CH-19-20 Sales and Operations Planning – Operations and Supply Chain Management : Book Guide

This Document Contains Chapters 19 to 20 CHAPTER 19 SALES AND OPERATIONS PLANNING Discussion Questions 1. What are the basic controllable variables of a production planning problem? What are the four major costs? Basic controllable variables: production rate, work force levels, and inventories. Major costs: production costs (fixed and variable), production rate change costs, inventory holding costs, and backlog costs. 2. Distinguish between pure and mixed strategies in production planning. Pure strategies use only one variable to absorb demand fluctuations. Mixed strategies combine variables from two or more pure strategies. 3. What are the major differences between aggregate planning in manufacturing and aggregate planning in services? There are two main differences. One is that services typically need to be provided when demanded – there are not many opportunities for backorders in a service firm. When demand cannot be met, the typical result is lost sales. The second difference compounds that problem: services cannot be inventoried during slow periods to satisfy demand during peak periods. Capacity in excess of demand in any period is almost always wasted capacity, unlike in manufacturing. 4. How does forecast accuracy relate, in general, to the practical application of the aggregate planning models discussed in the chapter? A highly accurate forecast encourages the use of deterministic techniques such as linear programming which in turn permits the development of near optimal plans. Clearly, though, any reduction in uncertainty enhances the likely accuracy of any production planning method. 5. In what way does the time horizon chosen for an aggregate plan determine whether it is the best plan for the firm? Many factors affect the selection of an appropriate time horizon. Perhaps, the most important is what the firm intends to plan during that time period. An aggregate plan implies a period of up to 18 months wherein the firm takes its forecast and plans production using inventory, work force size, overtime and under time, subcontracting, and backlogging orders to achieve a reasonable schedule at reasonable costs. A very stable firm in a very stable environment with a very stable demand really doesn’t need to go out very far with its aggregate plan. However, when there is variation, especially when this variation is considerable, then a longer aggregate plan will show the need to find subcontractors, new workforce availability, etc. Planning for these can start early. 6. Define yield management. How does it differ from the pure strategies in production planning? Yield management is the process of allocating capacity in a fixed-capacity system to customers at the right price and time to maximize revenue. In practice it is a variable pricing model that reduces prices for time periods when demand is low and excess capacity exists, and increases prices for time periods when demand is high and there is limited capacity remaining. It works best for systems where capacity is essentially fixed due to the high cost of the system structure, variable costs are low, inventory is perishable, and the product can be sold in advance. There are several examples in the travel industry: airlines, hotels, and car rentals among others. This approach is different from the pure strategies in a number of ways. Product cannot be inventoried, so a level approach is infeasible. There is a strict capacity limit in the system (number of seats, number of rooms, number of cars, etc.) that cannot be temporarily increased by adding workers, working overtime, or subcontracting, so a pure chase strategy would not work. Also, yield management includes active efforts to manage demand and revenue in a dynamic manner, where the pure strategies are designed to simply react to forecasted demand. 7. How would you apply yield management concepts to a barbershop? A soft drink vending machine? The first step would be to determine when peak and off-peak times existed. For the barbershop, lower prices could be given during off-peak times. For example, price discounts could be given during days of the week, or times of the day when demand is low. Another approach would be to offer a discount and an appointment to people that walk-in during peak times, thus transferring them to an off-peak time. Hopefully, lack of capacity would not be a problem for a vending machine, so reallocating peak demand should not be an issue. But, trying to increase usage during non-peak times is difficult because most vending machine can charge only one price. However, new technology could allow the prices to be changed based on time of day, or even the day of the week. Therefore, during off-peak times, a lower price could be charged to stimulate sales. Objective Questions 1. Major operations and supply planning activities can be grouped into categories based on the relevant time range of the activity. What time range category does sales and operations planning fit into? Medium range 2. What category of planning covers a period from a day to six months, with daily or weekly time increments? Short range planning 3. In the agriculture industry, migrant workers are commonly