Classifications

• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
  • G06Q10/00—Administration; Management
  • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
  • G06Q10/00—Administration; Management
  • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
  • G06Q10/063—Operations research, analysis or management
  • G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
  • G06Q10/06315—Needs-based resource requirements planning or analysis
• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
  • G06Q30/00—Commerce
  • G06Q30/02—Marketing; Price estimation or determination; Fundraising
  • G06Q30/0283—Price estimation or determination

Definitions

• This invention relates to computer- implemented enterprise management tools, and more particularly to a method for revenue optimization in a make to order material planning problem.
• JIT Just In Time
• a typical supplier contract may be an agreement to purchase a certain quantity, Q, of a component over a time period, T.
• the PCM may be above or may be below Q without penalty. That is, so long as the actual purchased quantity is within a negotiated band around Q, the PCM pays only for the actual purchase at the negotiated per unit price. Outside these bands there could be penalties for over or under purchase. On the upside however, over purchase cannot exceed some limit. The penalty for over purchase is a measure of the expediting cost. Also there is a lead time to inform the suppliers of the intention to buy components to help them plan for their next quarter component needs.
• FCFS First Come First Serve
• FCFS means, if an order comes m and there are parts to make it (available or can be expedited within negotiated limits with suppliers) , then the order will be satisfied whether economically it makes sense or not. What is needed is a model that can predict the optimal amounts of key components to purchase m a multi-platform system.
• a method of calculating supplies of key components based on enhancing revenues m a made to order scheme is provided.
• Products are designed by identifying product components, and combining the components m various combinations.
• Key component supplies are calculated using an algorithm that considers demand probability of component and product as well as calculating the marginal value of each component m an iterative scheme.
• An advantage of the invention is that it provides a method of determining the supply of key components m a make to order situation.
• FIGURE 1 illustrates a method of pricing products m terms of their components, using probabilistic demand calculations m accordance with the invention.
• FIGURES 2A and 2B illustrate how component values, product prices, and product demand probabilities can be graphically represented m three dimensions.
• FIGURE 3 represents the pricing process m terms of its inputs and outputs.
• FIGURE 4 illustrates MAV values as a function of available supply.
• FIGURE 5 illustrates the revenue displaced by charging MAV for a quantity Q.
• FIGURE 6 illustrates a process of determining MAV for lead time pricing.
• FIGURES 7 and 8 illustrate MAV as a function of order size, Q, and lead time, LT, respectively.
• FIGURE 9 illustrates a price-demand curve for a product, and compares maximum revenue at a single price to total potential revenue at multiple prices.
• FIGURE 10 illustrates how expected revenue for a make-to-order manufacturer can be calculated from a binary tree;
• FIGURE 11 illustrate a six component, three product case showing the use of the components for each product.
• FIGURE 12 is a flowchart illustrating the solving of subopt and opt over a single time period.
• VM value management
• This pricing tool is a synthesis of two other computer-implemented business management tools: yield management practice, such as is used by airlines to price tickets, and tools for decision support across supply chains, such as are commercially available from ⁇ 2 Technologies Inc.
• yield management practice such as is used by airlines to price tickets
• tools for decision support across supply chains such as are commercially available from ⁇ 2 Technologies Inc.
• the present invention is a novel combination of these two software applications, and can be beneficial m a number of areas, such as pricing, product design and product control.
• the invention can be implemented as program code and data, which are executed on a computer system and provide results to a user both as stored and displayed data.
• Value Management for Product Pricing Value management may be used as a pricing solution that balances supply with demand.
• the prices of components that make up a product are determined based on probabilistic demand and available supply. More specifically, using statistical forecasts for standard products (SP) that consume known amounts of some underlying materials, called critical components (CC) , together with known prices for the SPs, the values of the CC ' s are calculated based on their available supply at the time of the calculation. The CC values are calculated using an iterative process.
• SP standard products
• CC critical components
• CCS component usage set
• FCFS first-come first-serve
• Price of a SP is an input that serves as a starting amount that the customer is willing to pay for the product and has an associated probability distribution that specifies the probability of various levels of unconstrained demands (irrespective of availability of CC's or any constraining factor) .
