Optimal production and pricing policies in a combined make-to-order/make-to-stock system

In this paper, we consider a production system which is capable to produce two types of products. The first type of products is make-to-order, while the second type is make-to-stock whose demand is satisfied by the on-hand inventory. The demand arrival rates of both types of products are price-sensitive. The excess demand that cannot be satisfied immediately is either backlogged or lost. The system costs include the holding costs of product inventories and shortage costs of unsatisfied demand. The objective is to maximise the total discounted profit over an infinite planning horizon by coordinating the production process and pricing decisions. By analysing the properties of objective functions, we characterise the optimal control policy by two switch curves and the optimal price is also given for different ordering and inventory levels. We also explore the monotonicity of both switch curves which will reduce the computation effort. Numerical experiments are conducted to demonstrate the use of the switch curves in managing the production system and illustrate that compared with the static pricing policy, the optimal integrated price and inventory control policy can result in a significant profit improvement in the make-to-order/make-to-stock system that is much higher than in a single-product system.     

Optimal pricing policy for a deteriorating product by dynamic tracking control

We study the optimal selling price of a deteriorating product under a deterministic situation in a finite time horizon where the time horizon is either known or unknown. Inventory holding cost is expressed as a quadratic function of the current inventory level. Given a known time horizon, we develop a model by considering the deterioration dynamics of the product, and show its equivalence to a generalised optimal control problem of a linear quadratic form, i.e. an optimal dynamic tracking problem with constraints on the control variable. An optimal pricing policy is derived based on the maximum value principle. The control policy takes a state feedback form; it exhibits a closed-loop relationship between the optimal selling price (control variable) and the optimal inventory level (state variable). Given an unknown time horizon, an optimal pricing policy is derived through a similar approach when the initial inventory level meets certain conditions. Numerical situations are conducted to illustrate the effectiveness of the derived price control policies. Some interesting managerial insights are discussed.     

Joint optimisation of tracking capability and price in a supply chain with endogenous pricing

Tracking systems have been widely used to resolve the issues of product recall and food safety. Thus far, few researches have been done on designing the tracking capability from the perspective of supply chain. In this paper, using the traceable unit size at the manufacturer level to measure the tracking capability, we propose a non-convex non-linear programming to jointly optimise the tracking capability and price considering the tracking cost and recall cost in a supply chain with endogenous pricing. Results show that, in both centralised and decentralised supply chains, there is a unique tracking capability and retailing/wholesale price with closed-form solutions to optimise the supply chain profit. When the cost ratio (unit tracking cost/unit recall cost) is sufficiently large and small, the optimal tracking strategy is barcode tracking and unit tracking, respectively, and otherwise, the optimal tracking strategy is batch tracking with an economic traceable unit size which depends on the cost ratio, quality inspection threshold, supply defection rate and the supplier’s tracking capability. Furthermore, in the context of large and small cost ratio, we find that improving tracking capability will enlarge and mitigate the effect of double marginalisation, respectively. In particular, we find that the strict tracking regulation policy is more robust than the subsidy policy to improve the supply chain tracking capability.     

Optimal pricing and trade-in policies in a dual-channel supply chain when considering market segmentation

Many companies are implementing trade-in programmes through multiple channels. This may ultimately lead to fiercer channel conflict and competition. Few studies have explored firms’ optimal trade-in policies in such an environment. To fill the gap, we build a theoretical model that captures the features of a dual-channel situation in which a manufacturer implements a trade-in programme through retail and direct channels simultaneously. Compared with the case in which there is no trade-in rebate, the results show that a trade-in programme can intensify or mitigate the double marginalisation effect if the retailer can initially decide the trade-in rebate in the retail channel. This significantly relies on market segmentation. However, when the retailer cannot decide the trade-in rebate in the retail channel, the trade-in programme aggravates the double marginalisation effect. Second, the trade-in rebate offered by the retailer may be higher than the subsidy offered by the manufacturer, as long as the retailer can autonomously decide the trade-in rebate in the retail channel. Furthermore, we find that both the manufacturer and retailer prefer to obtain the right to autonomously decide the trade-in rebate in the retail channel, but the supply chain prefers that the manufacturer do it. Some numerical examples are provided to further explain these outcomes.     

Joint product variety,pricing and scheduling decisions in a flexible facility

This paper studies a manufacturer’s optimal product variety, pricing and scheduling decisions in a single flexible production facility when customers have private information in their marginal valuations for product qualities. In addition to determining the product variety and price of each product, the manufacturer needs to optimise a detailed schedule of production (batch sizes and production sequences) to fully utilise the flexibility of this facility. To achieve the second-degree discrimination, the manufacturer provides multiple products and follows a priority rule in the production schedule. To obtain economies of scale, the manufacturer may offer a composite product targeting the whole population, or choose a dedicated product to serve a proportion of customers. Comparing these three production choices, we observe that the optimal product variety strategy is threshold controlled by the relative ratio of customer arrival rates, the relative difference between customers’ marginal valuations and the production technology.     

Maximal covering location problem with price decision for revenue maximization in a competitive environment

In this article, we extend the classical maximal covering model in a competitive environment by including a price decision. We formulate a revenue maximization model and propose two procedures to solve it. By a careful examination of the relationships between the maximal covering problems for different prices, we reveal interesting properties of the deduced revenue maximization model, leading to a full enumeration solution approach. With the help of two more properties we develop a second, more intelligent solution procedure. Computational experiments show promising results for a small, medium and large case study.