employed to pick crops ready for harvest. They are hired as needed and are laid off once the crops are picked. This approach is made necessary by the realities of the industry. Which production planning strategy would this best be an example of? Chase strategy 4. What is the term for a more complex production strategy that combines approaches from more than one basis strategy? Mixed strategy 5. List at least three of the four costs relevant to the aggregate production plan. Basic production costs, costs associated with changes in the production rate, inventory holding costs, backordering costs 6. Which of the four costs relevant to aggregate production planning is the most difficult to accurately measure? Backordering costs Fall Winter Spring Summer Forecast 10000 8000 7000 12000 Beginning inventory 500 -2300 0 200 Production required 9500 10300 7000 11800 Production hours required 19000 20600 14000 23600 Production hours available1 14400 14400 14400 14400 Overtime hours 6200 Temp workers2 20 Temp worker hours available 9600 Total hours available 14400 20600 14400 24000 Actual production 7200 10300 7200 12000 Ending inventory -2300 0 200 200 Workers hired 20 Workers laid off 20 Straight time $72,000 $72,000 $72,000 $120,000 Overtime 0 49600 0 0 Inventory $1,000 $1,000 Backorder $23,000 Hiring $2,000 Layoff $4,000 7. Total $95,000 $121,600 $73,000 $127,000 $416,600 130 workers*8*60 2Temp workers to be hired = (23,600-14400)/(8*60) = 19.17 workers 8. February March April May Forecast 80,000 64,000 100,000 40,000 Beginning inventory - - - (16,000) Production required 80,000 64,000 100,000 56,000 Production hours required 20,000 16,000 25,000 14,000 Regular workforce 125 100 100 100 Regular production 80,000 64,000 64,000 64,000 Overtime hours - - 5,000 Overtime production - - 20,000 - Total production 80,000 64,000 84,000 64,000 Ending inventory - - - 8,000 Ending backorders - - 16,000 - Workers hired 25 Workers laid off - 25 Straight time $200,000 $160,000 $160,000 $160,000 Overtime - - $ 75,000 - Inventory - - - 80,000 Backorder $0 $0 $320,000 $0 Hiring 1,250 - - - Layoff - 1,750 - - Total $201,250 $161,750 $555,000 $240,000 $1,158,000 9. Spring Summer Fall Winter Forecast 20,000 10,000 15,000 18,000 Beginning inventory 1,000 - - - Production required 19,000 10,000 15,000 18,000 Production hours required 38,000 20,000 30,000 36,000 Regular workforce 70 50 75 75 Regular production 14,000 10,000 15,000 15,000 Overtime hours 10,000 - - Overtime production 5,000 - - - Total production 19,000 10,000 15,000 15,000 Ending inventory - - - - Ending backorders - - - 3,000 Workers hired - 25 Workers laid off - 20 Straight time $280,000 $200,000 $300,000 $300,000 Overtime 150,000 - - - Inventory - - - - Backorder $0 $0 $0 $24,000 Hiring - - 2,500 - Layoff - 4,000 - - Total $430,000 $204,000 $302,500 $324,000 $1,260,500 10. Jan. Feb. March April May June July Aug. Sept. Oct. Nov. Dec. Avg. Forecast 2500 3000 4000 3500 3500 3000 3000 4000 4000 4000 3000 3000 Beginning inventory 500 1250 1500 2000 1750 1750 1500 1500 2000 2000 2000 1500 Production requirements 3250 3250 4500 3250 3500 2750 3000 4500 4000 4000 2500 3000 3458.3 Ending inventory 1250 1500 2000 1750 1750 1500 1500 2000 2000 2000 1500 1500 Total Cost Forecast 2500 3000 4000 3500 3500 3000 3000 4000 4000 4000 3000 3000 40500 Beginning inventory 500 1360 1720 1080 940 800 1160 1520 880 240 -400 -40 Production plan 3360 3360 3360 3360 3360 3360 3360 3360 3360 3360 3360 3360 40320 $403,200 Ending inventory 1360 1720 1080 940 800 1160 1520 880 240 -400 -40 320 Safety stock 1250 1500 2000 1750 1750 1500 1500 2000 2000 2000 1500 1500 Excess inventory 110 220 20 350 $1,750 Back order 400 40 440 $8,800 Total $413,750 This plan uses a workforce of 21 workers. Assumptions include no carrying cost for inventory used to satisfy safety stock, nor any cost for not having enough safety stock to satisfy company policy. Costs would vary under different assumptions. Next, try increasing or decreasing the number of workers by one, and recalculate the total cost. A better solution may be found. 11. There is more than one solution. The following solution assumes no backordered work at the end of the plan. January February March April May June Forecast work hours 5,000 4,000 6,000 6,000 5000 4,000 Beginning inventory (work done earlier) 200 1,400 600 (200) - Work hours required 5,000 3,800 4,600 5,400 5,200 4,000 Regular work hours available 4,000 4,000 4,000 4,000 4,000 4,000 Overtime hours 1,200 1,200 1,200 1,200 1200 - Total planned hours 5,200 5,200 5,200 5,200 5,200 4,000 Ending inventory (early work completed) 200 1,400 600 - Ending backorders (work to be done later) - - - 200 - - Straight time $120,000 $120,000 $120,000 $120,000 $120,000 $120,000 Overtime 54,000 54,000 54,000 54,000 54,000 - Inventory 1,000 7,000 3,000 - - - Backorder $0 $0 $0 $2,000 $0 $0 Total $175,000 $181,000 $177,000 $176,000 $174,000 $120,000 $1,003,000 Allowing backordered work at the end of the plan can reduce the cost but will leave work to be done in the second half of the year. Following allows up to 500 hours backordered work. January February March April May June Forecast work hours 5,000 4,000 6,000 6,000 5000 4,000 Beginning inventory (work done earlier) (0) 1,200 400 (400) (500) Work