• Value on the other hand is the customer's willingness to pay for a product balanced with the supply of the product .
• value is computed by explicitly applying the supply and demand law on the inputs that consist of, m addition to others, available supply and demand, while “price” is used as an independent variable to determine value. At times the two terms may be used interchangeably, but the context should make clear which meaning is m force. "Price” is also used m the context of the price that is asked of a customer, which need not be the computed value. Rather, value serves as a reference that can be used for price negotiation.
• Determining values for all possible combinations of CCs would be a difficult and intractable problem. Instead the pricing method focuses on individual CC's and determines their values. As explained below, to determine the value of any product, it is first determined what CC ' s the product consumes and the amount consumed per unit (consume_per) . Then the values of the CCs consumed are calculated and added to arrive at a value for the product. The problem is thereby reduced to that of determining the values for the CC's.
• FCFS is one type of control (or no-control) .
• Another control is setting explicit allocations for various products, but this may be impractical when there are a large number of products and not all of them are predefined.
• the following control strategy is suitable for use with the present invention. If V x is the value of 1 th component, then:
• MAV ⁇ Q ⁇ V, ⁇ es p , where S p is the set of components used by product p (not necessarily a standard product) , MAV P is the minimum acceptable value for product p, and (3f is the consume_per value for product p for component l .
• FCFS policy is a control policy that permits a product p to be sold if its price is greater than MAV P . This control policy is referred to herein as MAV control
• the pricing problem may be solved as an optimization problem, m which the task is to maximize the total expected revenue, R(V, A) , to come at time t, where:
• the pricing problem is nonlinear and complex. Even without introducing the time variable t, it is difficult. It has a discrete variable, x, and a continuous variable, V, making it a mixed integer non linear program.
• the pricing problem can be simplified by making several assumptions: assume x is continuous, an assumption that is good for large values of x; drop the dependence on t, solve a static problem at a given value of t, and model the effect of varying t by repeatedly revising the solution m real time; when possible model F k (x) as a known distribution, for example, a normal distribution.
• the latter assumption allows specification of the demand distribution by only a few parameters.
• the assumption permits distribution to be specified as the mean and the standard deviation of each demand. If needed, a truncated form of the distribution can be used to disallow negative values.
• FIGURE 1 illustrates the steps of a heuristic method that provides optimal values of component prices, V.
• Step 11 is initializing an increment counter value, k.
• Step 12 is assuming a set of beginning values for the components.
• Step 14 involves calculating a value, w, that represents the prorated value of a product on a component. Given a price p for a standard product, a vector V of component values, and its CS given by S, its prorated value, w, on a component c (belongs to its CUS) ,
• Equation (1) An interpretation of Equation (1) is that the value the product brings for component c is its price minus the value displaced from all the other components it uses.
• Dividing the displaced revenue by the consume_per for c gives the value per unit of component.
• Step 15 is calculating a new component value, given known prices of products and their associated demand probability distributions.
• the "known" prices are those of standard products that use the component .
• Step 15 to be use a process referred to herein as ALG are assumed.
• the ALG process is described herein by example.
• 012 is the probability that demand for product 1 (price PI) arrives before that of product 2.
• 013 is the probability that demand for product 1 arrives before that of product 3. It is assumed these probabilities can be computed as:
• 012 pi/ (pi + p2)
• 021 p2/ (pi + p2)
• 013 pi/ (pi + p3)
• 023 p2/ (pi + p3)
• the component value calculations use values representing both the probability that demand will materialize, i.e., pi, p2 , p3 , and the probability that demand will arrive in a certain order, i.e., 012, 021, 013, 023.
• the initial estimate of component values is Vll and V21.
• Set k and r to 1.
• Vlk MAX(MV1, MV2) Prorated values on component 2 are calculated as:
• MV2 021(pl*P12 + (1 - pl)*p3*P3) + 022*(p3*P3 + (1 - p3) *pl*Pll) .
• V2r MAX(MV1, MV2 )
• Vlk and V2r have converged, the ALG process is ended. Otherwise, the proration and ALG steps are repeated by incrementing k and r.
• the converged values are the "values", or the prices for the two components.
• These component values represent values for a given time horizon, i.e., one day, for which demand distributions and other inputs are specified.
• FIGURES 2A and 2B illustrate how component values, product prices, and product demand probabilities can be graphically represented m three dimensions.
