Demand Forecasting

Overview

  • problems
    • long lead times
    • unreliable supply processes
    • high demand variability
    • a large number of SKU's
  • where do we hold inventory
    • suppliers and manufacturers
    • warehouses and distribution centers
    • retailers
  • types of inventory
    • raw materials
    • work in process (WIP)
    • finished goods

Handling inventory

  • reasons
    • economies of scale
      • encourage firms to transport large quantities of items, and therefore hold large inventories
    • unexpected changes in customer demand
      • the short life cycle of an increasing number of products – historical data is unavailable
      • the presence of many competing products in the marketplace – group vs. single
    • delivery lead time
    • significant uncertainty quantity / quality
      • supply, supplier costs, and delivery times
  • coordination
    • relationship
      • the need for the coordination of inventory decisions & transportation policies
    • impact
      • each types of inventory needs its own inventory control mechanism; interactions of the various levels in the supply chain
  • two important issues
    • demand forecasting
    • order quantity calculation
  • tradeoffs
    • inventory cost
    • ordering cost (e.g., shipment)

Inventory Management

Inventory policy

  • key factors
    • customer demand
      • pattern or random
    • replenishment lead time
      • certain or uncertain (lead time: time between placing order and receiving order)
    • the number of different products stored at the warehouse
    • the length of the planning horizon
    • costs
    • service level requirement
  • cost factors
    • order cost
      • product cost
      • transportation cost
    • holding cost (or inventory carrying cost)
      • state taxes, property taxes, & insurance on inventories
      • maintenance costs
      • obsolescence cost
      • opportunity costs

A single warehouse inventory

  • the economic lot size model
    • constant demand for a single item
    • unlimited capacity of the product supply
    • demand is constant at a rate of D items/day
    • order quantities are fixed at Q items/order
    • a fixed setup cost (K) for each order
    • an inventory carrying cost (h) holding cost - for every unit held in inventory per day
    • the lead time, the time that elapses between the placement of an order and its receipt, is 0
    • initial inventory is 0
    • the planning horizon is long (infinite ∞)
    • optimal order policy to minimize annual purchasing and carrying costs without shortage
    • zero inventory ordering property
    • economic order quantity (EOQ)
      • total cost (per cycle) = setup cost + holding cost
      • setup cost = K
      • holding cost = (per unit per time period holding cost) × (average inventory level) × (the length of the cycle) = h × Q/2 × T
      • total cost = K + hTQ/2
      • average total cost = total cost/T = K/T + hTQ/2T = KD/Q + hQ/2
      • total inventory cost is insensitive to order quantity
      • changes in order quantities have a relatively small impact on annual setup costs and inventory holding costs
  • the effect of demand uncertainty
  • fixed order costs
  • no fixed order costs
  • variable lead times

Managing Uncertainty

The effect of demand uncertainty

  • real conditions
    • many treat the world as if it were predictable
      • production & inventory planning based on forecasts of demand far in advance of the selling season
      • companies are aware of demand uncertainty when create a forecast, but design their planning process as if the forecast truly represents reality
    • recent technological advances have increased the level of demand uncertainty
      • products with short life cycle
      • large variety of products compete in market
  • risk/reward trade-off
    • production quantity \(\uparrow\)
      • the probability of large losses - risk \(\uparrow\)
      • the probability of large gains \(\uparrow\)
  • 3 principles of all forecasting techniques
    • forecasting is always wrong
    • the longer the forecast horizon the worse is the forecast
    • aggregate forecasts are more accurate