hours required 5,000 4,000 4,800 5,600 5,400 4,500 Regular work hours available 4,000 4,000 4,000 4,000 4,000 4,000 Overtime hours 1,000 1,200 1,200 1,200 900 - Total planned hours 5,000 5,200 5,200 5,200 4,900 4,000 Ending inventory (early work completed) - 1,200 400 - Ending backorders (work to be done later) 0 - - 400 500 500 Straight time $120,000 $120,000 $120,000 $120,000 $120,000 $120,000 Overtime 45,000 54,000 54,000 54,000 40,500 - Inventory - 6,000 2,000 - - - Backorder $0 $0 $0 $4,000 $5,000 $5,000 Total $165,000 $180,000 $176,000 $178,000 $165,500 $125,000 $989,500 12. The decision variables are how many regular and OT hours to assign to production of each product each month. The constraints are the limits of total regular and OT hours each month, and no backorders. The costs are a combination of production and inventory carrying costs. APRIL MAY JUNE JULY Demand A 800 600 800 1200 Demand B 600 700 900 1100 Demand C 700 500 700 850 Total Demand 2100 1800 2400 3150 Regular hours Available 1500 1300 1800 2000 Overtime Available 700 650 900 1000 Costs Regular Hours A 200 100 200 50 4 Regular Hours B 600 700 900 1100 5 Regular Hours C 700 500 700 850 6 Total Regular Hours 1500 1300 1800 2000 OT Hours A 600 500 750 1000 6 OT Hours B 0 0 0 0 7.5 OT Hours C 0 0 0 0 9 Total OT Hours 600 500 750 1000 Total Hours A 800 600 950 1050 Total Hours B 600 700 900 1100 Total Hours C 700 500 700 850 Excess Hours A 0 0 150 0 3 Excess Hours B 0 0 0 0 4 Excess Hours C 0 0 0 0 5 Production Costs 11600 9900 14000 16800 Inventory Costs 0 0 450 0 TOTAL COST: 52750 Objective value = $52,750. There may be alternative optimal solutions. 13. Number of workers = (6700-200)10/(249*8) = 32.6 or 33 workers Monthly production (except July) = 22(8)33/10 = 580 units/month Jan. Feb. March April May June July August Sept. Oct. Nov. Dec. Total Forecast 600 800 900 600 400 300 200 200 300 700 800 900 6700 Beginning inventory 200 180 0 0 0 180 460 444 824 1104 984 764 Available Production 580 580 580 580 580 580 184 580 580 580 580 580 6564 Ending inventory 180 -40 -320 -20 180 460 444 824 1104 984 764 444 Costs Total Lost Sales 0 800 6400 400 0 0 0 0 0 0 0 0 7600 Inventory 900 0 0 0 900 2300 2220 4120 5520 4920 3820 2220 26920 Total 900 800 6400 400 900 2300 2220 4120 5520 4920 3820 2220 34520 14. The following solution assumes no backorders, and includes safety stock in inventory cost calculations. January February March Forecast 1,000 1,500 1,200 Safety stock 500 750 600 Beginning inventory 500 503 751 Net production required 1,000 1,747 1,049 Workers required 57 115 63 Hired 7 58 Laid off 52 Actual production 1,003 1,748 1,058 Ending inventory 503 751 609 Labor $60,192 $104,880 $63,504 Inventory $ 1,509 $ 2,253 $ 1,827 Hiring $ 1,400 $ 11,600 $ - Layoff $0 $0 $15,600 Total $63,101 $118,733 $80,931 Total: $262,765 15. The following plan assumes no backorders. The only cost data provided is for inventory carrying costs. The 24% per year works out to 2% per month based on the $40 cost per unit, or $0.80 per unit per month. May June July August Forecast 3200 2,800 3,100 3,000 Beginning inventory 403 158 148 3 Production required 2,797 2,642 2,952 2,997 Regular workforce 12 12 12 12 Regular production 2,460 2,460 2,460 2,460 Temp workforce 3 2 3 4 Temp production 495 330 495 660 Total production 2,955 2,790 2,955 3,120 Ending inventory 158 148 3 123 Inventory Cost $126.40 $118.40 $2.40 $98.40 $345.60 16. The widespread scientific application of yield management began within what industry? Airline 17. Under what type of demand is yield management most effective? Highly variable 18. In a yield management system, pricing differences must appear logical and justified to the customer. The basis for this justification is commonly called what? Rate fences 19. The essence of yield management is the ability to manage what? Demand ANALYTICS EXERCISE: Bradford Manufacturing This exercise can be left as a homework exercise or used as a teaching case. A solution to the problem is shown in the plan below. Afterwards, teaching notes for use as a case are presented. Aggregate Plan Quarter (Week Numbers) 1st (1-13) 2nd (14-26) 3rd (27-39) 4th (40-52) Lines run 10 10 12 11 Overtime hours per day 0 0 0 0 Beginning Inventory 200.0 393.8 387.5 520.0 Production 2,193.8 2,193.8 2,632.5 2,413.1 Expected Demand 2,000.0 2,200.0 2,500.0 2,650.0 Ending Inventory 393.8 387.5 520.0 283.1 Ending Inventory Target (Rounded) 338 385 408 338 Deviation from Inventory Target 55.8 2.5 112.0 -54.9 Employees 60 60 72 66 Cost of Plan Labor Regular Time $624,000 $624,000 $748,800 $686,400 Labor Overtime Hiring and Training $0 $0 $60,000 $0 Layoff $0 $0 $0 $18,000 Inventory Carry Cost $13,950 $650 $28,025 $0 Stockout Cost $0 $0 $0 $32,880 Quarter Budget $637,950 $624,650 $836,825 $737,280 Total Cost of Plan $2,836,705 The plan above is from the Excel spreadsheet at the book website, and is just one possible solution. It is based on the following assumptions: - Inventory carrying costs are based on inventory in excess of safety stock. - Backorder costs are incurred on negative deviation from planned safety stock, even though total inventory may be positive. - Overtime is planned in hours per day across an entire quarter. A more reasonable approach might be to plan