• a component values is identified as a MAV (minimum acceptable value) as calculated above.
• FIGURE 2A illustrates the MAV for component 1 and the price and demand probability for product 2;
• FIGURE 2B illustrates the data for component 2.
• demand distributions can be modeled as normal, Poisson or binary or some known distribution, which require only a limited number of parameters. For normal, only mean and standard deviation is required.
• the pricing calculations can be modified to accommodate various distributions.
• some pricing information such as an elasticity curve, is needed.
• These input prices are for SPs only, and may be prices that a business is already comfortable with or obtained from price-demand curves. As explained above, these prices are used to arrive at component values, which m turn can be used to price NSPs based on supply and demand.
• the component values represent a mapping of forecasted SP demand (with uncertainty) and SP prices onto a limited supply of components.
• Calculated component values can be the basis of a variety of pricing decisions. For example, a component that has a 0 component value indicates an oversupply of the component or a lack of demand -- two sides of the same coin since oversupply is with respect to demand only. If all components have 0 component values that means there are no critical components. But this does not imply a selling price of $0. This situation also suggests potential oversupply or lack of demand. If it is known that a new product is going to be introduced that will adversely affect the current line of products, the affected component values may drop to a very low value, indicating that the current line should be quickly unloaded.
• the above-described component value calculation provides a minimum acceptable value (MAV) for a component, which differs for different production days.
• MAV minimum acceptable value
• An enhanced process can implemented to take all component values as inputs across a time horizon and perform a smoothing operation, to obtain uniform component values for each component across the time horizon.
• the physical meaning of this operation is that material supply is moved forward m time. Each component then has the same MAV for all future time horizons. As a by product of this step, it is conceivable that this inventory movement could be used to adjust the supply alignment with the suppliers, given enough lead time. Assume a manufacturer has a certain supply arrangement of materials for each day over the next several days. After calculating component values, a new arrangement can be designed, optimized with respect to supply and demand. The plan may be changed repeatedly, as often as the calculation of component values is carried out.
• the process described above to calculate pricing for a three-product two-component case can be generalized to include more complex situations.
• Examples of complexities are: inclusion of available supplies of components to be greater than 1; more complex continuous probability distributions for demand of products; consume_per of components greater than 1; multiple time horizons, where component values that differ over various time horizons will are smoothed so only one value is seen over all horizons; generalization to volume orders (similar to group bookings for airlines) ; and inclusion of demand and/or price curves for products instead of a static value.
• FIGURE 3 illustrates the pricing process m terms of its inputs and outputs.
• the inputs are: unconstrained demand distribution of each SP for each time horizon of interest, price offered for each SP, component list for each SP, the consume_per of each component for each SP, the available supply of each critical component for each time horizon of interest, volume of order, pricing and demand curves as a function of time (if known) .
• the outputs are: value for each critical component for each time horizon, and optionally, a smoothed value for each critical component over all time horizons of interest.
• VM pricing process can be extended to determine pricing based on varying lead time requirements of the customer.
• An environment m which lead time pricing might operate is one m which a manufacturer is negotiating a price with a customer.
• the manufacturer might be attempting land an order of, say 50,000 personal computers (PC s) .
• the customer typically wants various options, configurations and each option or configuration m specific quantities delivered over a specified time period.
• the customer does not want the complete order delivered at the same time. Rather, it wants the flexibility to call anytime during the specified time period to draw against this bulk order, each time the quantity requested not exceeding an agreed upon number, Q. But once the order is placed, the delivery should occur within LT weeks.
• lead time pricing method determines answers to the following issues: What price to quote to the customer for each option (each option is a particular type of PC requiring certain components to build it) based on Q? How does this price vary as a function of LT? What is the maximum frequency of customer orders that should be negotiated? Is there an economic value that can be assigned to this frequency?
