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York University
ECON 1540
George Georgopoulos

Chapter 13 - Inventory Control CHAPTER 13 INVENTORY CONTROL Review and Discussion Questions 1. Distinguish between dependent and independent demand in a McDonald’s, in an integrated manufacturer of personal copiers, and in a pharmaceutical supply house. The key to the answer here is to consider what must be forecasted (independent demand), and, given the forecast, what demands are thereby created for items to meet the forecasts (dependent demand). In a McDonald’s, independent demand is the demand for various items offered for sale—Big Macs, fries, etc. The demand for Egg McMuffins, for example, needs to be forecasted. Given the forecast, then, the demand for the number of eggs, cheese, Canadian bacon, muffins, and containers can then be computed based on the amount needed for each Egg McMuffin. The manufacturer of copiers is integrated, i.e., the parts, components, etc. are produced internally. The demand for the number of copiers is independent (must be forecasted). Given the forecast, the Bill of Materials is exploded to determine the amounts of raw materials, components, parts, etc. that are needed (more on the BOM in chapter 16). The pharmaceutical supply company is an extreme case where only end items are carried and nothing is produced internally. The bill of materials is the end item and, therefore, the independent demand (forecasted from customers) is the same as the dependent demand. One might attempt to consider that when the demand for items occurs together, that this is similar to a bill of materials. However, this is not a bill of materials, but rather a causal relationship making it easier to forecast. 2. Distinguish between in-process inventory, safety stock inventory, and seasonal inventory. In-process inventory consists of those items of materials components and partially completed units that are currently in the production process. Safety-stock inventory is set so that inventory is maintained to satisfy some maximum level of demand. It could be stated that safety stock is that level of inventory between the minimum expected demand and the desired level of demand satisfaction. Seasonal inventory is that inventory accumulated to meet some periodic increase in demand. 3. Discuss the nature of the costs that affect inventory size. The optimum inventory size is one that minimizes the combined total of holding cost, ordering (or setup) cost, shortage cost, and purchase cost. 13-1 Chapter 13 - Inventory Control 4. Under which conditions would a plant manager elect to use a fixed-order quantity model as opposed to a fixed-time period model? What are the disadvantages of using a fixed-time period ordering system? Fixed-order quantity models–when holding costs are high (usually expensive items or high deprecation rates), or when items are ordered from different sources. Fixed-time period models—when holding costs are low (i.e., associated with low-cost items, low-cost storage), or when several items are ordered from the same source (saves on order placement and delivery charges). The main disadvantage of a fixed-time period inventory system is that inventory levels must be higher to offer the same protection against stockout as a fixed-order quantity system. It also requires a periodic count and closer surveillance than a fixed-order quantity system. A fixed-order quantity system can operate with a perpetual count (keeping a running log of every time a unit is withdrawn or replaced) or through a simple two-bin or flag arrangement wherein a reorder is placed when the safety stock is reached. This latter method requires very little attention. 5. What two basic questions must be answered by an inventory-control decision rule? Any inventory control model or rule must establish (1) when items should be ordered, and (2) how many should be ordered. 6. Discuss the assumptions that are inherent in production setup cost, ordering cost, and carrying cost. How valid are they? Investigation of ordering and production setup cost will likely show that a single, unique cost does not exist for each product, nor is it linearly related to the number of order (as implied in the equations or inventory models). In the purchasing department, for example, an employee is paid either a salary or an hourly rate for a normal work week. The cost for that employee is sometimes divided among the number of items or orders for which he has responsibility, resulting in an averaged or allocated cost for each order he places. However, when we consider an inventory ordering cost based on the number or orders per year (as is done in most inventory models), reducing the number of orders the individual places does not necessarily decrease the net cost to the firm since his weekly pay remains the same. What happens is really an increase in the ordering cost for each of the remaining items within his responsibility. Nonlinearity of costs also occurs in production setups. Consider the time for making a setup in preparation for a production run. Setup time is roughly based on an expected frequency of making this particular product run. However, as the frequency increases, familiarity with the setup allows some shaving of the setup time. Moreover, if the setup is repeated often, an investment in specialized equipment or the construction of jigs may become warranted, reducing the setup time even more. The terms carrying or holding costs for maintaining goods in inventory include a multitude of cost elements. To determine the nature and amounts of these costs can be a challenging feat. Fortunately, total inventory cost curves tend to be dish shaped and can, therefore, tolerate some error. The holding costs associated with insurance, obsolescence, and personnel who are handling materials are extremely difficult to ascertain on an item-by-item basis, yet each 13-2 Chapter 13 - Inventory Control requires realistic analysis. Warehouse storage costs of an item, for example, may be based on a ratio of its required square footage and the entire available warehouse space, but this may not be