A local printing company provides a custom printing service. Since each job is differ- ent, demand is forecast in hours per week. Over the next 5 weeks, the company expects that demand will be 100 hours per week. There is an existing backlog of 100 hours, and at the end of 5 weeks, the company wants to reduce that to 80 hours. How many hours of work will be needed each week to reduce the backlog? What will be the backlog at the end of each week?

A local printing company provides a custom printing service. Since each job is differ- ent, demand is forecast in hours per week. Over the next 5 weeks, the company expects that demand will be 100 hours per week. There is an existing backlog of 100 hours, and at the end of 5 weeks, the company wants to reduce that to 80 hours. How many hours of work will be needed each week to reduce the backlog? What will be the backlog at the end of each week?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section7.7: Portfolio Optimization Models

Problem 41P

See similar textbooks

Similar questions

The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Can you guess the results of a sensitivity analysis on the initial inventory in the Pigskin model? See if your guess is correct by using SolverTable and allowing the initial inventory to vary from 0 to 10,000 in increments of 1000. Keep track of the values in the decision variable cells and the objective cell.
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. As indicated by the algebraic formulation of the Pigskin model, there is no real need to calculate inventory on hand after production and constrain it to be greater than or equal to demand. An alternative is to calculate ending inventory directly and constrain it to be nonnegative. Modify the current spreadsheet model to do this. (Delete rows 16 and 17, and calculate ending inventory appropriately. Then add an explicit non-negativity constraint on ending inventory.)
The Pigskin Company produces footballs. Pigskin must decide how many footballs to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next six months are 10,000, 15,000, 30,000, 35,000, 25,000, and 10,000. Pigskin wants to meet these demands on time, knowing that it currently has 5000 footballs in inventory and that it can use a given months production to help meet the demand for that month. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.) During each month there is enough production capacity to produce up to 30,000 footballs, and there is enough storage capacity to store up to 10,000 footballs at the end of the month, after demand has occurred. The forecasted production costs per football for the next six months are 12.50, 12.55, 12.70, 12.80, 12.85, and 12.95, respectively. The holding cost incurred per football held in inventory at the end of any month is 5% of the production cost for that month. (This cost includes the cost of storage and also the cost of money tied up in inventory.) The selling price for footballs is not considered relevant to the production decision because Pigskin will satisfy all customer demand exactly when it occursat whatever the selling price is. Therefore. Pigskin wants to determine the production schedule that minimizes the total production and holding costs. Modify the Pigskin model so that there are eight months in the planning horizon. You can make up reasonable values for any extra required data. Dont forget to modify range names. Then modify the model again so that there are only four months in the planning horizon. Do either of these modifications change the optima] production quantity in month 1?
Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.
If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.
Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?
How much influence can the employee requirements for one, two, or three days have on the weekly sched-ule in the employee scheduling example? Explore this in the following questions:a. Let Monday’s requirements change from 17 to 25in increments of 1. Use SolverTable to see how thetotal number of employees changes.b. Suppose the Monday and Tuesday requirementscan each, independently of one another, increasefrom 1 to 8 in increments of 1. Use a two-waySolverTable to see how the total number ofemployees changes. c. Suppose the Monday, Tuesday, and Wednes-day requirements each increase by the same amount, where this increase can be from 1 to 8in increments of 1. Use a one-way SolverTableto investigate how the total number of employeeschanges.
SureStep is currently getting 160 regular-time hours from each worker per month. This is actu-ally calculated from 8 hours per day times 20 days per month. For this, they are paid $9.375 per hour(51500y160). Suppose workers can change theircontract so that they only have to work 7.5 hours perday regular-time—everything above this becomesovertime—and their regular-time wage rate increasesto $10 per hour. They will still work 20 days per month. Will this change the optimal no-backloggingsolution?
Jean Clark is the manager of the Midtown Saveway-Grocery Store. She now needs to replenish hersupply of strawberries. Her regular supplier can provide as many cases as she wants. However,because these strawberries already are very ripe, she will need to sell them tomorrow and thendiscard any that remain unsold. Jean estimates that she will be able to sell 12, 13, 14, or 15 casestomorrow. She can purchase the strawberries for $7 per case and sell them for $18 per case. Jeannow needs to decide how many cases to purchase. Jean has checked the store’s records on dailysales of strawberries. On this basis, she estimates that the prior probabilities are 0.1, 0.3, 0.4, and 0.2for being able to sell 12, 13, 14, and 15 cases of strawberries tomorrow. a. Develop a decision analysis formulation of this problem by identifying the decisionalternatives, the states of nature, and the payoff table. b. How many cases of strawberries should Jean purchase if she uses the maximin payoffcriterion? c. How…
How much influence can the employee requirements for one, two, or three days have on the weekly schedule in the employee scheduling example? Explore this in the following questions: a. Let Monday’s requirements change from 17 to 25 in increments of 1. UseSolverTable to see how the total number of employees changes.b. Suppose the Monday and Tuesday requirements can each, independently of one another, increase from 1 to 8 in increments of 1. Use a two-way SolverTable to see how the total number of -employees changes.c. Suppose the Monday, Tuesday, and Wednesday -requirements each increase by the same amount, where this increase can be from 1 to 8 in -increments of 1. Use a one-way SolverTable to -investigate how the total number of employees changes.
Demand for a product is forecasted for the six periods is 263, 256, 301, 312, 304, and 294 respectively. If a CHASE DEMAND strategy is adopted, and the regular production cost is RO 12 per unit with a maximum regular production of 280 units per period. While, the overtime and subcontract costs are RO 20 and RO 25 per unit respectively, There is no limit on subcontracting: however, maximum overtime production capacity is 10. Average inventory holding cost is RO 5 per unit per period. How many units in total are held as inventory? Select one Oa 40 Ob 51 Oco Od None is correct Oe. 1629
An electronics firm has a contract to deliver thefollowing number of radios during the next three months;month 1, 200 radios; month 2, 300 radios; month 3, 300radios. For each radio produced during months 1 and 2, a$10 variable cost is incurred; for each radio produced duringmonth 3, a $12 variable cost is incurred. The inventory costis $1.50 for each radio in stock at the end of a month. Thecost of setting up for production during a month is $250. Radios made during a month may be used to meet demandfor that month or any future month. Assume that productionduring each month must be a multiple of 100. Given thatthe initial inventory level is 0 units, use dynamicprogramming to determine an optimal production schedule.