on overtime-weeks in a quarter (integer constraint, Protection > Unprotect). Finish this section by putting a solution in the Aggregate Plan portion of the spreadsheet that seems to be a good one. Now move to the Simulation Worksheet part of the spreadsheet. Here the plan has been reorganized into a weekly master schedule with the data from the Aggregate Plan initially seeding the schedule. The idea is to now work through the weekly schedule by putting in what actually happened in terms of sales and production rates. After seeing the data each week, students should be given the opportunity to change next week’s schedule. You should do this for at least the first 13 weeks. Then you can click on the Actual Costs worksheet and compare the budgeted cost to the actual cost of running the plant. To make the simulation interesting use actual demand that demonstrates the old “hockey stick” phenomenon. Sales should be real slow at the beginning of the quarter and then surge at the end. Remember there is a sale at the end of the 1st quarter. Try to be real straight when you go from week to week and don’t hint at the fact that demand will take off at the end. This can be a good lesson for the student. The following are a set of production rates and demand that work well: Week Production Rate Demand Week Production Rate Demand 1 423 140 11 465 112 2 455 120 12 450 200 3 430 100 13 455 450 4 435 125 14 450 160 5 435 125 15 430 165 6 460 105 16 450 160 7 465 115 17 455 145 8 470 120 18 470 150 9 455 105 19 460 155 10 460 110 20 455 160 You can complete the exercise by discussing the following items: - Why did demand vary the way it did during the first quarter? - Why is it important for manufacturing and marketing to coordinate plans? - What types of things can marketing do to make it easier on manufacturing? (Separate the deals from the deliveries. Everyday low pricing, etc.) - Do you think that management should change their inventory target? Teaching Plan for a class using Bradford Manufacturing Explain how Aggregate Planning fits into the overall process of Planning and Control – show chart. What is Aggregate Planning? - Setting workforce levels - Aggregate inventory levels - Production rate - 6-18 month horizon - Product groups – rather than individual products A strategy for how demand will be met, given current resource constraints. Why is Aggregate Planning important? - Key interface to the capital budgeting process 10 minutes into the class Bradford Manufacturing - What are the key drivers of this plan? Forecast -> Marketing/market Research Ending Inventory Target -> Management Technical Parameters – define current resource constraints and costs. - Evaluate the costs associated with the current plan. Develop a solver plan. Rationalize the plan. – Integerize 30 minutes into class - Two basic strategies – chase demand or level demand (use inventory) - Put a high hiring and firing cost into the solution and generate a level plan. Use hiring and training cost of $15,000 and layoff cost of $5,000. 35 Minutes into class - Explain the relationship between the Aggregate Plan and the Master Schedule Run the simulation (takes about 40 minutes) Conditions Inventory target – 1 week Hiring/training = $5,000 Layoff cost = $3,000 Initial inventory = 200(000) units Offer prize! First, each student (or pair of students) needs to finalize an Aggregate Plan, and then move to the simulation worksheet. Make sure initial inventory is set correctly. Show actual cost worksheet. Run simulation per the previous instructions. CHAPTER 20 INVENTORY MANAGEMENT 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 21). 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. There are three main categories of costs: purchase cost, ordering costs, and holding costs. The purchase cost may affect inventory levels if quantity discounts are offered. Suppliers will offer a discount for placing larger orders, which might provide an incentive for carrying the resultant larger inventory levels. Ordering costs directly influence the optimum order quantity. As ordering costs increase, the effect is to order less often but in higher quantities, thus increasing inventory levels. Holding costs have an inverse effect on inventory levels. As holding costs increase, there is an incentive to reduce order quantities resulting in lower average inventory levels. a. How does shrinkage (stolen stock) contribute to the cost of carrying inventory? How can this cost be reduced? Stock cannot be stolen unless it is on hand, and it is reasonable to assume that shrinkage will increase as on-hand inventory levels increase. Shrinkage costs can be reduced through increased security measures (security-related workforce, electronic tracking tags) and/or reducing the amount of inventory on hand at any one point in time. b. How does obsolescence contribute to the cost of carrying inventory? How can this cost be reduced? Obsolescence costs are relevant primarily in hi-tech industries. As inventory ages, market influences and advancements in technology drive the value of that inventory lower. The cost of making the item in inventory has likely decreased, and the “latest and greatest” new innovation lowers the value of the older technology. Obsolescence costs can be reduced by producing in smaller quantities as the product matures. That however will increase total setup costs. 