an accurate representation since it is an allocation of cost rather than true cost. Take the warehouse that is too large, or is used to stock products in an off season or depressed period. Allocation based on a share of total warehouse cost will result in a high cost for storage, when, in fact, excess storage space should create pressure for higher—not lower—order quantities. In the simple inventory model, holding costs are based on the average inventory on hand. “Average” inventory presumes that, as stock is depleted, other product lines will be moved in to occupy the space. It may be that costs should be based on maximum inventory, especially if these is an excess of space, or if the needs of an item are so specialized that no other products can use the space (for example, due to environmental requirements). Each remaining cost may be similarly challenged. Breakage, pilferage, deterioration, and insurance costs are not constant but, rather, vary with inventory size. As the value of inventory increases, insurance rates are lower, more refined handling procedures can be installed to reduce breakage, some environmental control and maintenance can be used to reduce deterioration, and better security procedures can reduce theft. These challenges to determining true costs are not intended to discourage the use of inventory models. The intent, rather, is to prevent the use of any model without clear knowledge of its requirements and assumptions. Indeed, each application must consider the operating conditions and needs of the firm. An appropriate model can then be developed in a fashion similar to those covered in this chapter. 7. “The nice thing about inventory models is that you can pull one off the shelf and apply it so long as your cost estimates are accurate.” Comment. Unfortunately, there is no model or set of models universally applicable to all inventory situations. As stated in the chapter several times, each situation is different and requires a model to suit those conditions. Students frequently try to memorize specific models rather than the process of building any inventory model. See also the answers to question 9 below. 13-3 Chapter 13 - Inventory Control 8. Which type of inventory system would you use in the following situations? a. Supplying your kitchen with fresh food. b. Obtaining a daily newspaper. c. Buying gas for your car. To which of these items do you impute the highest stockout cost? (a) Supplying kitchen with food—both a periodic model and order quantity. Generally, a household will shop once weekly for the majority of items (periodic), then pick up items such as bread and milk as the supply runs low (fixed quantity with reorder point). (b) Obtaining a daily newspaper—a daily newspaper is obviously a periodic model. One does not usually wait until he has finished one daily paper before buying the next day’s paper. (c) Buying gas for your car—generally, this is a hybrid type model wherein a reorder point is signaled when the gas indicator is low, then the tank is filled. Many people, however, have a fixed quantity purchase when the reorder point is reached, such as “put in 10 gallons or $10.00 worth.” Still others (drawing upon our own experience) use a periodic ordering system on their wife’s car, such as taking it out and filling it every Sunday after church (or in Chase’s case, after the football game). The highest stockout cost for most well-fed, well-read individuals would be running out of gas in your car. The cost could range from practically zero if one runs out in front of a gas station—to being late for an appointment or causing an accident on the highway. 9. Why is it desirable to classify items into groups, as the ABC classification does? Using a classification scheme such as this one allows a greater portion of time to be spent in controlling specific groups or classes or items. For the ABC grouping, greater control is afforded those items which comprise the greatest dollar volume in usage. The result of this classification is a reduction in the overall inventory size and, therefore, decreased costs for the same level of satisfying inventory demands. 13-4 Chapter 13 - Inventory Control Problems 1. Cu= $10 - $4 = $6 Co= $4 - $1.50 = $2.50 Cu 6 P ≤ = = .7059 , NORMSINV(.7059)=0.541446 C oC u 2.50+ 6 Should purchase 250 + .541446 (34) = 268.4 or 268 boxes of lettuce. 2. Cu = $125 Co= $250 P ≤ Cu + 125 =.333 C +C 250+125 , NORMSINV(.333)=-0.43164 o u Should purchase 25 + (-.43164)(15) = 18.5254. Super Discount should overbook 19 passengers on the flight. 3. 2DS 2(1000 )25 Q opt= = H 100 = 22.36→ 22 4. Service level P = .95, D = 5000, = 5000/365, T = 14 days, L = 10 days, = 5 per day, and I =150. q = d(T + L) + zT +L− I 2 2 σ T +L (T + L)σ = (14 +10)(5) = 24.495 From Standard normal distribution, z = 1.64 5000 q = 365 (14 + 10) + 1.64(24.495) − 150 = 218.94 219 13-5 Chapter 13 - Inventory Control d σ 5. Service level P = .98= 150, T = 4 weeks, L = 3 weeks,= 30 per week, and I =500 pounds. q = d(T + L) + zT +L I 2 2 σ T +L (T + L)σ = (4 + 3)(30)= 79.4 From Standard normal distribution, z = 2.05 q = 150(4+3) + 2.05(79.4) – 500 = 712.77 713pounds 6. Q = 2DS = 2(25750 )250 opt H .33(10) → a. = 1975.23 1975 From Standard normal distribution, z = 1.64 R = dL + zσL = 515(1) + (1.64)25 = 556 Q 1975 b. Holding cost = H = (.33)10 = $3,258.75 2 2 D 25750 Ordering cost Q S = 1975 (250 = $3,259.49 Q H = 2000 (.33)10 c. Holding cost = 2 2 = $3,300.00 Ordering cost = S = 25750 (250 = $3,218.75 Q 2000 Total annual cost with discount is $6,518.75 – 50(25750/2000) = $5,875.00, without discount it is $6,518.24. Therefore, the savings would be $643.24 for the year. 13-6 Chapter 13 - Inventory Control d σ 7. Service level P = .9= 5 per day, T = 30 days, L = 2 day= 1 per day, and I =35. q = d(T + L) + zT +L I σT +L= (T + L)σ2= (30 + 2)(1) 5.657 From Standard normal distribution, z = 2.05 q = 5(30 + 2) + 2.05(5.657 ) − = 136.60→ 137chips The most he would ever order would be when on-hand was zero. q = 5(30 + 2) + 2.05(5.657= 171.60 → 172 chips 8. 2DS 2(10000 )150 Qopt= H = .20(10) → a.
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