The multi-period continuous review inventory model

  • overview
    • normally distributed random demand
    • fixed order cost + a cost proportional to amount ordered
    • inventory cost - charged per item per unit time
    • if an order arrives and there is no inventory, the order is lost
    • the distributor has a required service level - the likelihood not stock out during lead time
  • inventory level based
    • the (s,S) policy or a min max policy
      • s as the reorder point
      • S as the order-up-to-level
      • the reorder point is a function of
        • lead time
        • average demand
        • demand variability
        • service level
      • notations
        • AVG = average daily demand
        • STD = standard deviation of daily demand
        • L = replenishment lead time from the supplier to the distributor in days
        • h = cost of holding one unit of the product for one day at the distributor
        • K = fixed cost
        • α = service level (probability of stocking out is 1 - α)
        • inventory position at any time is the actual inventory plus items already ordered, but not yet delivered
      • with fixed order costs
        • s = (average inventory during lead time) + (safety stock) = (average daily demand × the lead time) + (safety stock)
          • ensures that there will be enough inventory to last until the next order arrives
          • the amount of inventory at the warehouse and in the pipeline to protect against deviations from average demand during lead time
        • prob{demand during lead time ≥ L × AVG + z × STD × \(\sqrt{L}\)} = 1 − α
        • reorder point, s = L × AVG + z × STD × \(\sqrt{L}\)
        • order quantity, Q, economic lot size model, Q = \(\sqrt{\frac{2K × AVG}{h}}\)
        • order-up-to-level, S, order during the lead time and safety stick, S = Q + s = Q + L × AVG + z × STD × \(\sqrt{L}\)
      • without fixed order costs
        • transportation cost is 0
        • s = S = (average inventory during lead time) + (safety stock) = (average daily demand × the lead time) + (safety stock)
        • reorder point, s, is identical to the reorder point obtained in the case of “no fixed order cost”, s = L × AVG + z × STD × \(\sqrt{L}\)
      • variable lead times
        • the lead time is not constant
        • normally distributed with average lead time AVGL standard deviation STDL
        • AVG × AVGL - average demand during lead time
        • the amount of safety stock \(z × \sqrt{AVGL × {STD}^2 + {AVG}^2 + {STDL}^2}\)
        • s = AVG × AVGL + \(z × \sqrt{AVGL × {STD}^2 + {AVG}^2 + {STDL}^2}\)
        • S = Q + s = Q + AVG × AVGL + \(z × \sqrt{AVGL × {STD}^2 + {AVG}^2 + {STDL}^2}\)
  • time/cycle based
    • base-stock level policy
      • determine a target inventory level, base-stock level
      • each review period, review the inventory position is reviewed and order enough to raise the inventory position to the base-stock level
        • r = length of the review period
        • L = lead time
        • AVG = average daily demand
        • STD = standard deviation of this daily demand
      • average demand during an interval of r + L days = (r + L) × AVG
      • safety stock = z × STD × \(\sqrt{r + L}\)
  • service level optimization
    • optimal inventory policy assumes a specific service level target
    • appropriate level of service?
      • may be determined by the downstream customer
      • retailer may require the supplier, to maintain a specific service level
      • supplier will use that target to manage its own inventory
      • facility may have the flexibility to choose the appropriate level of service
    • trade-off - retail strategy
      • everything else being equal
        • service level \(\uparrow\), inventory level \(\uparrow\)
        • for the same inventory level, lead time \(\uparrow\) to the facility, level of service provided by the facility \(\downarrow\)
        • inventory level \(\downarrow\), the higher the impact of a unit of inventory on service level \(\uparrow\) and hence on expected profit
      • given a target service level across all products determine service level for each SKU so as to maximize expected profit
      • everything else being equal, service level \(\uparrow\) with
        • \(\uparrow\) profit margin
        • \(\uparrow\) volume
        • \(\downarrow\) variability
        • \(\downarrow\) lead time
  • profit optimization and service level
    • target inventory level = 95% across all products
    • service level > 99% for many products with high profit margin, high volume and low variability
    • service level < 95% for products with low profit margin, low volume and high variability

Managing Inventory in Supply Chain

Risk pooling

  • 2 warehouses \(\rightarrow\) 1 warehouse
    • increase delivery time (disadvantage)
    • either the same service level with much lower inventory or a higher service level with the same amount of total inventory (advantage)
  • coefficient of variation
    • = standard deviation / co-efficient of variation
    • standard deviation measures the absolute variability of customer demands
    • co-efficient of variation measures variability relative to average demand
  • benefits
    • demand variability is reduced
      • high demand from one customer will be offset by low demand from another
      • allows to reduce safety stock, therefore reduce average inventory for the same service level
      • the higher the coefficient of variation, the greater the benefit obtained from centralized systems
      • the benefits from risk pooling depend on the behavior of demand from one market relative to demand from another
      • one distribution center is better than two centers, two better than three (centralized better than decentralized)
  • reduce systemwide cost
    • echelon inventory at any stage or level of the system is the inventory on hand at the echelon, plus all downstream inventory
    • individual retailers are managed using the appropriate (s, S) inventory policy
    • warehouse policy controls its echelon inventory position by (s, S) inventory policy
    • whenever the echelon inventory position for the warehouse is below s, an order is placed to raise its echelon inventory position to S

Supply Contract

Overview

  • key insights
    • the optimal order quantity is not necessarily equal to average forecast demand
    • the optimal quantity depends on the relationship between marginal profit & marginal cost
    • as order quantity increases, average profit first increases and then decreases
    • as production quantity increases, risk increases; the probability of large gains and of large losses increases
    • effective supply contracts allow supply chain partners to replace sequential optimization by global optimization
    • buy back and revenue sharing contracts achieve this objective through risk sharing
  • contracts
    • sequential
    • buy back
    • revenue sharing
    • quantity flexibility contracts
      • supplier provides full refund for returned items as long as the number of returns is no larger than a certain quantity
    • sales rebate contracts
      • supplier provides direct incentive for the retailer to increase sales by means of a rebate paid by the supplier for any item sold above a certain quantity