• the lead time pricing method focuses on the value of the constrained resource (materials) based on the projection of future sales of SPs that can be made from the materials, the advertised prices for the SPs, and the available supply of materials.
• the component values (MAVs) calculated m accordance with FIGURE 1 are marginal values, that is, the value obtained from the last unit of the available supply of each component.
• the expected revenue that is displaced m generally not marginal value times the quantity consumed. This is because m a limited supply and high demand situation, each additional unit of supply costs more than the previous one.
• FIGURE 4 illustrates a typical MAV curve as a function of the supply of a critical component.
• the curve is usually monotonically decreasing although its slope decreases at either end and is maximum somewhere close to the middle.
• the area under the curve is the expected revenue from the available supply of the component.
• demand is probabilistic, "demand less than supply” is meant m a probabilistic sense. Generally, it is mean + 3*standard deviation, which covers, for a normal distribution, close to 99.99% of possible demand values.
• the curve of FIGURE 4 illustrates how MAV varies as a function of supply of material for a particular time horizon, i.e., one day.
• MAV can be thought of as the value of the last unit of supply.
• the price to charge for a quantity Q for that day is not Q*MAV because MAV increases as each unit of supply is consumed. For Q less than some threshold, it may be acceptable to charge MAV as the price for each unit, but for larger Q such a price is unacceptable.
• FIGURE 5 illustrates the revenue displaced by pricing a component at MAV for a quantity Q.
• the total area under the curve is the total potential revenue from a supply S of the component.
• the shaded area represents the displaced revenue.
• the displaced revenue is not simply the MAV at S because as Q is removed (S decreases), the MAV increases.
• the floor for the negotiating price per unit of product for that component should be equal to:
• the pricing process can be interpreted m terms of displaced revenue.
• the displaced revenue could be calculated by integrating the curve between S and S - Q.
• a simpler variation uses the MAV process described in connection with FIGURE 1 to obtain a total potential revenue from a given supply, S. Then revenue from the MAVs for S - Q is similarly calculated. The difference in revenues between the two cases approximates the area of the curve between S and S - Q, and thus approximates the revenue displaced by the MAVs for Q.
• the formula for MAVs is applied with the displaced revenue coming from solving the MAV problem twice. For a product having multiple components, the MAVs are calculated for each components and the component revenues added, thereby obtaining revenues for the product .
• the value management pricing process can be used to determine what the negotiating price should be for a specified lead time. For purposes of this description, the following assumptions are made: the orders for Q max will come randomly and uniformly distributed within the period of contract; a subsequent order will only come after a current order has been fulfilled; the time it takes to manufacture the order is equal to LT , i.e., delivery is instantaneous; the horizon for MAV s is daily.
• the second assumption can be relaxed and generalized so as to become a negotiating variable with the customer.
• the third assumption is easy to relax, by adding another offset to the manufacturing period.
• the fourth assumption can be generalized such as to include multiple days horizon or several horizons within a day.
• FIGURE 6 illustrates a method of determining MAV for lead time pricing.
• the method assumes a MAV curve such as that of FIGURES 4 and 5, which may be obtained using the pricing process of FIGURE 1.
• Step 61 is randomly selecting a sample of N order points over the contract period with equal probability.
• Step 63 determine the displaced revenue.
• Step 64 repeat for all the sample points.
• Step 65 calculate the average displaced revenue.
• the result of the average is a floor on the negotiating price for the quantity Q, referred to herein as MAV nego t ⁇ at ⁇ on-
• MAV nego t ⁇ at ⁇ on- For a product having multiple components, the process of FIGURE 6 is repeated for each component and the results added together.
• FIGURES 7 and 8 illustrate MAV as a function of maximum order size, Q, and of lead time, LT, respectively.
• the MAV values are those calculated using the process of FIGURE 6.
• a manufacturer could insist on granting no more than a certain number of orders, Qmaxfreq, drawn against the total order over the contract period.
• Qmaxfreq a disruption on manufacturing operations, which the manufacturer would like to minimize.
• the order frequency is tied to Q max , m that a higher number generally reflects a lower frequency. But there is nothing preventing the customer from making a large number of small orders and still be within the contract unless Qmaxfreq is agreed upon.
• the process can include additional steps: First, assume a worst case of Q max occurring Q maXfreq times even though Q max x Q ma ⁇ freq may be greater than the total order quantity, Q.
