an external supplier according to the economic order quantity (EOQ) model and are sold to customers on a single market without competition following the simple monopolist pricing problem. Coordinated decision making of optimal pricing and ordering is influenced by operating costs – including ordering and inventory holding costs – and the demand rate obtained from a price response function. The retailer is allowed to vary the selling price, either in a fixed number of discrete points in time or continuously. While constant and continuous pricing have received much attention in the literature, problems with a limited number of price changes are rather rare. This paper illustrates the benefit of dynamically changing prices to achieve operational efficiency in the EOQ model, that is to trigger high demand rates when inventories are high. We provide structural properties of the optimal time instants when the price should be changed. Taking into account costs for changes in price, it provides numerical guidance on number, timing, and size of price changes during an order cycle. Numerical examples show that the benefits of dynamic pricing in an EOQ framework can be achieved with only a few price changes and that products being unprofitable under static pricing may become profitable under dynamic pricing.

Technical Note---Note on “Myopic Heuristics for the Random Yield Problem”

Bollapragada and Morton (1999) present several well-performing heuristics for solving the periodic inventory problem with random yield and demand. Their approach is essentially based on a transformation of the single-period problem into a standard newsvendor problem with deterministic yield and random demand which, however, is supply dependent. In our note, we show that their evaluation of the respective optimality condition is not correct. This explains the steady deterioration of their myopic heuristics for parameter constellations that correspond to increasing service levels. Some computational investigations reveal that the performance of the heuristics can become quite poor if service levels are high and exceed those values for which results are reported in the original study. Nonetheless, up to now these heuristics are still the best ones available for solving the joint random yield problem.

A hybrid general lot-sizing and scheduling formulation for a production process with a two-stage product structure

Tailored for a complex application in the process industry, this article examines a multi-product production planning and scheduling problem with sequence-dependent setup cost and times. The manufacturing process is characterised by a two-stage structure where the sequencing problem occurs on the first level and contribution margin, holding cost, penalty cost are accounted on the second level. We present a hybrid mixed-binary optimisation model based on the general lot-sizing and scheduling problem [Fleischmann, B. and Meyr, H. 1997. The general lotsizing and scheduling problem. OR Spectrum, 19 (1), 11–21], which combines discrete and continuous-time elements within a standard inventory and lot-size (I&L) formulation. Since the I&L formulation does not provide sharp linear programming-relaxation bounds, we present two alternative reformulations based on a transportation problem. In a numerical study inspired by real industry data, we show that on average, both reformulations yield significant improvements in computation time and integrality gap.

Order variability in perishable product supply chains

Empirical research has shown that the degree of order variability in supply chains is significantly influenced by product- and industry-specific factors. This paper analyzes the impact of perishability on order variability and the bullwhip effect in supply chains. We decompose the ordering process of a retailer into a sales and an outdating process and quantify their short- and long-term variability and correlation. We find differences to non-perishable product supply chains driven by the impact of the inventory depletion policy, stock-out management, and retailers service level requirement. These three factors significantly affect the retailer’s order variability and thus the decision making process and the profitability of the upstream supply stage. For the majority of instances, the perishable nature of a product results in the ordering process having a lower variability than the demand process. Only when inventory depletion is dominated by last-in-first-out in high service level environments, variability amplification can be observed. We propose a dynamic ordering policy for the upstream supply stage, taking into account negative correlation of retailer orders between periods. This dynamic policy may lead to substantial performance improvements. In a sensitivity analysis, we investigate the impact of shelf life, lead time and demand correlation.

Coordinated Lot-Sizing and Dynamic Pricing under a Supplier All-Units Quantity Discount

We consider an economic order quantity model where the supplier offers an all-units quantity discount and a price sensitive customer demand. We compare a decentralized decision framework where selling price and replenishment policy are determined independently to simultaneous decision making. Constant and dynamic pricing are distinguished. We derive structural properties and develop algorithms that determine the optimal pricing and replenishment policy and show how quantity discounts not only influence the purchasing strategy but also the pricing policy. A sensitivity analysis indicates the impact of the fixed-holding cost ratio, the discount policy, and the customers’ price sensitivity on the optimal decisions.