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 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 8 below. 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 $20.00 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. What is the purpose of classifying 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. 10. When cycle counting inventory, why do experts recommend a lower acceptable tolerance for “A” items than “B” or “C” items? “A” items are more valuable, so quantity variations are less acceptable to the firm. Some students might suggest that the acceptable tolerance in item count should be related to the total value of inventory in each category, which is another way of stating the same concept. Objective Questions 1. What is the term used to refer to inventory while in distribution – i.e. being moved within the supply chain? In-transit inventory 2. Almost certainly you have seen vending machines being serviced on your campus and elsewhere. On a predetermined schedule the vending company checks each machine and fills it up with various products. Which category of inventory model is this an example of? Fixed-time period model 3. To support the manufacture of desktop computers for their customers, Dell needs to order all the parts that go into the computer, such as hard drives, motherboards and memory modules. Obviously the demand for these items is driven by the production schedule for the computers. What is the term to describe demand for these parts? Dependent demand 4. Cu = $10 - $4 = $6 Co = $4 - $1.50 = $2.50 Cu 6 .7059, NORMSINV(.7059) = 0.541446 P = = Co +Cu 2.50+ 6 Should purchase 250 + .541446 (34) = 268.4 or 268 boxes of lettuce. 5. Cu = $125 Co = $250 Cu 125 .333, NORMSINV(.333)=-0.43164 P + = Co +Cu 250+125 Should purchase 25 + (-.43164)(15) = 18.5254. Super Discount should overbook 19 passengers on the flight. 6. Cu = 25 – 15 = 10, Co = 15-10 = 5, Cu/(Co+Cu) = 10/(5+10) = .6666 Increase Q as long a Pr[demand < Q] < .6666 Pr[demand < 1]=0, Q: Is this (strictly) less than 0.66..? A: Yes. Pr[demand < 2]=0.2, Q: Is this (strictly) less than 0.66..? A: Yes. Pr[demand < 3]=0.3, Q: Is this (strictly) less than 0.66..? A: Yes. Pr[demand < 4]=0.4, Q: Is this (strictly) less than 0.66..? A: Yes. Pr[demand < 5]=0.6, Q: Is this (strictly) less than 0.66..? A: Yes. Pr[demand < 6]=0.9, Q: Is this (strictly) less than 0.66..? A: No. Therefore the optimal order quantity = 5. 7. Cu = 2.15 – .2 = 1.95 Co = .2, Cu/(Co+Cu) = 1.95/(.2+1.95) = .90697 From the standard normal table, Z-value is 1.325. Combined demand has mean 2000*4=8000, and standard deviation = sqrt(4*5002) = 1000. Using the above, the optimal production quantity is 8000+1.325*1000 = 9325. 8. Cu = 17.99 – 6.75 = 11.24, Co = 6.75 – 0.99 = 5.76 a. If demand is 5 (probability 0.1), we will sell 5 apple pies and have 10 leftover. If demand is 10 (probability 0.2), we will sell 10 apple pies and have 5 leftover. If demand is at least 15 (probability 0.7), we will sell all the 15 apple pies. The expected profit is 0.1(5*11.24 – 10*5.76) + 0.2(10*11.24 – 5*5.76) + 0.7(15*11.24) = $134.60 b. Cu = 17.99 – 6.75 = 11.24, Co = 6.75 – 0.99 = 5.76 Increase Q so long as P(demand < Q) < 11.24/(11.24+5.76) = .663 The optimal quantity of apple pies is 20. 9. a. What is the key probability (service rate)? Co = 8 – 4 = $4 Cu = 20 – 8 = $12 The key probability (service level) is: 12/ (12+4) = 0.75 b. How many T-shirts should she produce for the upcoming event? Demand Probability Cumulative Probability 300 0.05 0.05 400 0.10 0.15 500 0.40 0.55 600 0.30 0.85 700 0.10 0.95 800 0.05 1.00 She should produce 600 T-shirts. 10. Co = $0.25, Cu = $0.75 a) Service level = ($0.75)/($0.75 + 0.25) = 0.75. Z-value for 75% is 0.67. Q = 250 + 0.67 * 50 = 283.5 b) Based on part (a), what is the probability that you will run out of stock? 25% 11. a. Demand Probability (dozen) of demand Probability of selling nth unit Expected number sold Sold (rev.) Unsold (rev.) Total revenue Cost Profit 1800 0.05 1.00 1800 $1242.00 $0.00 $1242 $882 $360 2000 0.10 0.95 1990 1373.10 2.90 1376 980 396 2200 0.20 0.85 2160 1490.40 11.60 1502 1078 424 2400 0.30 0.65 2290 1580.10 31.90 1612 1176 436 2600 0.20 0.35 2360 1628.40 69.60 1698 1274 424 2800 0.10 0.15 2390 1649.10 118.90 1768 1372 396 3000 0.05 0.05 2400 1656.00 174.00 1830 1470 360 b. The optimal number to make would be 2,400 dozen. This yields an expected profit of $436. c. Cu = $0.69 - $0.49 = $0.20 Co = $0.49 - $0.29 = $0.20 P = Cu = .20 = .50 Co +Cu .20+.20 Demand (dozen) Probability of demand Cumulative Probability (P) 1800 0.05 .05 2000 0.10 0.15 2200 0.20 0.35 2400 0.30 0.65 2600 0.20 0.85 2800 0.10 0.95 3000 0.05 1.00 Produce 2,400 dozen cookies. 12. 2DS 2(1000)25 H 100 Qopt = = = 22.36 → 22 13. Service level P = .95, D = 5000, d = 5000/365, T = 14 days, L = 10 days,  = 5 per day, and I =150. q = d(T +L)+ zT+L −I T+L = (T+L)2 = (14+10)(5)2 = 24.495 From standard normal distribution, z = 1.64 q= (14+10) +1.64(24.495) −150 = 218.94 → 219 14. Service level P = .98, d = 150, T = 4 weeks, L = 3 weeks,  = 30 per week, and I =500 pounds. q = d(T +L)+ zT+L −I T+L = (T+L)2 = (4 + 3)(30)2 = 79.4 From Standard normal distribution, z = 2.05 q= 150(4+3) + 2.05(79.4) – 500 = 712.77 → 713 pounds 15. a. Qopt = 2DS = 2(25750)250 = 1975.23 → 1975 H .33(10) From Standard normal distribution, z = 1.64 R = dL+ zL = 515(1) + (1.64)25 = 556 b. Holding cost = QH = 1975(.33)10 = $3,258.75 2 2 Ordering cost = DS= 25750(250)= $3,259.49 Q 1975 c. Holding cost = QH = 2000(.33)10 = $3,300.00 2 2 Ordering cost = DS= 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. 