• Make-to-order manufacturers are characterized by low inventory and cycle time. Many hi-tech manufacturers such as computer system integrators fall into this category. They cater to retailers as well as to individual customers, taking orders by telephone or online. MTOs tend to not produce a product until it is ordered. Usually MTOs advertise their items at a fixed price, with a maximum delivery time. At times, they may deliver sooner if the customer. However, conventionally, the price charged is the same, barring any volume discounts .
• FIGURE 9 illustrates a linear price-demand curve for a product, P. As explained below, when only a single price is to be charged, the curve can be used to determine an optimal price. The curve can also be used to determine a total potential revenue that could be realized (theoretically) if multiple prices were charged.
• One aspect of the invention is realizing, for a MTO manufacturer, the potential profit opportunity described above.
• the item is a personal computer, which the MTO sells that for a price of $800, with a delivery time of 3 weeks. However, if the customer wants it the next day it could be done but for a price of $1200. Another price-delivery pair might be ($1100, 1 week) .
• the manufacturer does not want to simply fill the demand for various products as it comes m, but would rather deny some m the hope that there will be later demand. To make an objective evaluation, there needs to be a forecast of demand for the products out m future.
• a first involves redesigning product and delivery times.
• a second involves forecasts of demand and an effective product control (PC) policy.
• Value management is fully realized by taking advantage of both levels of benefits.
• Product design is insufficient because of limited capacity (capacity includes both assets and materials) , and without product control, the MTO may end up not realizing higher paying demand if demand at lower prices is high and comes first .
• demand values can be assigned as single deterministic numbers. But m reality, demands are stochastic and are better characterized by a probability distribution. A better approach is to assign demand values for different "buckets" of prices. To this end and as a simple example, assume that the demand is 1 unit with a probability of .5. That is, there is a 50% chance the demand of 1 may not materialize.
• the demand probability table looks like:
• Appendix A compares expected revenues with and without product design (PD) for various values of available capacity (AC) , measured as the units of the scarce material available for a particular time unit, say, one day, of manufacturing.
• AP is asking price (explained below)
• ER is expected revenue.
• For the non-PD case there are 3 items with the same price of $800.
• the 3 products are PI ($1200), P2 ($1100) and P3 ($800) .
• the order in which they arrive is P3 , P2 and PI.
• the same labels indicate the corresponding price, and the context will make clear what the label means.
• the control policy is assumed to be FCFS.
• the units of capacity (and the resulting APs) are for a given time horizon, i.e., one day.
• the expected revenue (ER) from the last single product for a given capacity is the difference between the ER for the AC minus the ER from one less AC, resulting m the AP .
• the value of each additional unit of capacity goes down as AC increases, everything else remaining same.
• the additional value of a unit of capacity is related to PC, as will be explained below.
• FIGURE 10 illustrates how the expected revenue for a MTO manufacturer (different prices for different delivery times for the same product) can be graphically represented as a binary tree.
• the formulas for ER are the same as set out above .
• FCFS first-come first-serve
• PCP price control policy
• Appendix B sets out APs and ERs , assuming a PCP (non FCFS) .
• the PCP is that at any given time, for various units of capacities for particular time horizons (days for example) , for each row (product) , calculate the ER from those resources (capacities) if it is decided to accept an order.
• For AC 1, PC(3W), the ER is $825 as opposed to $850 if only PC(1W) were accepted.
• PC(3W) ($800) is rejected since its ER is less than the AP .
• the asking price (AP) for a given value of AC is the maximum expected revenue for this last unit of capacity.
• AP $850 with the control policy being to reject PC(3W) .
• a control mechanism assigns allocations to each product based on the available capacity for the time horizon (day, week or whatever is appropriate) under consideration. In the example, all capacity is available for an order of PC (ID), and then there is some fraction of the capacity available to PC(1W), and a lower fraction to PC(3W). Because the calculations assume one order at a time, the calculations may change if the order quantity is large.
• the following steps can be taken to make a significant positive impact on revenue and profit.
• Various computer- implemented supply management tools could be used, each corresponding to one of the steps.
• the modules could be, for example, Demand Analyzer, Forecasting Engine and Optimizer modules, such as those available from i2 Corporation.