Managing production of high-tech products with high production quality variability

We consider production systems in technology industries where output quality of a single production run has a large variance. Firms operating such systems classify products into different quality bins and sell units in one bin at the same tagged quality level and the same price. Consumers have heterogeneous quality preferences and choose that quality that maximises their net utility. We examine firms’ assortment, production and pricing problem. We present a three-stage solution procedure that optimises the production quantity, quality specification and number of bins. In that regard, we show that for a manufacturing technology with known quality distribution and known distribution of customers’ quality preference, the optimal assortment and production quantity are set such that on average, the demand of each bin is exactly fulfilled. We examine the impact of an improved manufacturing technology, variation in consumer preferences and changing price premium on the optimal assortment, lot size, market share, yield loss and the overall profitability. We further show that when the quality distribution of the manufacturing process is unknown, downward substitution leads to product offering of higher quality and higher prices. Finally, we discuss practical considerations for pricing, technology and optimal product offerings, and explain the proliferation of bins witnessed in the last decade in the processor industry.

Inventory management under price-based and stockout-based substitution

Abstract We examine a stochastic inventory and pricing problem for a firm that sells two vertically differentiated products. The demands for the two products are determined by total (random) market size and the customers’ net utility from buying the two products, which is determined by the products’ quality attributes, the individual quality valuation (unknown to the firm), and the selling prices. In case the preferred product is out of stock, customers may be willing to buy a substitute instead, if their net utility is non-negative. Therefore, we analyze an inventory and pricing model, considering price-based and stockout-based substitution. We show that the demand function is not continuous in price. By decomposing the profit function into different price regimes, we are able to derive closed-form expressions for the stockout-based substitution rates (upward and downward substitution) and the optimal inventory levels under exogenous pricing. Under endogenous pricing, we find that the profit function is not necessarily unimodal. However, we show that a unique solution exists for the integrated price and inventory problem under price-based substitution only. Numerical results reveal that not considering stockout-based substitution (i) leads to lower profit margins for high-quality products and (ii) may cause severe supply-demand mismatches throughout the entire assortment. Finally, we show the performance of two approximated pricing policies.

An inventory control model for modal split transport: A tailored base-surge approach

Firms are increasingly interested in transport policies that enable a shift in cargo volumes from road (truck) transport to less expensive, more sustainable, but slower and less flexible transport modes like railway or inland waterway transport. The lack of flexibility in terms of shipment quantity and delivery frequency may cause unnecessary inventories and lost sales, which may outweigh the savings in transportation costs. To guide the strategic volume allocation, we examine a modal split transport (MST) policy of two modes that integrates inventory controls.We develop a single-product–single-corridor stochastic MST model with two transport modes considering a hybrid push–pull inventory control policy. The objective is to minimize the long-run expected total costs of transport, inventory holding, and backlogging. The MST model is a generalization of the classical tailored base-surge (TBS) policy known from the dual sourcing literature with non-identical delivery frequencies of the two transport modes. We analytically solve approximate problems and provide closed-form solutions of the modal split. The solution provides an easy-to-implement solution tool for practitioners. The results provide structural insights regarding the tradeoff between transport cost savings and holding cost spending and reveal a high utilization of the slow mode. A numerical performance study shows that our approximation is reasonably accurate, with an error of less than 3% compared to the optimal results. The results also indicate that as much as 85% of the expected volume should be split into the slow mode.

Capacity Investment and Pricing Decisions in a Single-Period, Two-Product-Problem

We consider a profit-maximizing firm that produces two products with a single capacity. The products are characterized by different demand patterns and the initial capacity is allocated such that the entire demand of one product is satisfied before the other. We develop and analyze a model that determines the optimal initial capacity investment and the selling prices for both products simultaneously. We provide analytical results and develop an algorithm. In a numerical example, we compare this centralized planning approach with decentralized planning where two product managers plan the selling prices and the required production capacity separately but manufacturing produces both products on a common resource. We show that through coordination of pricing and capacity decisions a better capacity utilization can be achieved.