16. q = d(T +L)+ zT+L −I T+L = (T+L)2 = (30+ 2)(1)2 = 5.657 98% S.L.  From standard normal distribution, z = 2.05 q= 5(30+ 2) + 2.05(5.657) −35 = 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 17. a. Qopt = 2DS = 2(10000)150 = 1224.74 →1225 units H .20(10) R =dL+ss = (10000/52)(4) + 55 = 824.23 →824 units b. q = d(T +L) +ss−I = (5000/52)(3+1) + 5 – I = 390 – I 18. 98% S.L.  From standard normal distribution, z = 2.05 R=dL+zL = 300(4) + (2.05)180 = 1200.0 + 369 = 1569 If safety stock is reduced by 50 percent, then ss = 185 units. ss=zL , z = ss 185 = 1.03, so the service probability is 84.8%  180 20. Service level = .98, d = 100 per day, T = 10 days, L = 6 days,  = 25 per day, and I =50. q = d(T +L)+ zT+L −I T+L = (T+L)2 = (10+6)(25)2 = 100 98% S.L.  From standard normal distribution, z = 2.05 q=100(10+6) + 2.05(100) −50 = 1755 units 21. 2DS 2(2000)10 → 89 a. Qopt = = = 89.44 H 5 b. Ordering cost = DS= 2000(10) = $224.72 Q 89 c. Holding cost = QH = 89(5) = $222.50 2 2 22. Qopt = 2DS = 2(13000)100 = 2,000 units H .65 L = L2 = 4(40)2 = 80 units 98% S.L.  From standard normal distribution, z = 2.05 R=dL+zL = 250(4) + (2.05)80 = 1000 + 164 = 1164 If safety stock is reduced by 100 units, then ss = 64 units. ss= zL , z = ss =64 = .80 L 80 From standard normal distribution, z = .80, service probability is 79% 23. a. Qopt = 2DS = 2(5000)10 = 408.25 →408 bottles H .20(3) b. L = L2 = 3(30)2 = 52 units 95% S.L.  From standard normal distribution, z = 1.64 R = dL+ zL = 100(3) + (1.64)52 = 300.00 + 85.28 = 385.28 →385 bottles 24. a. Qopt = 2DS = 2(2400)5 = 77.46 →77 sets H 4 b. L = L2 = 7(4)2 = 10.583 sets 98% S.L.  From Standard normal distribution, z = 2.05 R=dL+zL = (2400/365)(7) + (2.05)10.583 = 46.03 + 21.70 =67.73 →68 sets Order 77 sets when the on-hand inventory level reaches 68 sets. 25. Service level = .98, d = 60 units per day, T = 10 days, L = 2 days,  = 10 units per day, and I =100 units. q = d(T +L)+ zT+L −I T+L = (T + L)2 = (10+2)(10)2 = 34.64 98% S.L.  From Standard normal distribution, z = 2.05 q= 60(10+ 2) + 2.05(34.64) −100 = 691 units 26. Service level = .99, d = 2000 capsules per day, T = 14 days, L = 5 days,  = 800 capsules per day, and I =25000 units. q = d(T +L)+ zT+L −I T+L = (T+L)2 = (14+ 5)(800)2 = 3487 capsules 99% S.L.  From Standard normal distribution, z = 2.3263 q= 2000(14+5) +2.3263(3487.12) −25000 = 21,112 capsules 27. 2DS 2(3500)50 = 216.02 →216 mufflers Qopt = = H .25(30) L = L2 = 2(6)2 = 8.49 mufflers 90% S.L.  From Standard normal distribution, z = 1.28 R=dL+zL = (3500/300)(2) + (1.28)8.49 = 23.33 + 10.87 = 34.20 →34 sets Order 216 sets when the on-hand inventory level reaches 34 sets. 28. Service level = .98, d = 5000/365 boxes per day, T = 14 days, L = 3 days,  = 10 boxes per day, and I = 60 boxes. q = d(T +L) + zT+L −I T+L = (T+L)2 = (14+3)(10)2 = 41.23 boxes 98% S.L.  From Standard normal distribution, z = 2.05 q= (5000/365)(14+ 3) + 2.05(41.23) −60 = 257.40 → 257 boxes 29. 2DS 2(500)100 = 31.62 →32 refrigerators Qopt = = H .20(500) L = 10 refrigerators 97% S.L.  From Standard normal distribution, z = 1.88 R = dL+ zL = (500/365)(7) + (1.88)10 = 9.59 + 18.8 = 28.39 →28 refrigerators Order 32 refrigerators when the on-hand inventory level reaches 28 refrigerators. 30. 2DS 2(1000)20 = 75.59 →76 tires Qopt = = H .20(35) L = L2 = 4(3)2 = 6 tires 98% S.L.  From Standard normal distribution, z = 2.05 R=dL+zL = (1000/365)(4) + (2.05)6 = 10.96 + 12.3 = 23 tires Order 76 tires when the on-hand inventory level reaches 23 tires. 31. Service level = .99, d = 600 hamburgers per day, T = 1 day, L = 1 day,  = 100 hamburgers per day, and I = 800 hamburgers. q = d(T +L)+ zT+L −I T+L = (T+L)2 = (1+1)(100)2 = 141.42 hamburgers 99% S.L.  From Standard normal distribution, z = 2.326 q= 600(1+1) + 2.326(141.42) −800 = 728.94 → 729 hamburgers 32. a. Qopt = 2DS = 2(20)(365)10 = 540.37 →540 cans H .50 R=dL = 20(14) = 280 cans b. L = L2 = 14(6.15)2 = 23.01 cans 99.5% S.L.  From Standard normal distribution, z = 2.57 R = dL+ zL = 20(14) + (2.57) 23.01 = 280.00 + 59.14 = 339 cans Order 540 cans when the on-hand inventory level reaches 339 cans. 33. Service level = .98, d = 20 gallons per week, T = 1 week, L = 1 week,  = 5 gallon per week, and I = 25 gallons. q = d(T +L) + zT+L −I T+L = (T+L)2 = (1+1)(5)2 = 7.07 gallons 98% S.L.  From Standard normal distribution, z = 2.05 q= 20(1+1) + 2.05(7.07) −25 = 29.49 → 29 gallons 34. a. Total demand (D) = 3*12 months * 3000 units * 0.5 pound = 54000 pounds Total purchasing cost per unit (C) = $2.5 + $0.20 = 2.70 Set up cost (S) = $100 Holding cost per unit = 2.70 * 20% = $0.54 (2)(54,000)(100) Q == 4472 pounds 0.54 b. Number of orders per year = Total demand / EOQ = 54000 / 4472 = 12.08 That is the SYM orders 12.08 times a year. The company orders every 12 months / 12.08 = 0.99 months or about once a month. c. The delivery lead-time is 2 weeks. Thus, the company needs to order the cotton two weeks in advance, which is about March 15th. d. See answer to question b. e. Annual holding cost = H*Q/2 = 0.54 * 4472 / 2 = $1207 per year. f. Annual ordering cost = Number of orders * ordering cost = 12.08 * 100 = $1208 g. If the holding cost is lower the batch size is larger, thus, the average inventory is larger. The number of orders would be smaller. 