• the above examples include simplifying assumptions to illustrate numerically the PC and PD process. However, there may be some real world realities that need to be addressed. If the order quantity is more than a given threshold, the PC scheme will have to be made more sophisticated since the calculated AP is for the last unit of capacity and may change as orders come in. If the MTO manufacturer has other suppliers, the complete upstream supply chain may have to be considered and its reliability factored in depending upon the relationship between the two. The downstream chain may also be important. If there are multiple items and capacity units (say more than one work center or materials) the VM model needs to be generalized. Once the multiple items have been mapped into multiple products, the problem is conceptually similar to one item that has been productized. The multiple resources can be handled by arriving at an AP for each resource (constrained or not - in which case it could be small or 0) . If the sum of the utilized resources' AP is less than the value being obtained then the product can be made available.
• the PC relies on the availability of unconstrained demand, i.e., demand that exists for a product regardless of whether it will be available or not. In reality the recorded history will only have actual realized demand (or constrained demand) . This can place additional burdens on the forecasting algorithms since they use the histories to forecast.
• the primary decision variables of the planning problem are the amount of key components to commit to buying over a planning period, T.
• T The primary decision variables of the planning problem are the amount of key components to commit to buying over a planning period, T.
• Q the amount of key components to commit to buying over a planning period
• T the amount of key components to commit to buying over a planning period
• Q the amount of key components to commit to buying over a planning period
• T the amount of key components to commit to buying over a planning period
• Q for different Ts are to be determined separately but are not independent of each other. For instance, if a product or component is at the end of its life cycle, its value will be zero or near that after some T. But for other key components, this value will not be zero.
• the planned quantities of the two should not fail to take into account this phenomenon. In some cases planned quantities can be a continuous function of time but the state of the current business environment disallows such a framework.
• a unique feature of the model of the present invention is that demands for the product are allowed to be probabilistic.
• the consume-per (usage) for the modeled level of products (also called platforms) of the key components is assumed to be a random variable with a known distribution. This number is statistical m nature.
• PCs personal computers
• each member (platform) consumes a potentially different amount of key component from that of another member of the family. Therefore, to represent the consume-per at a platform level these individual consume-pers of the key components must be aggregated.
• One way to do that is to use mean values.
• a distribution can be used to increase precision.
• the equations will only use up to the second central moment (the standard deviation) even though a distribution is being used.
• a personal computer manufacturer or similar manufacturer needs to plan key components for the next m time periods starting at ti, t 2 , . . . t m .
• the length of each time period may not be same Let this length be represented by li, 1 2 , . . . l m However it does not need to firm up the commitment for time periods t ]+ ⁇ and beyond because they are beyond the lead time requirements for the key components.
• the current time t is less than ti. Different components may need different lead times for ordering (planning) .
• the personal computer manufacturer or similar manufacturer will run a planning system to me plans for time periods 1,2, . . . m.
• the supplies for the next TP for which the lead time constraint is coming up can be determined. It is possible it may be for only a subset of the totality of key components. But all key components can be continued to be plan for on an ongoing basis, firming up only those whose lead time constraint is imminent thus utilizing latest available information.
• planning periods are divided in to periods, such as quarters.
• a larger planning horizon is established that covers a number of these periods.
• the system is run close whenever a supplier (for a key component or a set of key components) is close to a lead time limit. Usually this will be for the next planning horizon that is about to be entered, but could also be a later one (m which case the plan for these key components for the next planning horizon has probably already been firmed up) .
• Any shortfall/excess during a planning horizon is handled through the terms of the contract which may allow expediting key components at or above the agreed component cost depending on whether the excess amount is outside an agreed upon upward deviation from the agreed plan.
• the demand for a platform may not be satisfied in any period other than the one in which it materializes or expected to.
• the decision variables (supply vector) and the platform demands are continuous real number values.
• the decision variables can be discretized in the end.
• V N - Vector of unit product prices
• R(S,K) Optimal expected revenue resulting from a given supply S of components by following a given policy K for product control
• W(S) Incremental - cost vector of M functions for the M components (only the portion of cost resulting from the decision to procure S components)
