Ebook Static and Dynamic Pricing Of Excess Capacity in a Make- To-Order Environment
MetalFab, Inc. produces fabricated metal parts mostly for use in the power generation industry. The parts are made from expensive materials – some 4x8-foot sheets of material cost $20,000 – and, not surprisingly, the fabricated parts have very tight tolerances. MetalFab is a large job shop with about 60 highly skilled shop floor employees who operate metal bending and metal cutting machines, as well as a variety of welding equipment. At this writing, approximately 80% of MetalFab’s output is sold directly to General Electric, or to first tier GE suppliers. In keeping with MetalFab’s policy, we will refer to this output as belonging to GE.
MetalFab can forecast orders from GE and GE’s suppliers, but the forecast error can be quite high. Sometimes MetalFab production planners will have firm forecasts – and these forecasts remain firm until the order is delivered. More often, however, GE will change the order quantity and due date several times while the order is outstanding. In fact, GE’s systems will occasionally produce a purchase order that is already past due when the order is placed. (The authors observed a case in which an order placed in September had a due date of the previous May!) Taken together, the blend of firm forecasts, changes, and emergency orders create a situation that is well captured by a mean forecast with a fairly high variance around that mean. Similar situations could arise in cases when a single large customer aggregates demand forecasts from many different locations and provides an aggregate request to its supplier.
From MetalFab’s perspective, GE orders form the core of its business, while the other orders that may take up the remaining 20% of its capacity are treated as “fill-in” orders. From a marketing standpoint, one approach to accepting and pricing fill-in orders is to take as many as possible, charge the same price as the core orders, and let the production planners and factory workers try to keep up. The danger with this approach, of course, is that it may not be a long-run profit-maximizing strategy; and service performance, for both GE and fill-ins, could suffer. An alternative approach is to proactively seek fill-in orders when capacity utilization is running low, charging a low price to attract those customers; and when the capacity utilization is high, charging a high price and accepting only limited fill-in orders. This alternative raises the issue of how to (i) price dynamically over time depending on the state of the production system, (ii) endogenously determine “low” versus “high” capacity utilization, and (iii) incorporate core customer arrivals (i.e., orders from core customers) in determining the pricing policy for fill-in customers. For example, when a potential fill-in customer asks for a bid for a given part, what price should MetalFab quote? Should that price depend on the current level of congestion at the factory? If so, how? Finally, what benefits are available if the firm wisely uses capacity information when making pricing decisions? This paper addresses these questions.
We focus attention on four models that take into consideration both core and fill-in customer arrival rates: (1) state-independent (static) pricing – where MetalFab sets a price, p, for fill-in customers without regard to the current state of the factory; (2) allowing fill-in jobs at a chosen price p only when the factory is idle; (3) allowing fill-in jobs at a chosen price p only when there are s or fewer jobs in the production system, where both s and p are decision variables; and (4) general state dependent pricing – i.e. potentially setting a different price for fill-in orders for every possible state of the factory. To ensure satisfactory service, we impose a constraint on expected waiting time for core customers. We compare the optimal solutions obtained in the above four cases, report the magnitude of the benefit from utilizing increasing amounts of information, illustrate interesting properties of the solutions, and examine conditions under which one solution is superior to another.
Before reviewing the relevant literature, it is important to note that this problem is quite general and is generating much interest beyond high precision job shops like MetalFab. With the advent of modern pricing software such as that offered by DemandTec, ProfitLogic, and KhiMetrics, many companies now are devoting considerable time and energy to getting prices right. However, recent trade press articles suggest that firms have traditionally been slow to adopt sophisticated pricing models (Reda 2002), have priced products solely on cost (At What Price? Guidelines for a Customer-Focused Pricing Strategy 2000), and often simply employ “what-if” analyses without incorporating the interactions across functional areas (Retail Revenue Management 2001, Lester 2002). Further, the transition to the Euro has elevated this issue for companies doing business in Europe, and many are appointing senior “pricing officers” with direct responsibility over pricing decisions. Furthermore, many firms are beginning to realize that price changes should be made with a deeper understanding of the supply chain (Cisco Thought Leadership Summit 2001). If a firm cuts price to stimulate demand, but the factory or supply chain is currently overloaded, they risk some very unhappy customers. On the other hand, if the supply chain and factories currently have excess capacity, marketing personnel may wish to decrease price to consume some of that capacity. In addition, some of the leading suppliers of supply chain software are developing linkages to pricing software. Manugistics, for instance, has bought Talus, a revenue management software provider with the expressed intent of linking these two areas. This research is designed to generate insight for managers about the benefits of accounting for the supply chain when making pricing decisions.
The rest of this paper is organized as follows. In Section 2 we review the relevant literature. In Section 3, we present the four models and corresponding analytical results. A numerical comparison of the policies is presented in Section 4. Section 5 contains a summary discussion and directions for future research.
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