35. a. It is important to notice that the set up cost is $50 (This is the cost that is independent of the quantity shipped). The variable cost is $2 + $10 per unit. The annual holding cost is 12*20% = $2.40 / book. b. The annual demand is 250*50 = 12,500 (assuming 50 weeks per year). (2)(12,500)(50) Q= 722 pounds 2.4 c. To calculate the throughput time, we first calculate the number of orders: 12,500 Number of Orders = =17.3 722 Time Between Orders = = 0.694 months The average time a unit stays in the system is half of that, i.e., 0.347 months. 36. d = 10, T = 15, L = 2, 90% S.L.  z = 1.28, T+L = (15+ 2)62 = 24.74 a. d(T +L) +ZT+L =10(17) +1.28(24.74) = 201.67 b. If the service probability requirement is 95%, the optimal target level (your answer in part a) will (select one): INCREASE 37. a. To manage inventory, the company is using: Continuous Review System b. Q= (2)(36,000)(10) =1,200 pounds 0.5 c. 90% S.L.  z = 1.28, L = L2 = 5(15)2 = 33.54 R = dL+ zL = (100)(5) + (1.28)(33.54)  543 38. Quantity range Cost (C) EOQ Feasible Less than 100 pounds $20 per pound 219 pounds No 100 to 999 pounds $19 per pound 225 pounds Yes 1,000 or more pounds $18 per pound 231 pounds No Note: EOQ = 2DS iC Therefore, calculate total cost at Q=225, C=$19; and at Q=1000, C=$18 D Q 3000 225 = $58,068 TCQ=225,C=19 = DC + S + iC = 3000(19) + 40+ (.25)19 Q 2 225 2 D Q 3000 1000 = $56,370 TCQ=1000,C=18 = DC + S + iC = 3000(18) + 40+ (.25)18 Q 2 1000 2 The best order size is 1,000 units at a cost of $18 per pound. 39. Quantity range Cost (C) EOQ Feasible Less than 2500 pounds $0.82 per pound 4277 pounds No 2500 to 4999 pounds $0.81 per pound 4303 pounds Yes 5,000 or more pounds $0.80 per pound 4330 pounds No Note: EOQ = 2DS iC Therefore, calculate total cost at Q=4303, C=$0.81, and at Q=5000, C=$0.80 D Q TCQ=4303,C=0.81 = DC + S + iC Q 2 = 50000(0.81) + 30+ (.20)(0.81) = $41,197.14 TCQ=5000,C=0.80 D Q = DC + S + iC Q 2 = 50000(0.80) + (30) + (.20)(0.80) = $40,700.00 The best order size is 5,000 units at a cost of $0.80 per pound. 40. a. Item number Annual usage Class 18 61000 A 4 50000 A 13 42000 A 10 15000 B 11 13000 B 2 12000 B 8 11000 B 16 10200 B 14 9900 B 5 9600 C 17 4000 C 19 3500 C 20 2900 C 3 2200 C 7 2000 C 1 1500 C 15 1200 C 9 800 C 6 750 C 12 600 C b. If item 15 is critical to operations, it may be desirable to reclassify it from C to A to ensure more frequent reviews. 41. a. The obvious choice is ABC analysis. b. Item number Annual usage Class q 90000 A k 80000 A f 68000 A t 32000 B n 30000 B e 24000 B g 17000 B c 14000 B r 12000 B a 7000 B or C s 3000 C j 2300 C d 2000 C o 1900 C i 1700 C m 1100 C b 1000 C h 900 C p 800 C l 400 C 42. Item number Average monthly Price per unit demand Monthly usage Class 5 4000 21 84000 A 3 2000 12 24000 A or B 4 1100 20 22000 B 7 3000 2 6000 B 9 500 10 5000 B 1 700 6 4200 B or C 8 2500 1 2500 C 10 1000 2 2000 C 6 100 10 1000 C 2 200 4 800 C ANALYTICS EXERCISE: Inventory Management at Big10Sweaters.com 1. You are curious as to how much Rhonda and Steve made in their business last year. You do not have all the data, but you know that most of their expenses relate to buying the sweaters and having them monogrammed. You know they paid themselves $50,000 each and you know the rent, utilities, insurance, and a benefit package for the business was about $20,000. About how much do you think they made “before taxes” last year? If they must make their payment to the venture capital firm, and then pay 50% in taxes, what was their increase in cash last year? Last Year’s Pre-Tax Profit Unit Unit Sales Sale Price Cost Revenue Margin Ohio 2,300 $120 73.88 $276,000 $106,076 Michigan 1,468 $120 73.88 $176,160 $108,456 $67,704 Purdue 890 $120 73.88 $106,800 $65,753 $41,047 eBay 342 $50 60.88 $17,100 $20,821 Totals 5,000 $576,060 $364,954 Overhead: $120,000 Net Profit: $91,106 If they pay 25% to the venture capital firm, this is $22,776.50, their profit before taxes is $68,329.50. They then pay $34,164.75 in taxes leaving them with an increase in cash of about $34,165. Major point here is to show how relevant these decisions are to the success of the firm. 1. What was your reasoning behind using the aggregate demand forecast when determining the size of your order rather than the individual school forecasts? Should you rethink this or is there a sound basis for doing it this way? Here we argue that the aggregate forecast should be more accurate than the individual person’s forecast. You can easily calculate the coefficient of variation (CV) in the individual forecasts and compare that to the aggregate forecast to prove this (the CV for the individual forecasts are between 10% and 14%, and the CV for the aggregate forecast is less than 6%). A big assumption here is that the forecasts at each school are independent and that they are not biased. If this is true the errors will tend to cancel each other out. If there is major bias in the forecasts (for example, they are all high or low), then we have a problem and it might be better to use the individual forecasts. In our analysis here, we assume the forecasts are independent and not biased but we also calculate the orders by individual school. 