• P An N vector with the i' h component being the unconditional demand distribution for the ith product
• VAM Variation in attach rate matrix
• F u M vector of functions that specifies upper limits for the corresponding component supply
• H(S,K) Maximum Expected profit for a given S and PCP K
• FCFS there will be some other control variables (CV) .
• R(S,P,C, V,U U ⁇ ) Max Z(J,CV,S,P,C, V,U ,U ⁇ )
• a novel approach to solving SUBOPT that is computationally superior to the monte-carlo simulation based method can be formulated.
• the overall planning problem has implicitly been conceptually decomposed into a number of problems, one for each time period. After solving for a time period, the various solutions can be confirmed together towards the end. In the same way a computational decomposition of SUBOPT is needed.
• FCFS FCFS
• Equations 1 through 6 are constraints on the amount of each product that can be produced linked through linear equations. Equations 1 through 4 can be seen as resource constraints with each product consuming varying amount of each resource (and not all of them using each resource) . The right hand side of each of these is the maximum available resource. Equations 5 and 6 are lower limits on products 2 and 4 although they can be called as resource constraints by defining artificial resources by multiplying both sides by -1 and reversing the inequality sign. For purposes of this discussion each of these equations are assumed to represent a unique resource. The primal and dual solutions of the two are also shown.
• a known economic principle is that if two products with a stochastic demand are using the same resource then each is allocated up to the point when the marginal values of both become equal .
• This principle extends to multi product case too.
• the demands are deterministic naturally the product with the highest price (or margin if maximizing profit) is allocated up to the point there is no more product demand available. If any more resource is available, it is allocated to the next highest price product and so on.
• demand can be assumed to be infinite for each but due to limited resources only so much of it can be satisfied. But what if you have more than one resource. What is the criterion for allocation and how is the price of the product mapped onto the component? Is it the full price? Let us surmise that a product price maps according to the following formula:
• Product 1 uses component 1 only and 2 uses component 2.
• Product 3 uses both components. Their demands are characterized by a distribution function (actually its complement) .
• V- Revenue from i product V - Total Revenue
• the lagrangian of problem A will be calculated to convert the problem into an unconstrained one.
• v' v- ⁇ ⁇ ( ⁇ j + ⁇ 3 t/ 1 3 -5 1 - ⁇ 2 ⁇ 2 L + ⁇ 3 C/ -5 2 )
• the two equations (1) and (2) can be considered to be m 1 variable each (m terms of the corresponding lagrangian parameter ⁇ ) provided product prices are mapped according to the earlier stipulated mapping function. This mapping can be shown too be true for the case of N product- M component case.
• Each row corresponds to a platform (labeled as 1, 2,
• PCP is FCFS as opposed to discrete allocations
• FIGURE 11 is an illustration of the relationship between the platforms and components.
• component 2 To figure the marginal value of component 2, suppose its supply is ⁇ 2 and is raised by an amount ⁇ 2 . What is the additional revenue that is expected to be capture? If a quantum of demand is observed, it is expected that a mixture of demands of all six products m proportion to their respective mean demands will be seen. What is the chance that the demand seen first will be that of a particular product? By assumption number 4, it is the ratio of its mean demand and the mean demand of all platform demands. To calculate the additional revenue AR 2 , the chance that a given platform demand, once it has appeared will be accepted, is needed. Recall that due to the gating effect by other components, mere appearance of demand is no guarantee of acceptance.
• the chance, p can be interpreted as the average fraction of additional revenue of product j that is accepted by component 2.
• brackets is the average mapped price of all products using component 2
• P ⁇ P ⁇ P ⁇ _ 2-A 2 p r 2 + 4 f 4- p r 4 + 5.>_ 5 ⁇ + ⁇ + ⁇ + ⁇ + ⁇ + ⁇ + ⁇ + ⁇ + ⁇ + ⁇ + ⁇ + ⁇ + ⁇ + ⁇ + ⁇ ⁇ 2 P 4 P 5 6 2 ⁇ 4 ⁇ 5 6 2 4 5 6
• mapping (with non-unity consume-pers) by setting the corresponding ⁇ 's to be not same but according to the relative usage of the product under consideration of the component with respect to component 2, which is the ratio of the two usage.
• ⁇ and ⁇ stand as generic symbols for mean and standard deviation respectively.
• a subscript usually denotes a variable whose mean and standard deviation are under consideration.
• N( ⁇ , ⁇ ;x) N ⁇ ( ⁇ , ⁇ ;x) t ⁇ + (1 - (x) x ⁇ 0
• G d Expected Standard deviation ofN ⁇ (t, ⁇ , ⁇ ;x)
• N( ⁇ , ⁇ ; x) N ⁇ ( ⁇ ,v;x) t ⁇ + (1 - t) ⁇ (x) x ⁇ O ⁇ (- - ⁇ )
• ⁇ (x) is the delta-dirac function and ⁇ and ⁇ are parameter mean and standard deviation respectively
• G( ⁇ ) is prob ⁇ Component j demand ⁇ ⁇ ⁇
• each instance of N denotes N products.
• Each product is made up of several components, where the amount of each component is a random variable itself.
• a random variable of number of components associated with each of the N products and these are assumed to be independently and identically distributed (id) .
• RV random variable
• each request for each realization of X say l, be composed of U components (whatever their identity) , where U is a random variable with mean ⁇ 0 and standard deviation ⁇ ⁇ .
• U is a random variable with mean ⁇ 0 and standard deviation ⁇ ⁇ .
• There is an RV associated with each request within a realization of X It will be assumed that all these RV s denoted by U x are id. It is easy to show that the mean ⁇ ⁇ and standard deviation ⁇ ⁇ of the total number of components, the RV T, is given by:
• MARG__VALU can now be used to compute the new marginal value for k
• MARG_VALU can be used to directly compute the individual supply vectors since each equation for each component is m terms of its supply vector embedded m the probability term.
• avg For component j compute average component cost, p , using known MV's (corresponding component cost,)
• Figure 12 is a flowchart illustrating the solving of subopt and opt over a single time period.
• step 80 the marginal value of all components is set to a non zero value.
• m step 82 the first component is selected.
• the average component price is computed using the marginal value m step 84.
• the demand for each product using that component is converted into a component demand m step 86.
• step 88 the correlation coefficient between the products demand and the component demand is computed.
• step 90 the expected mean of the component demand and the expected standard deviation of the component demand is calculated.
• step 92 the parameter values for the expected mean of the component demand and the expected standard deviation of the component demand is calculated.
• step 94 a new marginal value set is calculated.
• step 96 it is determined if the component is the last component. If it is, step 100 is the next step. If not, the next component is selected and execution of the method starts over at step 84. If, m step 96 it is determined that all components have been checked, m step 100 it is determined if the marginal values have converged. If so, then the revenue for each component can be calculated m step 102. In step 104, the needed supply is calculated from the marginal values. Considering step 100 again, if the marginal values have not converged then the process starts over at step 82. A limit can be set on the number of time convergence is checked.
• the weighted mean (by expected demand) of service levels of all products is taken and used as a measure of component level then the earlier technique can be applied to this service level for a minimum component supply level .
• m ⁇ A_ALG also compute the expected expediting cost using the same procedure as m service level consideration. The probability of exceeding the component supply levels and thus the extra cost incurred can be figured. Thus a low value of supply will lead to higher expediting cost and low service levels (SL) and vice-versa. While the SL is handled through a lower limit on supply levels, expediting cost reduces the amount of revenue one would normally get by the increased cost due to expediting.
• the inventory cost is easily handled as the cost of carrying excess key component from one time period to the next.
• the expected carry over is the expected excess computed similarly as the above quantities.
• OPT is solved time period by time period.
• some optimality conditions can be modified for each time period.
• ⁇ EL > ⁇ [1 °- ] + [h(Q ) - h(0)]
• the order quantity for period 2 is s 2 - ⁇ EL>, where the leftover is from the first time period.
• the carryover will mitigate the impact of end of life cycle effect m that m the next time period it will not be needed to order as much because it is know what to expect from some previous time period.
• m the first time period it may be too conservative not knowing that the leftover has some value m the next time period. That is the second period's optimality (order quantity) has visibility into the earlier time period but not the other way round. To complete the loop, the optimality condition is modified
• O n Ordered quantity of the component in time period (tp) n
• R n Optimal revenue for tp n — 1
• O n S n - E n _ x , O ⁇ ⁇ ⁇ l
• — — — — - (— — - (1 - probfcomponent demand ⁇ S n _ )* ⁇ Value of component ⁇ _, dS n _ ⁇ _, in tp nj)
• V n Expected marginal value of leftover components in tp n . 3 ,., _ ⁇ i? stamp_, dW n _ ⁇ ⁇ ⁇ dS ⁇ dS,,,, dS hang_, "
• step 2 the end of TP effects need to be considered. Normally to achieve steady-state one considers periods beyond the last one for which the plan is desired. This prevents the plans from fluctuating too much. By considering a few periods beyond the last one it may be determined how to mitigate the effect of not knowing the marginal value beyond the last (of the additional periods) period.

Priority Applications (1)

Applications Claiming Priority (2)

Publications (2)

Family

ID=23427488

Family Applications (1)

Country Status (4)

Families Citing this family (79)

Family Cites Families (4)

• 1999
  • 1999-07-28 US US09/362,776 patent/US6826538B1/en not_active Expired - Lifetime
• 2000
  • 2000-06-29 AU AU59139/00A patent/AU5913900A/en not_active Abandoned
  • 2000-06-29 WO PCT/US2000/018407 patent/WO2001009744A2/en active Application Filing
  • 2000-07-11 TW TW089113773A patent/TW484071B/zh not_active IP Right Cessation

Non-Patent Citations (1)

Also Published As

Similar Documents

Legal Events