2. How many sweaters should you order next year? Break down your order by individual school. Document your calculations in your spreadsheet. Calculate this based on the aggregate forecast and also the forecast by individual school. Here the single period model is applicable. The cost of underestimating demand is the lost profit. In this case a sweaters would be sold for $120 and it would cost $73.88 (supplier plus subcontractor cost), so the return is $46.12 per sweater. The cost of overestimating demand is the difference between the supplier cost of $60.88 and the eBay price of $50 which is $10.88. The critical probability then is Cu/(Co+Cu) = 46.12/(10.88+46.12) = .809123 Now, using the aggregate demand forecast, which has a mean of 7,400 and standard deviation of 430 units, you should order NORMINV(.809123,7400,420) = 7,776 units. Based on the forecast data Ohio State gets 33.78% or 2,627 units, Michigan get 23.87% or 1,856 units, Purdue get 13.51% or 1,051 units, Michigan State gets 21.85% or 1,699 units, and Indiana gets 6.98% or 543 units. If we base this on the individual forecasts we would order the following: Ohio State = NORMINV(.809123,2500,300) = 2,762 Michigan = NORMINV(.809123,1767,252) = 1,987 Purdue = NORMINV(.809123,1000,100) = 1,087 Michigan State = NORMINV(.809123,1617,126) = 1,727 Indiana = NORMINV(.809123,517,76) = 583 Total order size would be 8,146. There is a difference of 8,146 - 7,767 = 379 sweaters. 3. What do you think they could make this year? They are paying you $40,000 and you expect your benefit package addition would be about $1,000 per year. Assume that they order based on the aggregate forecast. We base this on the expected average sales from our forecast and an aggregate order size of 7,767 sweaters. Assuming sales are as forecast, the safety stock would be sold on eBay. We also need to adjust overhead to account for the $41,000 increase due to the new employee. This Year’s Expected Pre-Tax Profit Unit Unit Sales Sale Price Cost Revenue Cost Margin Ohio 2,500 $120 73.88 $300,000 $184,700 $115,300 Michigan 1,767 $120 73.88 $212,040 $130,546 $81,494 Purdue 1000 $120 73.88 $120,000 $73,880 $46,120 Michigan State 1617 $120 73.88 $194,040 $119,464 $74,576 Indiana 517 $120 73.88 $62,040 $38,196 $23,844 eBay 366 $50 60.88 $18,300 $22,282 ($3,982) Totals 7,767 $906,420 $569,068 $337,352 Overhead: $161,000 Net Profit: $176,352 Using the same logic as before, the venture capital people get $44,088 leaving us with $132,264 to pay taxes on. Taxes would be $66,132. This creates an increase in our cash of about $66,132. 4. How should the business be developed in the future? Be specific and consider changes related to your supplier, the monogramming subcontractor, target customers, and products. This is open ended, so you may get many different ideas. Here you can begin the discussion by talking about the core competencies of this firm. Actually, this firm does not have much that could not be quickly duplicated. They have their website, a marketing channel through the game programs, and the unique design of their monogram. So in developing the business they should think about ways they could make better use of these capabilities and assets. Here are some thoughts: Supplier – Here it would be good to try to reduce cost, reduce the minimum order quantity, and reduce the lead time associated with the order. Any of these would be desirable. If it were possible to reduce the minimum order quantity and the lead time, then instead of a single order, multiple orders could be place during the season. One order could cover the initial half of the season and a second for the rest, for example. This should allow for more accurate forecasts and less product sold through eBay. They might consider using a domestic (US) supplier or possibly even consider subcontracting the making of the sweaters to locals. A quick web search shows that automated machines at fairly low cost are now available that might be used. Monogramming subcontractor – Might consider doing this in-house. They have a pretty good deal right now, though, since the subcontractor is providing space for inventory and shipping the product to the customer. Target customers – They could expand this to the rest of the Big Ten teams. Other sports, particularly international venues, such as soccer could be developed. Products – Many similar products that would be personalized could be developed such as sweatshirts, jackets, blankets, and blazers. These would possibly use the same or similar suppliers, and have the same requirements related to monogramming. Getting into totally different kinds of products, such as coolers, might be another idea. It’s probably important to try to exploit the idea of high end products that are attractive as gifts. Solution Manual for Operations and Supply Chain Management F. Robert Jacobs, Richard B. Chase 9780078024023, 9780077824921, 9781260238907, 9780077228934, 9781259666100